JSCE Guidelines for Concrete
No.15

STANDARD SPECIFICATIONS FOR CONCRETESTRUCTURES  2007
"Design"Japan Society of Civil Engineers

JSCE Guidelines for Concrete
No.15

STANDARD SPECIFICATIONS FOR CONCRETESTRUCTURES  2007
"Design"

Published bySubcommittee on
English Version of Standard Specifications for Concrete Structures - 2007
Japan Society of Civil Engineers (JSCE)
Yotsuya 1-chome, Shinjuku-ku, Tokyo 160-0004, JAPANFAX +81-3-5379-2769 E-mail pub@jsce.or.jp
December 2010

Copyright  JSCE 2010 Concrete Committee
Printed in Japan
英文版 2007 年制定コンクリート標準示方書［設計編］ 1.0

ISBN 978-4-8106-0752-9

Preface
Concrete structures have supported our society as infrastructures. The society can only preserve itself inwholesome with tough, beautiful and durable concrete structures. Concrete Committee of Japan Society of Civil
Engineers (JSCE), leading organization for investigation, research, technological promotion and education of
concrete in Japan, considers the issuance and revision of Standard Specifications for Concrete Structures as its
most important activity. Standard Specifications for Concrete Structures (JSCE-SSCS), which show the model
for plan, design, execution, maintenance and repair of concrete structures, have been highly recognized in practiceand contributed to the development of concrete technology in Japan since its first publication as “Standard
Specifications for Reinforced Concrete – 1931.”
In order to cope with the development of concrete technology in Japan and the worldwide trend, Concrete
Committee converted all Specifications in JSCE-SSCS namely ‘Structural Performance Verification,’ ‘Seismic
Performance Verification,’ ‘Materials and Construction,’ ‘Maintenance,’ ‘Dam Concrete’ and ‘Pavement,’ from the“Prescriptive Code” to “Performance-based Code” and completed the work in 2002.
This revised edition adopts the technological development after 2002 and intends to enhance theperformance-based nature in Standard Specifications. For practical efficiency, the three Specifications ‘Design,’ ‘Materials and Construction’ and ‘Dam Concrete’ present not only general provisions for verification of
specified performance requirements but also standard methods as simplified methods to achieve the performancerequirements under certain conditions. JSCE-SSCS is ready for practical use as it describes the role of eachSpecification during the plan, design, execution, maintenance and repair phases as well as the relationship among
them. And for the first time, it also describes roles of engineers for construction works. This JSCE-SSCS is yet
an ultimate one. There are still remaining tasks, such as inclusion of provisions for scenario of concrete
structures during service life. What readers can find in this revised edition is rationality with “theperformance-based concept” and the applicability for practice, showing the high level of technology in Japan.
This revised JSCE-SSCS consists of five Specifications; ‘Design,’ which combines the previous ‘Structural
Performance Verification’ and ‘Seismic Performance Verification’ together, ‘Materials and Construction,’‘Maintenance,’ ‘Dam Concrete’ and ‘Test Methods and Specifications.’ Specification of ‘Test Methods andSpecifications’ was issued separately in May 2007. Specification of ‘Pavement’ was published as “Standard
Specifications for Pavements – 2007” by the Committee on Pavement Engineering of JSCE, which has taken overthe issuance and revision works from JSCE-SSCS.
Finally I would like to show my most sincere gratitude to Prof Taketo UOMOTO and Dr Tadayoshi ISHIBASHI,
Chairman and Secretary General of Sub-committee on Revision of Standard Specifications for Concrete
Structures as well as its Secretaries, Conveners and Members who devoted themselves continuously despite thetight drafting schedule. My gratitude also goes to Advisors, Secretaries, Executive Members and Members ofConcrete Committee, who reviewed the draft.
December 2007

Toyoaki MIYAGAWA, Chairman
Concrete Committee of Japan Society of Civil Engineers

Preface to the English Version
The Japan Society of Civil Engineers’ (JSCE) Concrete Committee has been publishing the Standard
Specifications for Concrete Structures in Japanese since 1931.

The English versions were published twice in1987 and 2005 when the limit state design and the performance-based concept were introduced in the 1986 and2002 editions of Standard Specifications for Concrete Structures (JSCE-SSCS) for the first time, respectively.

Since 2004 the Concrete Committee has put efforts to enhance information dissemination overseas by presenting
various English publications including the series of “JSCE Guidelines for Concrete.”also decided to prepare the English version of every edition of JSCE-SSCS.

Concrete Committee hasThis Sub-committee on English

Version of Standard Specifications for Concrete Structures was established in 2008.

Our task is to prepare the English version of four Specifications: ‘Design,’ ‘Materials and Construction,’‘Maintenance’ and ‘Dam Concrete’ of the 2007 edition of JSCE-SSCS.

Specification of ‘Test Methods andSpecifications’ of JSCE-SSCS is not included in this English version.

However, some of these standard test

methods and specifications have been translated for publication in a series of “JSCE Guidelines for Concrete.”
Please visit the website of Concrete Committee at http://www.jsce.or.jp/committee/concrete/e/index.html for the
information on the English publications.

This English version includes most of the contents in the original Japanese version.

Utmost efforts have been

made to ensure that the translation accurately convey the description in the original Japanese version. If there
were any discrepancy between the Japanese and English versions, however, reference should be made to theoriginal Japanese version.

Translation of technical work does not only require expertise but a lot of time and dedication.
the members for their tiring efforts.

I am grateful to all

My heartfelt appreciations go to Prof YOKOTA Hiroshi (Secretary General),

Dr SHIMOMURA Takumi (Head, WG for Design), Prof SUGIYAMA Takafumi (Head, WG for Materials andConstruction), Dr MAEDA Toshiya (Head, WG for Maintenance), Prof AYANO Toshiki (Head, WG for Dam
Concrete) and Dr ISHIZUKA Takayuki who proof-read all the translated Specifications. Without them thisEnglish version would not have been published.

December 2010

UEDA Tamon, Chairman
Sub-committee on English Version of Standard Specifications for Concrete Structures

JSCE Committee on
Revision of Standard Specifications for Concrete Structures
Taketo UOMOTO, Chairman
Tadayoshi ISHIBASHI, Secretary
Members
Hiroyuki IKEDA

Tomoya IWASHITA

Tamon UEDA

Kimitaka UJI

Hidetaka UMEHARA

Nobuaki OTSUKI

Hiroshi ONUMA

Satoshi OKAZAWA

Tsutomu KANAZU

Yuichi KANEKO

Toru KAWAI

Hirotaka KAWANO

Etsuo SAKAI

Koji SAKAI

Tsutomu SATO

Ryoichi SATO

Motoyuki SUZUKI

Shigeyuki SOGO

Koji TAKEWAKA

Takao CHIKADA

Yukikazu TSUJI

Tomoaki TSUTSUMI

Rokuro TOMITA

Kazuyuki TORII

Junichiro NIWA

Yoshinobu NOBUTA

Chikanori HASHIMOTO

Makoto HISADA

Tsutomu FUKUTE

Koichi MAEKAWA

Yasunori MATSUOKA

Kyuichi MARUYAMA

Tetsuya MISHIMA

Toyoaki MIYAGAWA

Hiroshi MUTSUYOSHI

Hiroshi YOKOTA

Keitetsu ROKUGOFormer Members
Takashi SASAKI

Yasuo INOKUMA

Working Group for 'Design'
Junichiro NIWA, Chairman
Hiroyuki IKEDA, Vice Chairman
Tsutomu SATO, Secretary
Members
Tadatomo WATANABE

Motoyuki SUZUKI

Takumi SHIMOMURA

Yoshiki ISHIKAWA

Katsuhiro ICHINAMI

Tamon UEDA

Isao UJIKE

Yuichi UCHIDA

Soji OHSHIRO

Akira OGAWA

Tsutomu KANAZU

Toshiro KAMADA

Kenji KAWAI

Takanobu KIMURA

Hiroshi SHIMA

Takafumi SUGIYAMAYukihiro TANIMURA

Tetsuo SANTO

Takeshi TSUYOSHI

Toru TERAYAMA

Hikaru NAKAMURA

Takashi HANASHIMA

Yuzuru HAMADA

Mitsuo HARADA

Koichi MAEKAWA

Tetsuya MISHIMA

Hiroshi MUTSUYOSHI

Shinichi YAMANOBE

Hiroshi YOKOA

Hiroshi WATANABE

Former Members
Yasuo INOKUMA
Yasuhiko NISHI

Shizuo TANAKA

Shinichi TAMAISubcommittee on English Version of Standard Specifications for Concrete Structures
Tamon UEDA, Chairman
Hiroshi YOKOTA, Secretary General

Secretaries
Toshiki AYANO

Takayuki ISHIZUKATakafumi SUGIYAMA

Toshiya MAEDA

Takumi SHIMOMURA

Members
Tetsuya ISHIDA

Hajime ITO

Mitsuyasu IWANAMI

Takao UEDA

Atsushi UENO

Masahiro OUCHI

Yoshinobu OSHIMA

Yoshitaka KATO

Minoru KUNIEDA

Yoshimori KUBO

Hirohisa KOGA

Koichi KOBAYASHI

Shigehiko SAITO

Goro SAKAI

Yasutaka SAGAWA

Toshiya TADOKORO

Hiroaki TSURUTA

Hideki NAITO

Kohei NAGAI

Kenichiro NAKARAI

Akira HOSODA

Tomohiro MIKI

Maki MIZUTA

Hiroshi MINAGAWA

Shinichi MIYAZATO

Toshinobu YAMAGUCHI

Ken WATANABE

Working Group for 'Design'
Takumi SHIMOMURA, Chairman

Members
Hajime ITO

Mitsuyasu IWANAMI

Shigehiko SAITO

Toshiya TADOKORO

Hideki NAITO

Kohei NAGAI

Kenichiro NAKARAITomohiro MIKI

Ken WATANABE

JSCE Guideline for Concrete No. 15

Standard Specifications for Concrete Structures -2007“Design”
CONTENTS
Application of Standard Specifications for Concrete Structures .................................................... i

GENERAL REQUIREMENTS
CHAPTER 1 GENERAL ................................................................................................................ 1
1.1 Scope ........................................................................................................................................ 1
1.2 Basic Rules of Design .............................................................................................................. 2
1.3 Definitions ................................................................................................................................ 5
1.4 Notation .................................................................................................................................... 8
CHAPTER 2 PERFORMANCE REQUIREMENTS ................................................................ 14
2.1 General ................................................................................................................................... 14
2.2 Durability ............................................................................................................................... 14
2.3 Safety...................................................................................................................................................... 15
2.4 Serviceability.......................................................................................................................... 15
2.5 Restorability ........................................................................................................................... 15
2.6 Other Performance Requirements .......................................................................................... 16
CHAPTER 3 STRUCTURAL PLANNING ................................................................................ 17
3.1 General ................................................................................................................................... 17
3.2 Studies on Performance Requirements .................................................................................. 18
3.3 Studies on Construction ......................................................................................................... 20
3.4 Studies on Maintenance ......................................................................................................... 21
3.5 Studies on Environmental and Landscape Compatibility ...................................................... 22
3.6 Studies on Economical Aspects.............................................................................................. 23
CHAPTER 4 RULES FOR PERFORMANCE VERIFICATION............................................ 24
4.1 General ................................................................................................................................... 24
4.2 Prerequisite for Verification ................................................................................................... 27
4.3 Verification Method ............................................................................................................... 27
4.4 Calculation of Response Values and Limit Values ................................................................. 28
4.5 Safety Factors ......................................................................................................................... 28
4.6 Modification Factors .............................................................................................................. 33
4.7 Documentation of Design Calculations ................................................................................. 33
4.8 Design Drawing ..................................................................................................................... 33
CHAPTER 5 DESIGN VALUES FOR MATERIALS ............................................................... 36
5.1 General ................................................................................................................................... 36(1)

5.2 Concrete ................................................................................................................................. 38
5.2.1 Strength ........................................................................................................................... 38
5.2.2 Design fatigue strength ................................................................................................... 42
5.2.3 Stress-strain curve ........................................................................................................... 43
5.2.4 Tension-softening properties ........................................................................................... 48
5.2.5 Young’s modulus ............................................................................................................. 49
5.2.6 Poisson’s ratio ................................................................................................................. 49
5.2.7 Thermal characteristics ................................................................................................... 49
5.2.8 Shrinkage ........................................................................................................................ 50
5.2.9 Creep ............................................................................................................................... 56
5.2.10 Influence of low temperature ........................................................................................ 60
5.2.11 Carbonation rate............................................................................................................ 60
5.2.12 Diffusion coefficient of chloride ions in concrete ........................................................ 62
5.2.13 Relative dynamic modulus of elasticity for freezing-thawing action ........................... 63
5.2.14 Concrete properties for verification of initial cracking ................................................ 64
5.3 Reinforcing Steel .................................................................................................................... 64
5.3.1 Strength ........................................................................................................................... 64
5.3.2 Design fatigue strength ................................................................................................... 66
5.3.3 Stress-strain curve ........................................................................................................... 69
5.3.4 Young’s modulus ............................................................................................................. 71
5.3.5 Poisson’s ratio ................................................................................................................. 71
5.3.6 Coefficient of thermal expansion .................................................................................... 72
5.3.7 Relaxation ratio of prestressing steel .............................................................................. 72
5.3.8 Influence of low temperature .......................................................................................... 74
CHAPTER 6 LOAD ...................................................................................................................... 75
6.1 General ................................................................................................................................... 75
6.2 Characteristic Values of Loads ............................................................................................... 77
6.3 Load Factors ........................................................................................................................... 78
6.4 Kind of Load .......................................................................................................................... 79
6.4.1 General ............................................................................................................................ 79
6.4.2 Dead load ........................................................................................................................ 80
6.4.3 Live load ......................................................................................................................... 80
6.4.4 Earth pressure .................................................................................................................. 81
6.4.5 Water pressure, fluid dynamic force and wave pressure ................................................. 82
6.4.6 Prestress .......................................................................................................................... 83
6.4.7 Wind load ........................................................................................................................ 83
6.4.8 Snow load ........................................................................................................................ 84
6.4.9 Effect of shrinkage and creep of concrete ....................................................................... 85
6.4.10 Effect of temperature .................................................................................................... 85
6.4.11 Influence of earthquake ................................................................................................ 86
6.4.12 Loads during construction stage ................................................................................... 91
6.4.13 Other loads .................................................................................................................... 92
CHAPTER 7 CALCULATION OF RESPONSE VALUES ....................................................... 93
7.1 General ................................................................................................................................... 93
7.2 Modeling ................................................................................................................................ 94
7.2.1 General ............................................................................................................................ 94
7.2.2 Modeling of structure ...................................................................................................... 95
7.2.2.1 Modeling of members by use of finite elements ...................................................... 96
7.2.2.2 Modeling of members by use of linear elements ..................................................... 97(2)

7.3 Structural Analysis ............................................................................................................... 102
7.3.1 General .......................................................................................................................... 102
7.3.2 Structural analysis related to safety verification ........................................................... 103
7.3.2.1 Structural analysis for verification of cross-sectional failure ................................ 103
7.3.2.2 Structural analysis for verification of fatigue failure ............................................. 105
7.3.2.3 Structural analysis for verification of structural safety .......................................... 105
7.3.3 Structural analysis for verification of serviceability ..................................................... 106
7.3.4 Structural analysis for earthquake resistance evaluation .............................................. 108
7.3.4.1 General ................................................................................................................... 108
7.3.4.2 Method for analyzing the structure and the ground independently ....................... 110
7.3.4.3 Ground model for coupled analysis ....................................................................... 112
7.3.4.4 Ground model to analyze a structure independent of the ground .......................... 113
7.4 Calculation of Design Response Values ............................................................................... 115
7.4.1 General .......................................................................................................................... 115
7.4.2 Calculation of sectional forces ...................................................................................... 115
7.4.2.1 Calculation of sectional forces in bar members by the finite element method ...... 115
7.4.2.2 Calculation of sectional forces in the case where a fiber-based model is used...... 116
7.4.3 Calculation of material stress ........................................................................................ 116
7.4.4 Examination for flexural cracks .................................................................................... 119
7.4.5 Examination for displacement and deformation of member ......................................... 122
CHAPTER 8 VERIFICATION OF DURABILITY ................................................................. 128
8.1 General ................................................................................................................................. 128
8.2 Environmental Factors ......................................................................................................... 129
8.3 Verification Related to Steel Corrosion ................................................................................ 131
8.3.1 General .......................................................................................................................... 131
8.3.2 Limit value of crack width for corrosion of reinforcement........................................... 132
8.3.3 Examination for flexural cracks .................................................................................... 134
8.3.4 Examination for shear cracks ........................................................................................ 135
8.3.5 Examination for cracks due to torsion .......................................................................... 135
8.3.6 Examination for reinforcement corrosion due to carbonation ...................................... 136
8.3.7 Examination for chloride attack .................................................................................... 139
8.4 Verification Related to Concrete Deterioration .................................................................... 143
8.4.1 Verification for freezing-thawing action ....................................................................... 143
8.4.2 Verification related to chemical attack .......................................................................... 145
CHAPTER 9 VERIFICATION OF STRUCTURAL SAFETY .............................................. 148
9.1 Genera .................................................................................................................................. 148
9.2 Examination of Safety for Failure of Cross Section ............................................................ 150
9.2.1 Flexural moment and axial forces ................................................................................. 150
9.2.1.1 Design capacity of member cross section .............................................................. 150
9.2.2 Shear.............................................................................................................................. 154
9.2.2.1 General ................................................................................................................... 154
9.2.2.2 Design shear capacity of linear members .............................................................. 156
9.2.2.3 Design punching shear capacity of planar members .............................................. 166
9.2.2.4 Design member forces in planar members subjected to in-plane forces................ 171
9.2.2.5 The design capacity for shear transfer ................................................................... 173
9.2.3 Torsion........................................................................................................................... 177
9.2.3.1 General ................................................................................................................... 177
9.2.3.2 Design torsional capacity for members without torsion reinforcement ................. 179
9.2.3.3 Design torsional capacity for members with torsion reinforcement ...................... 182(3)

9.3 Examination of Safety for Fatigue ....................................................................................... 188
9.3.1 General .......................................................................................................................... 188
9.3.2 Design variable force and equivalent number of cycles ............................................... 188
9.3.3 Fatigue strength of concrete members without shear reinforcement ............................ 190
CHAPTER 10 VERIFICATION OF SERVICEABILITY...................................................... 191
10.1 General ............................................................................................................................... 191
10.2 Limit Value of Stresses ...................................................................................................... 192
10.3 Verification Related to Appearance ................................................................................... 193
10.3.1 General ........................................................................................................................ 193
10.3.2 Flexural cracks ............................................................................................................ 194
10.3.3 Shear cracks and torsion cracks .................................................................................. 194
10.4 Examination for Vibration ................................................................................................. 195
10.5 Examination for Displacement and Deformation .............................................................. 195
10.6 Examination for Water-Tightness ...................................................................................... 196
10.7 Examination for Fire Resistance ........................................................................................ 199
CHAPTER 11 SEISMIC DESIGN ............................................................................................ 200
11.0 Notation ............................................................................................................................. 200
11.1 General ............................................................................................................................... 200
11.2 Definition of Limit Values ................................................................................................. 205
11.3 Verification......................................................................................................................... 206
11.4 Safety Factors .................................................................................................................... 207
11.5 Verification by Experimental Tests .................................................................................... 209
CHAPTER 12 VERIFICATION RELATED TO INITIAL CRACKING ............................. 211
12.1 General ............................................................................................................................... 211
12.2 Verification Related to Cracking Caused by Hydration of Cement ................................... 214
12.2.1 General ........................................................................................................................ 214
12.2.2 Verification related to occurrence/nonoccurrence of cracking ................................... 215
12.2.3 Verification of crack width ......................................................................................... 218
12.2.4 Calculation of stress and crack width ......................................................................... 219
12.3 Verification Related to Cracking due to Shrinkage ........................................................... 221
CHAPTER 13 STRUCTURAL DETAILS OF REINFORCEMENT .................................... 222
13.0 Notation ............................................................................................................................. 222
13.1 General ............................................................................................................................... 222
13.2 Concrete Cover .................................................................................................................. 223
13.3 Clear Distance .................................................................................................................... 223
13.4 Arrangement of Reinforcement ......................................................................................... 223
13.4.1 Arrangement of longitudinal reinforcement ............................................................... 223
13.4.2 Arrangement of transverse reinforcement .................................................................. 226
13.4.3 Arrangement of torsion reinforcement ....................................................................... 228
13.5 Bend Configurations of Reinforcement ............................................................................. 230
13.6 Development of Reinforcement ......................................................................................... 230
13.6.1 General ........................................................................................................................ 230
13.6.2 Standard hooks ............................................................................................................ 232
13.6.3 Basic development length ........................................................................................... 234
13.7 Splices in Reinforcement ................................................................................................... 236
13.8 Reinforcement of Members ............................................................................................... 238(4)

CHAPTER 14 OTHER STRUCTURAL DETAILS ................................................................ 239
14.1 General ............................................................................................................................... 239
14.2 Beveling ............................................................................................................................. 239
14.3 Additional Reinforcement for Exposed Surfaces .............................................................. 239
14.4 Reinforcing for Concentrated Reactions............................................................................ 239
14.5 Reinforcing for Openings .................................................................................................. 240
14.6 Construction Joints ............................................................................................................ 240
14.6.1 General ........................................................................................................................ 240
14.6.2 Construction joints of columns or walls integrated with slabs ................................... 241
14.6.3 Construction joints of slab .......................................................................................... 241
14.6.4 Construction joints of arches ...................................................................................... 242
14.7 Expansion Joints ................................................................................................................ 242
14.8 Crack Induced Joints .......................................................................................................... 243
14.9 Water-Tight Structures ....................................................................................................... 244
14.10 Drainage and Water Proofing .......................................................................................... 245
14.11 Protection of Concrete Surface ........................................................................................ 245
14.12 Haunches ......................................................................................................................... 246
14.13 Joint Part of Members ..................................................................................................... 246
14.14 Structural Details of Members......................................................................................... 246
CHAPTER 15 PRESTRESSED CONCRETE ......................................................................... 247
15.0 Notation ............................................................................................................................. 247
15.1 General ............................................................................................................................... 249
15.2 Classification of Prestressed Concrete ............................................................................... 251
15.3 Prestressing Force .............................................................................................................. 253
15.4 Calculation of Response Values ......................................................................................... 262
15.4.1 General ........................................................................................................................ 262
15.4.2 Design stresses for materials due to bending moment and axial force ....................... 263
15.4.3 Design material stresses caused by shear force and torsional moment ...................... 270
15.4.4 Design flexural crack width ........................................................................................ 274
15.5 Verification of Durability ................................................................................................... 274
15.6 Verification of Safety ......................................................................................................... 277
15.6.1 General ........................................................................................................................ 277
15.6.2 Design flexural strength of PC members with internal tendons ................................. 278
15.6.3 Design flexural strength of PC members with unbonded prestressing tendonsor external tendons ...................................................................................................... 279
15.7 Verification related to Serviceability ................................................................................. 283
15.7.1 General ........................................................................................................................ 283
15.7.2 Maximum permissible value of stress ........................................................................ 284
15.8 Verification during Construction ....................................................................................... 286
15.9 Structural Details ............................................................................................................... 288
15.9.1 General ........................................................................................................................ 288
15.9.2 Prestressed concrete grout .......................................................................................... 288
15.9.3 Cover of prestressing tendon ...................................................................................... 289
15.9.4 Clear spacing between tendons ................................................................................... 290
15.9.5 Arrangements of tendons ............................................................................................ 290
15.9.6 Anchoring and connection of tendons and reinforcementof concrete in anchorage zones ................................................................................... 291
15.9.7 Minimum amount of reinforcement............................................................................ 293
15.10 Precast Concrete .............................................................................................................. 293(5)

15.10.1
15.10.2
15.10.3
15.10.4
15.10.5
15.10.6
15.10.7
15.10.8
15.10.9

General ..................................................................................................................... 293
Shrinkage and creep of precast concrete .................................................................. 294
Relaxation ratio of prestressing steel........................................................................ 294
Loads ........................................................................................................................ 295
Unit weight ............................................................................................................... 295
Connection................................................................................................................ 295
Joining by prestressing force .................................................................................... 396
Concrete cover .......................................................................................................... 301
Clear distance between reinforcing bars .................................................................. 302

CHAPTER 16 COMPOSITE STEEL AND CONCRETE STRUCTURE ............................ 303
16.1 General ............................................................................................................................... 303
16.2 General Requirements for Composite Structures .............................................................. 305
16.3 Design Method ................................................................................................................... 306
16.3.1 Selection of steel ......................................................................................................... 306
16.3.2 Verification method of performance ........................................................................... 306
16.3.3 Shear connector .......................................................................................................... 307
16.3.4 Examination of limit states during erection ................................................................ 307
16.4 Examination of Completed Structures Containing Steel
Sections Used During Erection .......................................................................................... 308
16.5 Structural Performance of Joints and Corners ................................................................... 308
16.6 Effect of Shrinkage and Creep of In-Filled Concrete ........................................................ 309
16.7 Steel Reinforced Concrete Members ................................................................................. 309
16.7.1 Classification of structural types ................................................................................ 309
16.7.2 Examination of safety ................................................................................................. 310
16.7.2.1 Examination of limit state of failure of cross section .......................................... 310
16.7.2.2 Examination of limit state of fatigue failure ........................................................ 311
16.7.3 Examination of serviceability ..................................................................................... 311
16.7.4 Structural details ......................................................................................................... 312
16.8 Concrete Filled Steel Column ............................................................................................ 313
16.8.1 Examination of safety ................................................................................................. 313
16.8.1.1 Examination of limit state of failure of cross section .......................................... 313
16.8.1.2 Examination of limit state of fatigue failure ........................................................ 314
16.8.2 Examination of serviceability ..................................................................................... 314
16.8.3 Examination for placing concrete ............................................................................... 314
16.8.4 Structural details ......................................................................................................... 314
16.9 Sandwich Member ............................................................................................................. 315
16.9.1 Examination of safety ................................................................................................. 315
16.9.1.1 Examination of limit state of failure of cross section .......................................... 315
16.9.1.2 Examination of limit state of fatigue failure ........................................................ 316
16.9.2 Examination of serviceability ..................................................................................... 316
16.9.3 Structural details ......................................................................................................... 317

STANDARD METHODSPART 1 STRUCTURAL ANALYSIS OF MEMBERS ............................................................. 319
1 GENERAL .................................................................................................................................. 319
1.1 Scope .................................................................................................................................... 319
2 BEAMS ....................................................................................................................................... 320(6)

2.1 General ................................................................................................................................. 320
2.2 Span Length ......................................................................................................................... 321
2.3 Effective Compression Flange Width of T-Beam ................................................................ 321
2.4 Isolated Beam ....................................................................................................................... 323
2.5 Continuous Beam ................................................................................................................. 323
2.6 Structural Details .................................................................................................................. 324
2.7 Deep Beam ........................................................................................................................... 325
2.8 Corbel ................................................................................................................................... 326
3 COLUMNS ................................................................................................................................. 328
3.1 General ................................................................................................................................. 328
3.2 Slenderness Ratio ................................................................................................................. 328
3.3 Short Column ....................................................................................................................... 329
3.4 Long Column ....................................................................................................................... 329
3.5 Tied Reinforced Column ...................................................................................................... 329
3.6 Spiral Reinforced Column.................................................................................................... 330
4 RIGID FRAMES ......................................................................................................................... 331
4.1 General ................................................................................................................................. 331
4.2 Structural Analysis ............................................................................................................... 331
4.3 Structural Details .................................................................................................................. 333
5 ARCHES ..................................................................................................................................... 334
5.1 General ................................................................................................................................. 334
5.2 Structural Analysis ............................................................................................................... 334
5.3 Structural Details .................................................................................................................. 337
6 DESIGN OF PLANAR MEMBERS........................................................................................... 338
6.1 Scope and Definitions .......................................................................................................... 338
6.2 Structural Analysis of Planar Members ................................................................................ 338
6.3 Design of Slab ...................................................................................................................... 338
6.3.1 Structural analysis ......................................................................................................... 338
6.3.2 Examination for applied member forces ....................................................................... 341
6.3.3 Examination for slabs having different shapes ............................................................. 342
6.3.3.1 One-way slab.......................................................................................................... 342
6.3.3.2 Two-way slab ......................................................................................................... 345
6.3.3.3 Cantilever slabs ...................................................................................................... 345
6.3.3.4 Skewed slab............................................................................................................ 347
6.3.3.5 Flat slab .................................................................................................................. 347
6.3.4 Structural details............................................................................................................ 350
6.4 Design of Footing ................................................................................................................. 351
6.4.1 General .......................................................................................................................... 351
6.4.2 Structural analysis ......................................................................................................... 351
6.4.3 Examination for flexural moment ................................................................................. 352
6.4.4 Examination for shear ................................................................................................... 354
6.4.5 Examination for punching shear ................................................................................... 357
6.4.6 Examination for pull-out shear...................................................................................... 358
6.5 Design of Shell and Wall ...................................................................................................... 359
PART 2 SEISMIC DESIGN ........................................................................................................ 363
1 GENERAL .................................................................................................................................. 363
1.1 Scope .................................................................................................................................... 363
1.2 Seismic Performance That Should Be Made Available........................................................ 363
2 DESIGN BY SEISMIC COEFFICIENT METHOD .................................................................. 365(7)

2.1 General ................................................................................................................................. 365
2.2 Loads .................................................................................................................................... 366
2.2.1 General .......................................................................................................................... 366
2.2.2 Calculation of equivalent natural period ....................................................................... 367
2.3 Calculation of Response Value ............................................................................................. 368
2.3.1 General .......................................................................................................................... 368
2.3.2 Modeling of structure .................................................................................................... 368
2.3.3 Calculation of design response value ............................................................................ 369
2.4 Seismic Performance Verification ........................................................................................ 369
2.4.1 General .......................................................................................................................... 369
2.4.2 Examination for bending moment................................................................................. 370
2.4.3 Examination for shear force .......................................................................................... 370
2.4.4 Examination for the amount of hoops in portion that becomes plastic ......................... 372
3 DESIGN USING NONLINEAR SPECTRA .............................................................................. 373
3.1 Scope .................................................................................................................................... 373
3.2 Loads .................................................................................................................................... 374
3.3 Calculation of Response Value ............................................................................................. 374
3.3.1 General .......................................................................................................................... 374
3.3.2 Modeling of structure .................................................................................................... 375
3.3.3 Calculation of equivalent natural period ....................................................................... 375
3.3.4 Calculation of design response value ............................................................................ 376
3.4 Seismic Performance Verification ........................................................................................ 377
PART 3 DURABILITY DESIGN ............................................................................................... 380
1 GENERAL .................................................................................................................................. 380
1.1 Scope .................................................................................................................................... 380
2 CONCRETE COVER OF STRUCTURES UNDER ORDINARY ENVIRONMENTS ........... 381
3 SIMPLE DESIGN METHOD CONCERNING DURABILITY ................................................ 383
3.1 General ................................................................................................................................. 383
3.2 Chloride Attack .................................................................................................................... 383
3.2.1 Check for steel corrosion due to chloride ion ingress ................................................... 383
3.2.2 Specification of coefficient of chloride Ion diffusion in concrete ................................ 387
3.2.3 Chloride ion concentration on concrete surface ............................................................ 389
3.3 Carbonation .......................................................................................................................... 389
3.4 Damage from Freezing and Thawing ................................................................................... 390
3.5 Chemical Attack ................................................................................................................... 391
PART 4 THERMAL STRESS ANALYSIS ................................................................................ 393
1 GENERAL .................................................................................................................................. 393
1.1 Scope .................................................................................................................................... 393
2 THERMAL ANALYSIS.............................................................................................................. 394
2.1 Analytical Methods .............................................................................................................. 394
2.2 Boundary and Initial Condition ............................................................................................ 394
2.3 Rate of Heat Generation of Concrete ................................................................................... 395
3 STRESS ANALYSIS .................................................................................................................. 397
3.1 Analytical Method ................................................................................................................ 397
3.2 Consideration of Autogenous Shrinkage .............................................................................. 402
3.3 External Restraining Body ................................................................................................... 403(8)

3.4 Effect of Restraining by Reinforcement............................................................................... 403
4 MATERIAL PROPERTIES ........................................................................................................ 404
4.1 Mechanical Properties .......................................................................................................... 404
4.1.1 Tensile strength of concrete .......................................................................................... 404
4.1.2 Young’s modulus of concrete ........................................................................................ 405
4.2 Thermal Properties ............................................................................................................... 406
4.2.1 Thermal properties of concrete ..................................................................................... 406
4.2.2 Thermal properties of soil and rock .............................................................................. 408
PART 5 GENERAL STRUCTURAL DETAILS ....................................................................... 409
1 GENERAL .................................................................................................................................. 409
1.1 Scope .................................................................................................................................... 409
2 CONCRETE COVER ................................................................................................................. 410
3 CLEAR DISTANCE ................................................................................................................... 413
3.1 Clear Distance ...................................................................................................................... 413
3.2 Clear Distance of Prestressing Tendon................................................................................. 414
4 BEND CONFIGURATIONS OF REINFORCEMENT.............................................................. 416
5 DEVELOPMENT OF REINFORCEMENT ............................................................................... 417
5.1 General ................................................................................................................................ .417
5.2 Development of Longitudinal Reinforcement ..................................................................... 422
5.3 Development of Transverse Reinforcement ......................................................................... 428
6 SPLICES IN REINFORCEMENT.............................................................................................. 430
6.1 General ................................................................................................................................. 430
6.2 Splices for Longitudinal Reinforcement .............................................................................. 430
6.3 Splices for Transverse Reinforcement ................................................................................. 431
7 RE-BAR ARRANGEMENT IN BEAM ..................................................................................... 435
7.1 General ................................................................................................................................. 435
7.2 Deep Beam ........................................................................................................................... 435
7.3 Corbel ................................................................................................................................... 436
8 RE-BAR ARRANGEMENT IN COLUMN ............................................................................... 438
8.1 Tied Reinforced Column ...................................................................................................... 438
8.2 Spiral Reinforced Column.................................................................................................... 439
8.3 Splices of Reinforcement in Column ................................................................................... 440
9 RE-BAR ARRANGEMENT IN SLAB ...................................................................................... 441
9.1 General ................................................................................................................................. 441
9.2 One-Way Slab ...................................................................................................................... 442
9.3 Two-Way Slab ...................................................................................................................... 443
9.4 Cantilever Slab ..................................................................................................................... 445
9.5 Skewed Slab ......................................................................................................................... 445
9.6 Circular Slab......................................................................................................................... 447
9.7 Flat Slab ............................................................................................................................... 447
10 RE-BAR ARRANGEMENT IN SHELL AND WALL ............................................................ 448
11 RE-BAR ARRANGEMENT IN FOOTING ............................................................................. 450
12 RE-BAR ARRANGEMENT IN RIGID FRAME .................................................................... 451
13 RE-BAR ARRANGEMENT IN ARCH ................................................................................... 457
14 RE-BAR ARRANGEMENT IN PRESTRESSED CONCRETE MEMBER ........................... 458
14.1 Reinforcement of Anchorage Zone .................................................................................... 458(9)PART 6 STRUT-AND- TIE MODEL ......................................................................................... 462
1 GENERAL .................................................................................................................................. 462
1.1 Scope .................................................................................................................................... 462
2 STRENGTH OF TIE ................................................................................................................... 464
2.1 Strength of Steel Tie ............................................................................................................. 464
2.2 Strength of Concrete Tie ...................................................................................................... 464
3 STRENGTH OF STRUT ............................................................................................................ 465
3.1 Strength of Concrete Strut .................................................................................................... 465
3.2 Strength of Concrete Strut with Reinforcement ................................................................... 467
3.3 Strength of Confined Concrete Strut .................................................................................... 467
3.4 Reduction in Strut Thickness ............................................................................................... 467
4 STRENGTH OF NODE AND ANCHORAGE OF REINFORCING BAR ............................... 468
4.1 General ................................................................................................................................. 468
4.2 Compression Node ............................................................................................................... 468
4.3 Anchorage of Reinforcing Bar ............................................................................................. 468(10)

Application of Standard Specifications for Concrete Structures

Application of Standard Specifications for Concrete Structures
Editorial notes for the English Version:(1) The Standard Specifications for Concrete Structures are a model code which is supposed to be
applied in Japan and have no legal bindings.
(2) Therefore, some contents, such as Chapters 2 and 3 of “Application of Standard
Specifications for Concrete Structures,” may not fit to practical scheme in construction industry inthe other countries.
(3) However, it is hoped that the Standard Specifications for Concrete Structures could be amodel code for the other countries after necessary modifications of the contents considering the
local conditions.

1. Basic concept concerning the organization of the Standard Specifications for Concrete
Structures
The Standard Specifications for Concrete Structures are regularly revised reflecting thestate-of-the-art concrete technologies developed in Japan and other countries, and provide standards
concerning the technical aspects of concrete structures in a series of phases from planning to design,
construction and maintenance.
In this revised edition, the “Standard Specifications for Concrete Structures, Design” iscomposed of the “Standard Specifications for Concrete Structures, Structural Performance
Verification” and “Standard Specifications for Concrete Structures, Seismic Performance
Verification” to enhance the convenience of design practice. Durability check and initial cracking
check, which should be discussed in the “Standard Specifications for Concrete Structures, Design”
have been transferred from the “Standard Specifications for Concrete Structures, Materials andConstruction” to “Standard Specifications for Concrete Structures, Design”. The preparation andrevision of the “Standard Specifications for Concrete Structures, Pavement” has been handed overto the Committee on Pavement Engineering, JSCE (Japan Society of Civil Engineers). The results
are now published separately under the title of the Standard Specifications for Pavement. Thus, theStandard Specifications for Concrete Structures include five components: Design, Materials andConstruction, Maintenance, Dam Concrete, and Test Methods and Specifications.
The General Requirements for “Design”, “Materials and Construction” and “Dam Concrete” aredescribed based on the concept of performance-based code. Performance requirements are specified
for structures and the methods for checking the compliance with requirements are shown in the
General Requirements. In the Standard Methods, standard methods for satisfying the General
Requirements under certain conditions are given for more efficient and simpler design andconstruction. In cases where no conditions specified in the Standard Methods are met, performanceverification should be conducted in accordance with the General Requirements. For establishing
new standards fitting for structures or regions to which no Standard Methods are applicable, theStandard Methods may be referred to.
Concrete structures are generally constructed for providing services in the phases of planning,
design, construction and maintenance in accordance with the respective components of the Standard
Specifications. Each type of work is not independent of the others. Data are handed over from an(i)Standard Specifications for Concrete Structures-2007, Design

upstream to a downstream phase that are required for carrying out the work downstream to meet theconditions specified upstream. Handing over the data is therefore important to proper
implementation of work in respective phases. In the Standard Specifications for Concrete Structures,“Design”, “Materials and Construction” and “Maintenance” are closely interrelated to one another.
Then, the required data shown in each Specifications should be accurately handed over to the next
phase without fail.
Performance requirements for durability, safety, serviceability and restorability that are specified
in the “Standard Specifications for Concrete Structures, Design” are determined in the design phase.
Construction and maintenance methods are roughly determined in the phase. The data that affectconstruction and maintenance should therefore be handed over to the next phase without fail in theform of design drawings.
Construction records that are specified in the “Standard Specifications for Concrete Structures,
Materials and Construction” provide important data for assessment, deterioration prediction andimplementation of remedial measures in the maintenance phase. Accurate construction records
should therefore be handed over to maintenance engineers. Construction plans and various
inspection reports should also be provided to engineers as required.

Planning

Data
Feedback

DesignData

Construction

Data

MaintenanceFeedback
Fig. 1

Flow of work

Figure 1 shows a flow of work from the planning of a concrete structure to service
commencement. Data collected in the maintenance phase are not transferred to engineering works
in the planning, design or construction phase. It should, however, be taken into consideration thatreflecting the data in the maintenance phase in the planning, design and construction of anotherstructure for improvement is important to extend the service life of the structure. Theinterrelationship is basically the same for design, construction and maintenance described in the“Standard Specifications for Concrete Structures, Dam Concrete.”
Each component of the Standard Specifications for Concrete Structures is described below.
The “Standard Specifications for Concrete Structures, Design” shows standard methods for
performance verification of concrete structures such as reinforced concrete, prestressed concreteand steel-concrete composite structures, and stipulates the preconditions for checking and structuraldetails. The revised Standard Specifications for Concrete Structures are not applicable tounreinforced concrete structures. Material design values or other applicable items may, however, beapplied to unreinforced concrete structures.
The “Standard Specifications for Concrete Structures, Materials and Construction” provides
basic general rules concerning the construction of concrete structures. In the construction phase, theconstruction method and the performance during the construction work are determined based on thedesign drawings and restrictions on construction. Then, materials are selected and concrete mix(ii)Application of Standard Specifications for Concrete Structures

proportions are determined, where a concreting plan is developed so as to meet the requirements forwater content, cement amount, cement type and other parameters. Whether the concreting plan
meets the construction requirements or performance requirements of the structure or not is verified
by an appropriate method. If the requirements are not satisfied, the concreting method is
re-specified or the mix proportions are modified as long as the conditions handed over from thedesign phase are met.
The “Standard Specifications for Concrete Structures, Maintenance” provides general basic
principles concerning the maintenance of concrete structures. In the maintenance phase, documents
such as the design drawings and maintenance plans handed over from the design phase, and theconstruction plans, as-built drawings, construction records and inspection reports handed over fromthe construction phase should be fully used for efficient and effective maintenance work. In cases
where the use or functions of the structure change due to social changes, performance verification
should be made to verify whether the structure meets the resultant performance requirements or not.
If designated performance requirements are not ensured, repair, strengthening or other remedial
measures should be considered.
The “Standard Specifications for Concrete Structures, Dam Concrete” stipulates performanceand quality requirements for dam concrete, and describes the methods for verifying the compliancewith the requirements and the basic design and construction principles. The descriptions concerning
design, construction and maintenance in the “Standard Specifications for Concrete Structures, Dam
Concrete” are different from the contents of the Standard Specifications “Design”, “Materials andConstruction” and “Maintenance” with many respects because of the factors unique to dam concretesuch as the unreinforced nature and low or zero slump of dam concrete. The “Standard
Specifications for Concrete Structures, Dam Concrete” therefore describes the matters concerning
the design, construction and maintenance of dam concrete.
The “Standard Specifications for Concrete Structures, Test Methods and Specifications” lists theJapan Industrial Standards, provisions of JSCE and other standards for the methods mentioned in
the other four components of the Standard Specifications. Figures 2 through 4 show work steps inrespective phases described in the Standard Specifications for Concrete Structures “Design,”“Materials and Construction” and “Maintenance.”

2. Roles and deployment of responsible engineers
To produce and maintain a reliable structure that meets the performance requirements, theengineers involved should have a capacity to carry out the work and a high level of ethics.
In the planning, design, construction and maintenance of a concrete structure, the engineers
should make appropriate decisions under varying work conditions. Therefore, the engineers withrequired technical skills should be deployed according to the level of difficulty of work. In theplanning, design, construction and maintenance, therefore, responsible engineers not only withrequired technical expertise but also with responsibility and authority should be deployed inorganizations of the owner, the consultant and the contractor.

(iii)

Standard Specifications for Concrete Structures-2007, Design

Use and functions of structure

Plan for the structure
Specifications for Design
Specification of performancerequirements
Structural planning

Design plans(Structural format, materials used, dimensions ofmajor elements, construction method, etc.)

Design of the structure
Specifications for Design
Specification of structural details
Structural details (Cross section,materials, bar arrangement, etc.)
NG

Performance verification
for the structure
OK

Design drawings and other materials(Structure, materials, construction method,maintenance plan, etc.)

Construction of the structure

Fig.2

Work steps described in “Specifications for Design”(iv)Application of Standard Specifications for Concrete Structures

Planning of the structure

Design of the structure

Construction of the structure
Specifications for Materials andConstruction
Construction planning

NG

Verification and approval
OK

Construction

Quality control

NG

Inspection
OKAs-built drawings and construction records

Maintenance of the structure

Fig. 3Work steps described in “Specifications for Materials and Construction”(v)Standard Specifications for Concrete Structures-2007, Design

Planning of the structure

Design plans

Design of the structure

Design drawings and other materials

Construction of the structure

As-built drawings and construction
records

Maintenance of the structure
Specifications for Maintenance
Maintenance plan

Investigation, deterioration
prediction and evaluation
Recording

Not required

Assessment
Remedial measuresrequired or not?
Required

Recording

Implementation ofremedial measures

Storage of maintenancerecords

Fig. 4Work steps described in “Specifications for Maintenance”(vi)Application of Standard Specifications for Concrete Structures

The technical skills required for responsible engineers should be defined according to a scale of
the work, importance and difficulty of planning, design, construction or maintenance.
As capacity classifications of engineers, engineer qualifications authorized by JSCE are listed inTable 1. The qualifications for the special senior engineers and senior engineers are generally
required for responsible engineers.
The JSCE technical qualifications cover several fields. Responsible engineers to be deployed inprojects need to have qualifications only for major fields related to the specific project.

Table 1Engineer qualifications authorized by JSCE

Qualification

Required skills

Executive
Professional
Civil Engineer

Japan’s leading civil engineer with high-level knowledge andexperience in his or her field of specialty, or with comprehensive
civil engineering expertise

SeniorProfessional
Civil Engineer

Engineer with high-level knowledge and experience in multiple
fields or with comprehensive knowledge on civil engineering who
can solve key problems as a leader

Professional
Civil Engineer

Engineer with knowledge and experience at least in one special field
who can carry out task at his or her discretion

Associate
Professional
Civil Engineer

Civil engineer with required basic knowledge who can carry out
assigned task

3. System for ensuring reliability
Many groups are involved in the planning, design, construction and maintenance of a structure.
In order to ensure the high reliability of the structure in each work phase, the organizations involved
should play their role providing their know-how and assuming due responsibility.
To ensure reliability in the design (and planning) phase, two independent groups should
basically check the design. After the design and check by the design company, engineers of thecontractor should re-check the design, or request a third party to check the design. Then, fully
skilled engineers should be selected for checking so that safety or other reliability parameters may
be satisfied. The design drawings serving as a basis for contracting should carry the signatures of
responsible engineers of the two groups that assume responsibility.
In the construction phase, reliability is ensured through the quality management by thecontractor and the quality verification by the inspector independent of the contractor. Inspections
have generally been conducted directly by the Owner and/or Consultant. Completed structures
should be inspected wherever possible. If inspecting completed structures is impossible, inspections
should be conducted while the structure is being constructed. If the Owner cannot directly inspect(vii)

Standard Specifications for Concrete Structures-2007, Design

the structure under construction, the Owner may request an agent independent of the contractor.
Adopting as many highly reliable methods as possible can reduce the labor required for quality
management and inspection. In cases where adopting not so reliable methods is inevitable, the levelof quality management should be raised or inspections should be conducted more frequently to
improve reliability. Inspection items and decision criteria should be specifically presented at thetime of contracting because they greatly affect the quality of the structure and the construction cost.
Ensuring safety requires regular investigations. When defects are detected, decision should bemade as to remedial measures. For decision making concerning remedial measures for extremely
difficult deformation, listening to the opinions of engineers with high skills who have experienced
numerous cases is important.
In order for a system for ensuring reliability to work properly, the people or organization withtechnical skills fit for the specific work should be granted explicit responsibility and authority andassigned to the work. The compensation for the work and time required for the work should also be
provided.

(viii)

General Requirements

Chapter 1

GeneralCHAPTER 1 GENERAL

1.1

Scope

This specification, “Design,” (hereafter, the Specification) provides principles forstructural design and verification of performances of all concrete structures including
those made with reinforced concrete, prestressed concrete and steel-concrete
composites, as well as the prerequisite for verification and the structural details.

[Commentary] The construction and management of concrete structures involves design,
construction planning, fabrication and erection, construction in practice, and maintenance. At eachstage, the work shall be carried out in a manner that all requirements specified in any upstream
stage are satisfied. In case the verification at a previous stage is not satisfied, or in the case there isa change in the requirements at an upstream stage, the verification shall be repeated so that thecondition above is met.
This specification provides the standard method of verification for durability, safety,
serviceability and restorability of structures in the design stage of all concrete structures, including
those made with reinforced concrete, prestressed concrete and steel-concrete composites, as well as
the prerequisite of verification and the structural details. In certain special cases, it is possible thatprovisions in the Specification may not be sufficient, or in fact, the provisions in the specification
may not be strictly applicable. In cases where adequate structural performance can be confirmed
using prototype experiments assuming design loads, scaled model experiments, or numericalanalyses whose accuracy and applicability have been ensured, the procedure for verification of
structural performance as laid down in the present specification may not be followed based on thedecision by a responsible engineer. However, even in such cases, the principles laid down in thepresent specification should be sufficiently respected. The provisions of the present specification
may be taken to be generally applicable in cases where the characteristic compressive strength of
concrete does not exceed 80 N/mm2.
In principle, the limit state design method is adopted in the present specification for theverification of structural performance for durability, safety, serviceability and restorability, in viewof the satisfactory performance of this methodology in the past.
Some structures may involve the use of special construction materials or special construction
methods, which are not completely covered by the Specification. Reference should be made toother publications of the JSCE, which may provide guidelines or recommendations for the designand construction of such special structures, or use of special materials.
Additional
recommendations may be published by the JSCE from time to time, depending upon therequirement. The following is a list of JSCE publications that are considered to complement theSpecification. Certain publications such as “Recommendations for Maintenance of Concrete
Structures” or “Proposed Specifications of Durability Design for Concrete Structures”, whose
provisions have been essentially included in the present specification, have not been included in thelist.
“Manual of Design and Construction for Lightweight Aggregate Concrete Structures,” 1985.
“Recommendations for Design and Construction of Structures by Prestressed Concrete Panel
Composite Slab Method,” 1987.
“Recommendations for Design and Construction of Concrete Containing Ground Granulated
Blast-furnace Slag as an Admixture,” 1988.

1

Standard Specifications for Concrete Structures-2007, Design“Recommendations for Design and Construction of Prestressed Concrete Structures,” 1991.
“Recommendations for Design and Construction of Anti-washout Underwater Concrete,” 1991.
“Recommendations for Design and Construction of Reinforced Concrete Structures Using D57
and D64 Large-diameter Threaded Reinforcing Bars,” 1992.
“Design Code for Steel-Concrete Sandwich Structures,” 1992.
“Recommended Practice for Expansive Concrete,” 1993.
“Recommendations for Design and Fabrication of Diffusion Bonded Joints in Reinforcing Bars
Using Amorphous Metal Foil,” 1993.
“Recommendations for Design and Construction of Concrete Structures Using Silica Fume inConcrete,” 1995.
“Recommendations for Design and Construction of Concrete Structures Using Continuous Fiber
Reinforcing Materials,” 1995.
“Recommendations for Design and Construction of Composite Structures,” 1997.
“Guidelines for Retrofit of Concrete Structures,” 1999.
“Recommendations for Design of Reinforced Concrete Columns with Steel Fiber,” 1999.
“Verifications of Seismic Performance of In-ground LNG Tank Structures,” 1999.
“Recommendations for Upgrading of Concrete Structures with Use of Continuous Fiber
Sheets,” 2000.
“Recommendations for Design and Construction of Self-Compacting High Strength and HighDurability Concrete Structures,” 2001.
“Recommendations for Design and Construction of Electrochemical Corrosion Control
Method,” 2001.
“Recommendations for Design and Construction of Concrete Structures Using Epoxy-Coated
Reinforcing Steel Bars [Revised Edition],” 2003.
“Recommendations for Concrete Repair and Surface Protection of Concrete Structures,” 2005.
“Recommendations for Design and Construction of Recycled Aggregate Concrete Using
Demolished Concrete of Electric Power Plants,” 2005.
“Recommendations on Environmental Performance Verification of Concrete Structures(Draft),” 2005.
“Recommendations for Mix Design of Fresh Concrete and Construction Placement related
Performance Evaluation,” 2007.
“Recommendations for Design, Fabrication and Evaluation of Anchorages and Joints in
Reinforcing Bars [2007],” 2007.

2

Chapter 1

1.2

General

Basic Rules of Design(1) Design shall include the identification of performance requirements for a structure,
structural planning and detailing to meet those performance requirements, and theverification to make sure the performance requirements are met throughout the design
service life of the structure.
(2) When designing a structure, all performance requirements that need to be met inorder to meet the intended purpose of the structure during construction and during thedesign service life of the structure shall be determined in accordance with Chapter 2.
(3) In structural planning, the type of structure and other requirements shall be
determined in accordance with Chapter 3, taking into consideration such factors as
structural characteristics, materials, construction method, maintenance method andeconomy, so that the performance requirements can be met.
(4) In structural detailing, structural details such as shapes, dimensions andreinforcement patterns shall be determined in accordance with the structural detailing
requirements described in this Specification for the type of structure determined instructural planning.
(5) In the verification with respect to performance requirements, it shall be verified inaccordance with Chapter 4 that the performance requirements for the structure related to
durability, safety, serviceability, restorability, and the impact on the environment andlandscapes are satisfied throughout the design service life.

[Commentary] When designing a structure, it is necessary to make effort to attain the required
performance and construct a highly rational structure according to the purpose of the design of eachstructure, taking into consideration such factors as natural conditions, social conditions,constructibility, economy and environmental compatibility. The safety, serviceability andrestorability of structures specified in this Specification are strongly affected by structural details
such as shapes, dimensions and reinforcement patterns and the mechanical characteristics ofmaterials. It may generally be said, therefore, that many of those details are determined by thisSpecification. Structural details, however, such as shapes, dimensions and reinforcement patterns
are deeply related to constructibility, etc., indicated in the Construction section of this Specification.
In order to develop a rational design, it is necessary to take those structural details into
consideration in advance so that the designed structure does not fail to meet the constructibility
requirement. Concrete structures may be difficult to repair or strengthen after they are constructed.
It is therefore necessary to determine structural details by conducting a thorough study at the initialstage of design and predicting events that can occur during the service life of the structure withreasonable accuracy, taking maintainability into consideration. The basic rules of maintenance aredescribed in the Maintenance section of this Specification.
(1) The design of a structure consists of a series of tasks, namely, the determination of
performance requirements, structural planning, structural detailing, and the verification of
performance requirements, and these tasks must be performed consistently (see Fig. C1.2.1).
(2) Performance requirements for a structure need to be determined appropriately in view ofsuch factors as the intended purpose of the structure and the degree of importance of the structure.
Performance requirements include those determined by the physical properties of a structure andthose determined by other factors. Both types of performance requirements need to be determinedfor each structure. This Specification deals mainly with performance requirements determined by3

Standard Specifications for Concrete Structures-2007, Design

physical properties.
Other performance requirements, therefore, need to be determined
appropriately on an as-needed basis.
(3) When determining the type of structure and other details in structural planning, it isnecessary to take into consideration all factors such as structural characteristics, materials to be used,
construction method, maintenance method and economy in order to meet the specified performancerequirements. From the viewpoint of the rationality of design, it is important in structural planning
to rely on performance requirement verification results wherever possible in order to preventchanges in details such as the type of structure.
It is also necessary at the stage of structural planning to take into consideration matters thatcannot be verified concretely in accordance with this Specification.
(4) In structural detailing, information necessary for the verification of such details as thedimensions of structural members, reinforcement patterns and the performance of the materials to
be used is specified for the type of structure specified at the structural planning stage. When doing
this, it is necessary to appropriately take into consideration the structural details indicated in thisSpecification, design manuals, details of similar structures, and empirical information. It is also
necessary, at this stage, to determine structural details giving consideration to maintenance facilities
related to the maintainability of the structure, such as inspection openings and stairways.
(5) In the verification of performance requirements, verification for the specified performancerequirements is made in accordance with this Specification by using the information on thespecified structural details. The term "performance verification" refers to the task of ascertaining,by an appropriate method, that the type of structure, structural cross sections, materials to be used,structural specifications, etc., that have been determined taking into consideration such factors as
natural conditions, social conditions, constructibility and economy meet the specified performancegoals. An "appropriate method" refers to an experiment using a material, member or structure to
be used or a model, a numerical analysis with known accuracy, etc. If it is difficult to use thesemethods, it is a basic rule in this Specification to make verification by the limit state design method.
In such cases, it is essential that the preconditions for verification specified in this Specification bemet.

4Chapter 1“Design”

GeneralRequirements“M aintenance”

Cha pte r 2

Method of maintenance

Performance Requirements
Cha pte r 3
S tructural Planning“Mater ials and Constr uction”
Type of Structure, Outline of
Structure (Cross section andMaterials), Construction Method

Materials (Concrete andreinforcement),
Construction Me thod

Chapter 13 and 14
Structural Deta iling

Structural Detail (Dimension,Materials and Reinforcement
Patterns)

Chapter 4, etc.
Verification

Design Drawings

Construction Planning

Fig. C1.2.1 Structural design flow
1.3

Definitions
The following terms are defined for general use in this Specification.

Design─An act consisting of the determination of the required performance of astructure, structural planning, structural detailing and performance verification
Required performance─Performance required of a structure according its purpose andfunction
Verification─The act of checking whether a structure has the required performance,
for example by a verification experiment on full-scale specimens or an empirically andtheoretically proven analysis method
Durability─The resistance of a structure to performance degradation over time due tothe deterioration of materials in the structure caused by expected deteriorating agencies
Safety─The performance of a structure in preventing risks to users and other people
in the vicinity
Serviceability─The performance of a structure that enables users to use the structure
comfortably or prevents other people in the vicinity from feeling uncomfortable becauseof the structure, and the performance that ensure other functions required of the structure
are performed appropriately
Restorability─Performance that enables functional restoration and continue use of adeteriorated structure5

Standard Specifications for Concrete Structures-2007, Design

Earthquake resistance─Earthquake-related performance encompassing safety during
an earthquake and post-quake serviceability and restorability
Service life─Period during which a structure is in service
Design life─Period specified in design during which the structure or the structuralmembers shall maintain the service requirements.
Verification index─Physically quantifiable index for the required performance
Limit state─The state in which a structure begins to fail to meet the performancerequirements
Load─Any action which causes variations in stresses or deformations in structures ormembers.
Permanent load─Load that acts continuously, or is such that the variations in themagnitude are rare or negligible.
Variable load ─ Load that varies frequently or continuously and is such that thevariations in the magnitude cannot be neglected compared with the permanent load.
Accidental load─ Load that occurs rarely during the design life, but has serious
consequences when it occurs.
Design load─Value of load that is obtained by multiplying each characteristic value ofload by a corresponding load factor.
Characteristic value of load─Value of load determined based on variations, limit statesconcerned, and combinations of loads, for all loads during construction period andthroughout design life of the structure.
Specified value of load ─ Value of load specified by other design codes or
specifications, apart from the characteristic value of load.
Nominal value of load─Value of load not specified in available relevant codes, but iscommonly used in practice.
Characteristic value of material strength─Value of material strength which guarantees
that the probability of tested strength being below this value is within the specified limit
based on statistical interpretation of test results.
Specified value of material strength─Value of material strength that is specified byother design codes or specifications in a manner other than characteristic value ofmaterial strength.
Design basic strength─Basic strength for design. For concrete, the characteristic
compressive strength may usually be taken as the design basic strength.
Design strength ─ Value obtained by dividing the characteristic value of material
strength by a material factor.
Material factor ─ Safety factor to consider the unfavorable deviations of material
strengths from the characteristic values, differences in material properties between test
specimens and actual structures, effect of material properties on the specific limit states,
and time dependent variations of material properties.
Load factor─Safety factor to consider the unfavorable deviations of loads from thecharacteristic values, uncertainty in evaluation of loads, effect of nature of loads on thelimit states, and variations of environmental actions.
Structure factor─Safety factor to account for the relative importance of the structure,
as determined by the social impact of the structure failing or reaching a particular limit
state.
Structural analysis factor─Safety factor to consider the uncertainty of computational
accuracy in determination of member forces through structural analysis.
Member factor─Safety factor to consider the uncertainties in computation of capacity
6Chapter 1

Generalof the member, differences in the design and actual size of the member, and theimportance of the member which reflects the influence on the overall structure when it
reaches a certain limit state.
Load modification factor─Safety factor to transform specified or nominal values ofloads into characteristic values of loads.
Material modification factor─Safety factor to transform specified values of material
strength into characteristic values of material strength.
Design response value─A value obtained by multiplying a response value under thedesign load by a structural analysis factor
Design sectional force─A value obtained by multiplying the sectional force due to a
combination of design loads by a structural analysis factor and a design response value
obtained by using force as a verification index
Design limit value─A value obtained by dividing the performance of a member or
structure calculated by using a material-specific design value by a member factor and averification limit value set according to the required performance
Design sectional capacity ─ A value obtained by dividing the sectional capacity
calculated by using the design strength of a material by a member factor and a design
limit value obtained by using force as a verification index
Linear analysis─Structural analysis based on elastic primary theory assuming a linear
stress-strain relationships for the materials used, and neglecting secondary effects ofdeformations.
Primary reinforcement─Reinforcement calculated and arranged to fulfill requirementsof each limit state.
Positive moment reinforcement─Primary reinforcement arranged to resist the tensile
force due to positive flexural moment.
Negative moment reinforcement─Primary reinforcement arranged to resist the tensile
force due to negative flexural moment.
Distribution reinforcement─Reinforcement that is usually placed at right angles to theprimary reinforcement for the purpose of appropriate distribution of stresses.
Shear reinforcement─Reinforcement arranged to resist the shear force.
Stirrup─Transverse reinforcement placed perpendicular or nearly perpendicular to theaxis of member enclosing positive and/or negative moment reinforcement.
Bent bar─Reinforcement formed by bending up or down positive or negative moment
reinforcement.
Tie─Transverse reinforcement enclosing longitudinal reinforcement at given intervals.
Hoop─Within the tie, the reinforcement enclosing longitudinal reinforcement circularly
or elliptically.
Intermediate tie─Transverse reinforcement arranged to intersect the cross section.
Spiral reinforcement─Spirally wound continuous transverse reinforcement enclosing
longitudinal reinforcement.
Additional reinforcement─Auxiliary reinforcement provided as a precaution againstconcentrated stresses caused by loads, or to guard against cracking due to variation oftemperature or shrinkage.
Prestressing steel─High strength steel mainly used for prestressing.
Tendon─Single or a bundle of prestressing steel.
Sheath ─ Tube to form voids in concrete for accommodation of tendons in
post-tensioned prestressed concrete members.
Anchorage─Device used to anchor tendons in concrete member.
7

Standard Specifications for Concrete Structures-2007, Design

Coupler─Device to connect one tendon with another.
Fretting fatigue─Accumulated fatigue in wire of tendon due to rubbing or pressing byloading in portions where they are in contact with one another.
Pretensioning system─Prestressing system in which tendons are tensioned before
concrete is placed. Tensile stress in tendon is transferred to hardened concrete by bond
between tendon and concrete.
Post-tensioning system─Prestressing system in which tendons are tensioned after
concrete has hardened. Tensile stress in tendon is transferred to concrete by anchorageat ends.
Effective depth─Distance measured from extreme compression fiber to centroid ofpositive or negative moment reinforcement.
Tension reinforcement ratio ─ Ratio of cross-sectional area of primary tension
reinforcement to effective cross-sectional area of concrete. The effective cross-sectional
area of concrete is defined as the product of effective depth and flange width.
Compression reinforcement ratio ─ Ratio of cross-sectional area of primary
compression reinforcement to effective cross-sectional area of concrete.
Balanced reinforcement ratio─Tension reinforcement ratio where both tensile stress ofprimary tension reinforcement and compressive strain of concrete at extreme fiber reachthe design yield strength and the ultimate compressive strain simultaneously.
Development length of reinforcement─Length of embedded reinforcement required todevelop the design tensile stress of reinforcement at the critical section.
Clear distance─Face to face distance between adjacent reinforcing bars, tendons or
sheaths.
Concrete cover ─ Minimum thickness of concrete between concrete surface andsurface of reinforcing bars, tendons or sheaths.
Clear span─Distance from face to face of supports for beams or slabs.
One-way slab─Rectangular slab supported by two opposite sides.
Two-way slab─Rectangular slab supported by four sides.
Deep beam─Beam of which depth is relatively greater than a span length.
Corbel─Cantilever attached to column with span to depth ratio being less than orequal to one.
Column─Member oriented vertical or nearly vertical, and the length of which is greaterthan three times of the least transverse dimension.
Beam element model─A model where a structure is represented as made up of a
combination of one-dimensional beam elements
Finite element model─A model where a structure is represented as made up of a
combination of two or three-dimensional finite elements
Nonlinear hysteretic model ─ A model that gives nonlinear hysteresis in the
stress-strain relationship of constitutive materials, or in the load-displacement
relationship of a member or a structure under reversed cyclic loading8

Chapter 1

1.4

General

NotationIn this Specification, the following notations have been used for design calculation forstructures.

A
Aa
Ac
Am
As
Asc
Ass
Atl
Atw
Aw
av
b
be
b0
bw
C d
c
c
cs
d
d0

:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:

Ec
Ep
Es

:
:
:

F
Fk
Fn
Fp
Fr
f
f a
fb

:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:

f bo

f c
fk
f ck
f ly
fn
f pu
f py

gross area of cross section
loaded area of bearing force
area of concrete section
effective area of concrete for resisting torsion
area of reinforcement, or area of reinforcing steel in tensile zone
area of reinforcement required by calculation
area of structural steel shape, plate or fabrication in tensile zone
area of longitudinal reinforcement which is effective for resisting torsion
area of transverse reinforcement which is effective for resisting torsion
area of shear reinforcement
distance from loading point to support facewidth of member
effective width of member
length of short leg of transverse reinforcement
web width of member
design diagonal compressive force per unit width in concrete
concrete coverconstruction error in covercenter-to-center distance of reinforcing steel
effective depth of member
diameter of concrete cross section enclosed by transverse reinforcement
for circular cross section, or length of long leg of transverse
reinforcement for rectangular cross section
modulus of elasticity of concrete
modulus of elasticity of prestressing steel
modulus of elasticity of reinforcement or structural steel shape, plate or
fabricationload
characteristic value of load
specified value of load
permanent load
variable loadmaterial strength
bearing strength of concrete
flexural strength of concretebond strength between concrete and reinforcing steel
compressive strength of concrete
characteristic value of material strengthcharacteristic compressive strength of concrete, design basic strength
yield strength of longitudinal torsion reinforcement
specified value of material strengthtensile strength of prestressing steel
yield strength of prestressing steel

9Standard Specifications for Concrete Structures-2007, Design

fr
ft
fu
f vy
f wy
fy
f y
h
Ie
Ig
Kt
k
k1
k2
kc

:
:
:
:
:
:
:
:
:
:
:
:
:
:
:

l0
ld
ls
M
M cr
Mt
M tc
M tcu
M tu
M ty

:
:
:
:
:
:
:
:
:
:

Mu
:
N
:
N
:
N1 , N 2 :

Pe
p
p
pw
R
Rr
r
S
Sp
Sr
s

:
:
:
:
:
:
:
:
:
:
:

Tc
Tx
Ty
u

:
:
:
:

fatigue strengthtensile strength of concretetensile strength of steel
yield strength of steel in shear
yield strength of shear reinforcement or transverse torsion reinforcement
tensile yield strength of steel
compressive yield strength of steel
total depth of member
moment of inertia of transformed cross section
moment of inertia of gross cross section
section modulus for torsion
coefficient to consider bond behavior of reinforcing steel
coefficient for size effect in tensile strength of concretecoefficient to consider effect of frequency of variable loadcoefficient to consider effects of concrete cover and transverse
reinforcement on development length of reinforcement
development length of reinforcement
basic development length of reinforcement
additional embedment length at supports or a at point of inflection
momentcracking moment
torsional moment
torsional moment capacity of member without torsion reinforcement
diagonal compressive capacity of web concrete for torsional moment
torsional moment capacity of member
torsional moment capacity of member determined by yield of torsion
reinforcement
flexural capacity
fatigue life, or equivalent number of cycles of fatigue load
axial compressive force
main in-plane forces acting on planar members, N 1 is in tension, not lessthan N 2
effective prestress force in tendon
ratio of tension reinforcement
ratio of compression reinforcement
ratio of shear reinforcement
limited value or capacity of cross-section
fatigue capacity of cross-section
inside radius of bend
member force
member force due to permanent loads
member force due to variable loads
spacing of shear reinforcement, torsional reinforcement, or transverse
reinforcement
total tensile force in concretetensile force in reinforcement in x direction, per unit width
tensile force in reinforcement in y direction, per unit width
perimeter of bar, or loaded area
10

Chapter 1

up

V
Vc
Vcw
Vh

Vp
V pc
V pe
Vr
Vrp
Vry
Vs
Vsry
Vsy
Vwc
Vy
w
wa
z




c
p
s
t
d
n
 nt
p


a
b
c
f
i
m
s

y
 c
 cc

General: effective perimeter for resisting punching shears in slab, that is the sumof perimeter of bearing area of concentrated load or reaction and πd.
(where, d is effective depth): shear force: shear capacity of member without shear reinforcement: shear transfer capacity of member at shear plane: additional vertical force due to variation of effective depth in the
direction of member axis
: shear force due to permanent loads: punching shear capacity of slab
: additional vertical force due to inclination of tendon: shear force due to variable loads: fatigue punching shear capacity of slab without shear reinforcement: shear capacity provided by reinforced concrete section in steel reinforced
concrete (SRC) member of cumulative type: shear capacity provided by shear reinforcement: shear capacity of SRC member of cumulative type: shear capacity provided by structural steel shapes, plates or fabricationin SRC member of cumulative type: ultimate diagonal compressive capacity of web concrete in shear: shear capacity: crack width: limit value of crack width: distance between resultant compressive force and centroid of tension
reinforcement: coefficient for development of reinforcement to consider effect ofconcrete cover and existence of transverse reinforcement: angle between compression fiber and member axis
: angle between tendon and member axis
: angle between shear reinforcement and member axis
: angle between tension reinforcement and member axis
: coefficient to consider effect of effective depth on shear capacity: coefficient to consider effect of axial force on shear capacity: coefficient to consider effect of axial force on torsional moment capacity: coefficient to consider effect of longitudinal reinforcement on shear
capacity: rate of apparent relaxation of prestressing steel: structural analysis factor: member factor: material factor for concrete: load factor: structure factor: material factor: material factor for steel: coefficient of variation of test results: yield displacement: compressive strain of concrete: compressive creep strain of concrete
11

Standard Specifications for Concrete Structures-2007, Design

 cu
 cs

 csd
f
m

 cp
 n
 pe
 pp
 pw
r
 se
 sp
w
 wr
 wpe
x
y
l






: ultimate compressive strain of concrete: shrinkage strain of concrete: value for evaluation of increment of crack width due to shrinkage andcreep in concrete: load modification factor: material modification factor: standard deviation: compressive stress in concrete due to permanent loads: average compressive stress in concrete due to axial force: stress increment in prestressing steel for checking crack width: stress increment in prestressing steel due to permanent loads: tensile stress in prestressing steel as shear reinforcement at yield ofother shear reinforcement: variable stress: stress increment in steel for checking crack width: stress increment in steel due to permanent loads: stress in shear reinforcement: stress in shear reinforcement due to variable loads: effective tensile stress in prestressing steel as shear reinforcement: normal stress: stress in direction orthogonal to that of  x: diagonal tensile stress: shear stress produced by shear force and/or torsional moment: creep factor for concrete: diameter of reinforcement or duct, nominal diameter of reinforcement[Commentary] It is preferable to use different symbols for different meanings.
following definitions have been adhered to:A: areab: widthc: concrete coverd: effective depthE: modulus of elasticity

F: loadf: material strengthI: moment of inertial: span length, development lengthM: momentN: cycle, axial forceP: prestress force in tendonp: reinforcement ratioR: capacity of cross section

S: member forces: spacing
12

In principle, theChapter 1

Generalu: peripheral lengthV: shearw: crack widthx: distance from support: inclination angle with respect to the axis of member








: safety factor, rate of relaxation: diameter: coefficient for shear capacity: coefficient of variation, displacement: strain: modification factor: stress: creep factor

There may be some cases, when the symbol defined above is used with a different meaning in
text, or when new symbols are used. In such cases, the symbols are appropriately explained in therespective sections.
Subscripts used in this specification have the following meanings unless otherwise explained
elsewhere:a: bearing, structural analysisb: member, balance, bendingbo: bondc: concrete, compression, creep

cr: crackd: design valuee: effective, transformedf: loadg: gross areak

: characteristic valuel: longitudinalm: material, meann: specified, standard, axialp: prestress, prestressing steel, permanent, punchingr: variables: steel, reinforcementt: tension, torsion, transverseu: ultimatev: shear

w

: web

13

Standard Specifications for Concrete Structures-2007, Designy: yield

The subscript, k, represents the characteristic value of load or material strength. The subscript,
d, represents the design value of member force or the capacity of member cross-section. However,these subscripts may be omitted when the meaning is obvious.
The Specification follows the sign convention that stresses and strains are regarded positive intension, and negative in compression. As an exception, the symbol with prime (’) stands forcompression as positive.

14

Standard Specifications for Concrete Structures-2007, Design

CHAPTER 2 PERFORMANCE REQUIREMENTS

2.1

General(1) The design life of a structure shall be determined in consideration of required
service period of the structure, maintenance methods, environmental conditions, andeconomy.
(2) For every structure, all performance requirements to meet the intended purpose of
the structure during construction and during the design life of the structure shall be
specified. As a general rule, performance requirements related to durability, safety,
serviceability, restorability, environmental compatibility, landscape compatibility, etc.,
shall be specified.

[Commentary] (1) For design of a structure, it is necessary to indicate the design life with wideconsideration to the purpose of the structure, economically determined period over which thestructure is required to be in service, environmental conditions in the neighborhood of the structure.
Generally, longer design life is specified, higher durability and fatigue resistance performance will
be required.
(2) All of the specified performance requirements must be met throughout the design life of thestructure. As a general rule, performance requirements must be specified with respect to durability,
safety, serviceability, restorability, environmental compatibility, landscape compatibility, etc.
Detailed items related to these performance requirements need to be identified. In order for astructure to meet safety, serviceability, restorability and other performance requirements throughout
the design life of the structure, the structure must be free from material deterioration or other typesof deformation that could affect those performance requirements due to environmental actions.
In this Specification, the resistance of a structure to deterioration over time is identified as oneof the durability-related performance requirements of a structure. It does not include, however, theresistance to time-dependent changes in performance due to repetition of external forces such as
variable loads (e.g., fatigue). Instead, such resistance is deemed to be part of safety-related
performance against external forces. The required performance of a structure here is theperformance of a structure as a whole. In general, the performance of a structure is closely related tothe performance of the structural elements constituting the structure. In order to meet theperformance requirements for a structure, therefore, it is necessary to give careful consideration to
the relationship with the performance of each structural element so that the performancerequirements for the entire structure can be met.

2.2

Durability

In this Specification, durability shall mean the resistance of a structure to performancedegradation over time resulting from the materials deterioration in the structure under
expected deterioration actions.

[Commentary] The durability of a structure should be specified for the purpose of maintaining
the required performance such as safety, serviceability and restorability throughout the design life of
the structure. Durability, therefore, is not independent of those performance requirements andshould be deemed to be the resistance to changes in those performance over time. It is still difficult
14

Chapter 2

Performance Requirements

at present, however, to evaluate performance such as safety, serviceability and restorability as afunction of time, and trying to do so is not necessarily economical, either. For this reason, it iscommon practice to specify the required durability of a structure so that problems due toenvironmentally induced deterioration of the materials in the structure do not occur during thedesign life of the structure, and to perform performance verification with respect to safety,
serviceability and restorability. This indirectly ensures that the structure meets various performancerequirements throughout the design life of the structure.

2.3

SafetyIn this Specification, safety shall mean the performance of a structure to prevent risks
to users and other people in the vicinity under all expected conditions. Safety includes
the structural safety and functional safety of a structure, and performance requirements
for both types of safety must be specified.

[Commentary] The safety of a structure can be broadly classified into performance that can be
determined by the mechanics of the structure such as failure or collapse due to variable loads or
accidental loads such as seismic loads and performance determined by the intended purpose of useor the loss of functionality. In this Specification, as a general rule, performance requirements forboth types of safety must be specified.

2.4

Serviceability

In this Specification, serviceability of a structure shall mean the performance thatenables users or other people in the vicinity to use the structure comfortably andfunctional performance required of the structure.

[Commentary] The serviceability of a structure is defined as the performance that enables
comfortable use of the structure and functional performance under normal conditions.
Generally, it is good practice to specify such requirements as trafficability, walkability,
appearance, noise and vibration with respect to the comfortability of use. With respect to functional
performance, it is generally good practice to specify shielding performance and permeability suchas watertightness, water permeability, sound-shielding performance, cold insulation and heatinsulation, and the performance in preventing serviceability-impairing damage due to such actions
as variable loads, environmental factors and accidental loads.

2.5

Restorability

In this Specification, restorability shall mean the performance in restoring theperformance of a structure that has degraded because of accidental loads such as
seismic loads, and making continued use of the structure possible. Restorability shall be
specified in view of the degree of difficulty in repairing the structure and all factors
affected by performance degradation.

[Commentary] Restorability is a performance requirement that indicates the degree of difficulty
in restoring degraded performance of a structure due to accidental loads such as seismic loads.
Usually, civil engineering structures are highly public in nature, and successful implementation and15

Standard Specifications for Concrete Structures-2007, Design

maintenance of their functions greatly affects the daily activities of individuals and social andproduction activities. This is why restorability is required as one of performance requirements of astructure. Restorability is greatly affected by not only the degree of difficulty in repairing adamaged structure (reparability) but also structural (tangible) measures such as preparing materials
for restoring a damaged structure and improving restoration technology and nonstructural(intangible) measures such as establishing an organizational system for restoration efforts. In thisSpecification, mechanical performance requirements related to the reparability of concrete
structures are specified as restorability on conditions that non-reparability-related factors are
separately taken into consideration. Accidental actions that could damage structures include
earthquakes, wind, fires, etc., but this Specification requires as a general rule that only the influenceof earthquakes be taken into consideration. When considering the reparability of concrete structures,
it is good practice to determine the performance level according to the magnitude of accidentalloads involved, keeping in mind, for example, the state of a structure that can be used without doing
repairs and the state of a structure that can be functionally restored in a short period of time.

2.6

Other Performance Requirements

Performance requirements such as environmental compatibility and landscapecompatibility shall be specified on an as-needed basis.

[Commentary] In this Specification, performance requirements are concretely specified withrespect to durability, safety, serviceability and restorability. When specifying requirements withrespect to other performance requirements such as environmental compatibility and landscapecompatibility, it is necessary to specify performance requirements, making sure that appropriate
verification can be made. Environmental compatibility encompasses compatibility with natural andother environments such as the global environment, the regional environment and the working
environment and compatibility with social environments such as landscapes. Environmental
compatibility is to be regarded as required performance on an as-needed basis, keeping in mind thegoal of mitigating environmental impact. Since, however, it is still difficult at present to verify these
performance requirements at the same level as the safety, serviceability and restorability describedin this Specification, it is recommended that performance requirements other than these beconsidered carefully at the stage of structural planning, and the verification be made if necessary.

16

Chapter 3

Structural Planning

CHAPTER 3 STRUCTURAL PLANNING

3.1

General(1) In structural planning for a structure, the type of structure, materials to be used andmain dimensions shall be specified so that the performance required of the structure canbe met in the most rational way.
(2) Structural planning for a structure shall involve a comprehensive study that takes
into consideration such factors as the construction methods, maintenance methods,
environmental and landscape impacts, and economy so that the performancerequirements specified in this Specification can be met.
(3) In order to draw up a rational structural plan, necessary studies and surveys shallbe conducted according to the state of the planned construction site, the size of thestructure, etc.

[Commentary] This Specification requires a method in which the type of structure, materials andmain dimensions are determined at the structural planning stage, after performance requirements bywhich to ensure the use and function of the structure are specified, and then performanceverification is made on the basis of the specifications thus determined in order to ascertain that thestructure meets the performance requirements. "Structural planning" mentioned in this chapter,therefore, is defined as a stage at which the type of structure, materials and main dimensions are
determined after the performance requirements for a structure are specified.
The use and function required for a structure should be preconditions for the structural planning.
The structural planning, therefore, must be consistent with the function requirements. The functionsof structures are often regulated in accordance with laws, regulations and standards establishedunder those laws and regulations. In the case of road bridges, for example, requirements related towidth and number of lanes are stipulated in the Road Structure Ordinance. Because functions likethis are obligatory requirements for the structures concerned, it is necessary to apply suchrequirements appropriately after carefully studying the content and interpretations of the applicablelaws, regulations and standards.
Functions of a structure include not only those corresponding to the purpose and requirements
for the structure but also those that are additionally required. In the case of bridge structures that
forms a grade-separated intersection with a road or railroad, for example, infrastructural facilities
such as waterworks, sewers and gas piping may also be installed. A structural plan, therefore, must
be developed through thorough consultation with the organizations involved.
In Construction Part of this Specification describes 13 types of concrete that are special in termsof materials used, performance, construction methods, construction environments, etc. If therequired performance of a structure cannot be achieved by a conventional method, it may benecessary to use these special types of concrete and new technologies. Special concretes include
expansive concrete, lightweight aggregate concrete, continuous fiber reinforced concrete, short fiber
reinforced concrete, high-strength concrete, high-fluidity concrete, shotcrete, prepacked concrete,
antiwashout underwater concrete, marine concrete, prestressed concrete, steel-concrete composites,
and factory products.
(1) and (2) The type of structure, materials and main dimensions must be determined through acomprehensive study in view of such factors as construction methods, maintenance methods,
17

Standard Specifications for Concrete Structures-2007, Design

environmental and landscape impacts, and economy so that the performance requirements(durability, safety, serviceability, and restorability) stipulated in this Specification can be met. It is
not an exaggeration to say that structural planning roughly determines construction costs andpractically determines future maintenance costs. It is therefore necessary to conduct careful studies,taking into consideration the future maintenance strategy of the structure.
If a sufficient amount of information is available concerning structures of similar types and sizes,
the type of structure and main dimensions can be determined on the basis of past project data. Since,
however, it is very difficult at the stage of performance verification to change the type of structure
and main dimensions determined at the stage of structural planning, it must be ascertained inadvance that there are no substantial differences between the preconditions for the past project andthose for the structure concerned, and that the application of the past project data does not pose any
problem.
If little or no data is available on structures of similar types or sizes, it is desirable that a detailed
study be conducted so as to prevent changes in the type of structure or main dimensions at the stageof performance verification.
(3) The planning, design and construction of a structure requires various studies and surveys,
and it is necessary to conduct various studies and surveys at the stage of structural planningaccording to the state of the planned construction site and the type and size of the structure to beconstructed. If these studies and surveys are inadequate, the type of structure or other details may
prove ill-suited to the site conditions, necessitating major changes in the structural plan. Thisrequires careful attention.

3.2

Studies on Performance Requirements

In structural planning for a structure, consideration shall be given so that the required
durability, safety, serviceability and restorability of the structure can be attained andmaintained throughout the design life of the structure.

[Commentary] (i) Durability: In order to attain and maintain the required performance of astructure throughout the design life of the structure, it is common practice either to try to prevent
material deterioration and deformation in the structure due to environmental actions or to design the
structure so as to keep material deterioration, if any, at a minor level so that structural performancedegradation does not result. In order to do this, it is important that the concrete used in the structure
have the required level of strength, durability and quality.
Performance verification as to whether a structure is durable enough to remain free from trouble
due to material deterioration throughout the design life of the structure is made in accordance with
Chapter 8. Passing this verification is necessary in order to maintain the required level of safety,
serviceability and restorability throughout the design life of the structure.
In Chapter 8, performance verification of durability is made using durability-relatedcharacteristics of concrete, stress in steel bars, thickness of concrete cover, etc. In cases where astructure is to be constructed in an environment that is highly corrosive to steel or in a highly
chemically corrosive environment, careful studies on durability needs to be conducted if attaining
the required resistance by the resistance of concrete itself is likely to be difficult and necessary
countermeasures are likely to be very expensive.
Recommended countermeasures that can be taken in such cases include the use of rust-proofed
steel bars and concrete surface protection. If a structure is constructed in a highly erosive
18

Chapter 3

Structural Planningenvironment such as hot-spring areas or in the vicinity of an acidic river where concrete
deterioration cannot be controlled completely, it may be necessary to plan exposure tests using
concrete specimens in a real exposure environment in order to verify the durability of concrete.
(ii) Safety: Chapter 9 requires as a general rule that the safety of a structure be verified byascertaining, for example, that no structural member reaches the limit state of cross-sectional failure,
and the structure does not reach the limit state of stability under the design loads. Because theseverifications are made by using detailed information such as dimensions of structural members andsteel bar arrangements, the safety of the structure is examined in detail at the stage of performanceverification.
If a sufficient amount of information is available concerning structures of similar type and size,studies on safety of the structure at the stage of structural planning can be made by referring to past
project data. In this case, if the size of the structure, topographical, geological and other conditions
at the site of existing structures differs considerably from those of the planned structure, it may benecessary to change the type of structure or the shape and dimensions of the structure determined at
the stage of structural planning, causing a major change in the structural plan. It is therefore
necessary to carefully study difference in the preconditions between existing structures and theplaned structure.
If little or no information is available concerning a structure of the same type and size as theplanned structure, it is desirable that general studies on safety of the structure be conducted to makesure that no changes in the type of structure or main dimensions occur at the stage of performanceverification.
In order to achieve a higher level of safety of a structure, it is desirable that the structure be
designed so as to prevent the entire structure from collapsing even if some of the structuralmembers reach the limit state of cross-sectional failure. This characteristic is called "redundancy" or"structural robustness." For example, a statically indeterminate structure is more redundant than astatically determinate structure.
(iii) Serviceability: Chapter 10 requires as a general rule that serviceability of a structure beverified by ascertaining that neither the structural members nor the structure reaches the limit stateof serviceability under the design loads. Commonly used verification indices for comfortability andfunctionality include crack width, displacement, deformation, stress, acceleration and vibration.
These indices are determined at the stage of design of the structure because they are calculated byusing such values as dimensions of structural members and steel bar arrangements.
A study on serviceability needs to be conducted at the stage of structural planning if applicationof waterproofing or other countermeasures becomes obviously necessary from the initial stage of
construction and such control measures are likely to be very expensive in case when a structure is tobe constructed in an environment that is highly corrosive to steel or when a high level ofwater-tightness is required.
(iv) Restorability: Chapter 2 defines the restorability of a structure as the performance related tothe degree of difficulty in restoring a function degraded by accidental loads such as seismic loads.
Restorability is a performance requirement of civil engineering structures and is greatly affectedby not only the degree of difficulty in repairing a damaged structure (reparability) but also the stateof implementation of structural measures such as preparation of materials for restoring a damaged
structure and developing restoration technologies and nonstructural measures such as establishingan organizational system for restoration efforts.
Chapter 11 requires that performance verification be made by specifying a mechanical limit

19

Standard Specifications for Concrete Structures-2007, Designstate for concrete structures. This performance verification is supposed to deal mainly with thereparability of concrete structures. The determination of limit states of this type is predicated on theimplementation of structural and nonstructural measures for a damaged structure. In structuralplanning, therefore, it is necessary to take into consideration both the structural and nonstructural
aspects on the restoration of civil engineering structures.
The reparability of a structure is affected by the type of structure. It is necessary, therefore, toselect a type of structure that makes repair and functional restoration as easy as possible in the eventof structural damage, taking into account such factors as the environment for restoration activities atthe construction site. For example, in the case of a structure that is required to remain usable evenduring an earthquake or even immediately after an earthquake, it is good practice to think of using
such methods of controlling structural damage as seismic base isolation or vibration mitigation
system. It is also necessary to see to it that the center of stiffness of the structure coincides with thecenter of action of the loads as much as possible so that horizontal torsion of the structure isminimized.
Regardless of the type of structure, if a structure is damaged, the time and costs required for
repair vary considerably depending on not only the degree of damage but also the position ofdamage in the structure. It is therefore desirable that possible damage areas be located ineasy-to-access areas where inspection and repair can be performed easily.
For details on seismic structural planning, refer to Section 11.1.

3.3

Studies on Construction

In structural planning, restraints related to construction shall be taken into
consideration.

[Commentary] If a structure is to fulfill its functions and retain the required performance, thestructure needs to be constructed so that the conditions indicated on the design drawings and otherdocuments can be met. In order to do this, it is necessary to develop a structural plan in due
consideration of restraints associated with construction.
Since the Hyogoken Nanbu Earthquake of 1995, there has been a tendency toward thecomplication of reinforcement arrangements in cross sections of structural members. Mainly byreason of economy, there have also been cases, such as pylons of concrete cable-stayed bridges, inwhich the cross sections of structural members were made smaller by using high-strength materials
such as high-strength concrete. In such cases, careful consideration needs to be given to concreting,and it is necessary to think about ways to ensure successful concreting such as using high-fluidity(self-compacting) concrete. Depending on the configuration of the structure to be constructed, there
are cases where the complication of the fabrication and erection of formwork and reinforcement
results in lower construction accuracy so as to make it difficult to attain the required quality ofconcrete and the required performance of the structure or where the date of completion be delayed
because of the needs to attain the required construction accuracy. In order to secure the required
accuracy of structures and rationalize the construction process, therefore, it is necessary to think of
employment such measures as using large steel formwork or prefabricated reinforcement cages atthe stage of structural planning.
There are also cases where the type of structure is determined by the construction methods. For
example, if supporting works are difficult because of topography at the construction site of a bridge
at a ravine in a mountainous region, the adoption of a precast concrete box girder structure to beconstructed by the cantilever erection method may be considered. In the case of a bridge to be20

Chapter 3

Structural Planning

constructed on flat land, the adoption of a precast concrete slab girder structure to be constructed by
movable supporting methods may be considered.
Thus, the type of structure may be determined according to such restraints as topography at theconstruction site, and there are also cases where a particular type of structure is adopted and, forexample, the use of special concrete is required or formwork and reinforcing work methods are
specified. The structural plan, therefore, needs to be drawn up taking into consideration such
construction-related restraints.
3.4

Studies on Maintenance

Structural planning shall take into consideration such factors as the degree ofimportance of the structure to be constructed, the design life of the structure, service
conditions, environmental conditions and the degree of difficulty in maintenance so as tofacilitate in-service maintenance.

[Commentary] As indicated in the Maintenance Part of this Specification, many inspections need
to be conducted for every in-service structure including the initial inspection conducted when
maintenance begins, daily inspections and periodic inspections conducted on a regular basis,
detailed inspections conducted to evaluate various states in details, and special inspections
conducted when the structure has been subjected to accidental external forces due to natural
disasters or other causes. Depending on the method of inspection used, inspection may be highly
costly and labor-consuming. Also, there may be cases where different repair, strengthening andreconstruction measures are taken for a structure according to the degree of performancedegradation of the structure. In such cases, the costs of countermeasures might be huge dependingon the degree of performance degradation. In structural planning, therefore, it is desirable that thetype of structure and materials to be used be determined so that maintenance activities duringservices can be performed efficiently, and the cost of countermeasures can be minimized.
Because maintenance-related problems associated with bridges often occur at expansion joint
devices or bearings, it is desirable, for example, that the adoption of a continuous rigid-frame
structure, which is relatively free from those devices, be considered.
If the degradation of a structure in a harsh environment and huge costs of countermeasures are
expected as when a structure is to be constructed at an offshore site, it is desirable, besides theselection of an appropriate type of structure, that studies be conducted on durability enhancement
measures such as surface treatment of concrete, rust-proofing treatment of steel bars and cathodic
protection to consider maintenance options in advance in order to reduce maintenance costs. If it isthought certain that such maintenance measures need to be taken while the structure is in service, it
is good practice to take some kinds of measures in advance at the stage of structural planning inorder to facilitate maintenance measures during services. Such measures are effective in reducing
maintenance costs.
Clearly indicating a maintenance strategy for the planned structure at the stage of structuralplanning will contribute to rationalization of maintenance because the information thus identified
can be reflected into the maintenance plan drawn up before the commencement of the maintenancestage. It is desirable, therefore, that a prototype of the maintenance plan be developed at the stage ofstructural planning.

21

Standard Specifications for Concrete Structures-2007, Design

3.5

Studies on Environmental and Landscape Compatibility

Structural planning shall take into consideration the influence of concrete structureson the natural, social and other environments and landscapes.

[Commentary] A concrete structure affects the natural, social and other environments andlandscapes at various stages such as the manufacture of materials for concrete structure and theconstruction, the service and maintenance of the structure. It is necessary to consider the influenceon the environment and landscapes at each of those stages, paying attention to factors causing suchinfluence.
When evaluating the influence on natural environments, it is necessary to take into
consideration impacts on discharge of greenhouse gases, air pollutants and water and soil pollutants,
the consumption of resources and energy, and discharge of waste. For example, in order to evaluate
the influence associated with water quality when an underwater concrete structure is to beconstructed under strict conditions imposed for the purpose of preventing water contamination, it isnecessary to consider the use of antiwashout underwater concrete.
The influence of the structure on natural landscape also needs to be taken into consideration.
Civil engineering structures are part of the infrastructure that exists over a long period of time after
they are constructed, and those structures themselves can affect landscapes. Since the appearance isgreatly dependent on the type of structure, thorough studies needs to be conducted at the stage ofstructural planning so that there is no adverse effect on natural landscape including the structure
itself. To do this, it is necessary to evaluate, in advance, the influence of the construction of theplanned structure on the natural landscape at and around the construction site and to draw up a planso that the completed structure will harmonize with the natural landscape.
From the viewpoint of effective use of resources, efforts are underway to promote reuse ofwaste generated by concreting work such as waste wood, metal scraps and concrete fragments
under the Act on the Promotion of Recycling of Resources (Recycling Act). Waste wood andconcrete fragments are among the resources covered by the Recycling Act. It is therefore necessary
reuse these resources for producing recycled aggregate concrete or for other applications in order tocontribute to environmental conservation. For further information on this, refer to the
Recommendations on Design and Construction of Recycled Aggregate Concrete Structures Using
Concrete from Demolished Power Plant Structures.
It is also necessary to take into account the influence of noise and vibration during theconstruction of a concrete structure on local environments around the construction site and theworking conditions for construction workers. There is a need for the management of theconstruction site in accordance with the Noise Regulation Act and the Vibration Regulation Act andthe use of low-noise and low-vibration vehicles and equipment.
In the area of environmental conservation, laws such as the Basic Environment Act
supplemented by environmental laws including Cabinet orders and ordinances and the Industrial
Safety and Health Act have been enacted in order to contribute to healthy and cultured living of thepeople and the welfare of humankind. Naturally, environmental studies at each stage of activities
related to concrete structures must be conducted in accordance with those laws and regulations.
Within the framework of comprehensive evaluation of environmental impact, however, it is also
necessary to take into consideration all factors affecting the environments. This makes it necessary
not only to conduct studies in accordance with those laws and regulations but also to evaluate theinfluence on global environments, regional environments and working conditions at each stage ofthe design life of the structure.

22

Chapter 3

Structural Planning

For information on environmental performance verification, refer to the Recommendations for
Verification of Environmental Performance of Concrete Structures.

3.6

Studies on Economical Aspects

As a general rule, structural planning for a structure shall take into consideration
economy from the viewpoint of life cycle costs of the structure.

[Commentary] In structural planning, it is very important to select a type of structure,
dimensions of structural members, materials to be used, etc., that are economical. Careful studies
are required with regard to economical aspects because total costs of the project will be dominantly
determined at the stage of structural planning.
The conventional approach to the evaluation of economy of a structure focused mainly on initial
the construction costs. In view of growing stock of infrastructure and increase in maintenance costs,
however, it is necessary to evaluate economy from the viewpoint of not only the initial construction
costs but also the life cycle costs taking maintenance and reconstruction into account.
Structures need to be repaired periodically and reinforced or reconstructed if they have become
unable to meet the performance requirements. Maintenance and other costs required after thecompletion of construction, therefore, are substantial. When a structure is reconstructed, it is notuncommon that the costs of reconstruction become greater than the initial construction costs,
though depending on construction-related restraints. At the stage of structural planning, therefore, it
is important not only to evaluate the initial construction costs but also to estimate the future
maintenance costs and reconstruction costs and to make evaluation taking those costs into account.
Because structural details such as dimensions of structural members have not yet been
determined at the stage of structural planning, construction, maintenance and other costs cannot be
evaluated accurately. It is also necessary, therefore, to refer to past project data. Since, however, theestimated costs may differ considerably from the actual costs if the preconditions for a past project
and those for the planned structure greatly differ, the preconditions for the past project need to be
examined carefully.

23

Standard Specifications for Concrete Structures-2007, Design

CHAPTER 4 RULES FOR PERFORMANCE VERIFICATION

4.1

General(1) As a general rule, the performance verification of a structure shall verify that a
structure or its member having the structural details, such as configuration anddimensions, assumed at the design stage does not reach the limit state specified to meetthe required performance during construction and during the design life of the structure.
(2) Generally, the limit state shall be specified for durability, safety, serviceability andearthquake resistance. The limit state of earthquake resistance shall be comprehensively
specified in view of the safety of the structure during an earthquake and post-quake
serviceability and restorability.
(3) In performance verification of a structure, the influence of changes in performanceover time due to environmental actions may be ignored if the requirements in Chapter 8
and Chapter 12 are met.
(4) As a general rule, performance verification of a structure shall be performed by
identifying an appropriate index for verification and comparing its limit value with the
response value.

[Commentary] (1) As a principle of this Specification, required performance of a structure
should be declared clearly at first. Thereafter, an equivalent limit state corresponding to eachperformance requirement should be specified. When a structure, or a part of it, reaches a certain
limit state, its serviceability may suddenly lose, or it may even reach failure in some cases. Then,the structure cannot perform its function nor meet the performance requirements because of various
defects. To prevent those situations, performance verification of the structure shall be done byexamining the limit state. In setting a limit state, an index representing the state of a structure,member or material should be selected, and then its limit value set in accordance with the required
performance. Performance verification is done by examining if its calculated response value under
given actions exceeds the limit values or not. The limit values should be set taking into accountreliability of analysis methods and models employed in calculating the response value.
In the case that a total structural system is not simple, consisting of several structures, a processwith a possibility that the structural system does not meet the requirements is selected. Required
performance is set for each constituent structure, and thereafter, the limit state may be set for eachelement in the structural system. In this case, the procedure to determine the limit state should beshown in a hierarchy way. Recommendations listed in Chapter 1, which show a series ofprocedures from embodiment of required performance to determination of the limit state of member,can be referred to.
(2) Generally, the limit state is to be determined for durability, safety, serviceability andearthquake resistance. Earthquake resistance is defined as a performance requirement of a structure
against seismic actions, and the limit state is comprehensively determined in view of the safety ofthe structure during an earthquake and its post-quake serviceability and restorability.
It is good practice to define the limit state for safety on the basis of mechanical properties asfollows. Other types of limit states than the mechanical safety need to be determined separately
according to the functions of the structure. These include performance requirements from the24

Chapter 4 Rules for Performance Verification

viewpoint of the users of the structure such as trafficability and walkability and performancerequirements associated with disasters involving third parties resulting from structural faults such as
falling of cover concrete.
1) Cross-sectional failure:
Defined as performance of a structure in retaining its load-carrying capacity under any loads
that can occur during the design life of the structure.
The performance of a structure as a whole in resisting failure is closely related to the state of
the members constituting the structure. If a structure consists of two or more members, whatneeds to be done in performance verification for safety is to ascertain that the structure as awhole does not fail even after one or more of the structural members fail. In this Specification,in order to be conservative in verifying the safety of a structure, Chapter 9 describes a concrete
verification method to be used when the failure of a structure is defined as the failure of one of
the structural members.
2) Fatigue failure:
Defined as performance of a structure in retaining its load-carrying capacity under repetitionof any variable loads that can occur during the design life of the structure.
3) Stability of a structure:
Defined as performance of a structure in retaining stability in spite of deformation,
displacement, mechanisms of deformation or displacement of foundation structures, etc., under
any actions that can occur during the design life of the structure.
With respect to serviceability, it is generally recommended that the limit states described below
be set as functional limit states determined by comfortability of use and other functions of astructure. Limit values for these limit states are to be determined according to the purpose andfunctions of the structure.
1) Appearance:
Defined as performance that ensures that cracks in concrete, soiled concrete surfaces, etc.,
neither make people uneasy or uncomfortable nor prevent the use of the structure.
2) Noise and vibration:
Defined as performance that ensures that noise and vibration generated from the structureneither have adverse effects on the environments nor prevent the use of the structure.
3) Trafficability and walkability:
Defined as performance that ensures that vehicles and pedestrians can move and walk
comfortably
4) Watertightness:
Defined as performance of a watertight concrete structure that ensures that it does not lose
its functionality due to water or moisture permeation
5) Resistance against damage:Defined as performance that ensures that a structure is not damaged by such causes as
variable loads and environmental actions so that the structure is not rendered unusable
25

Standard Specifications for Concrete Structures-2007, Design

Table C4.1.1 shows examples of the relationship among limit states, verification indices andloads to be considered for each performance requirement specified in this Specification. Specificsettings for earthquake resistance are indicated in Chapter 11.
Table C4.1.1

Examples of relationship among limit state, verification index and load
for each performance requirement

Required
performance

Limit state

SafetyCross-sectional
failureFatigue failure
Displacement,
deformation,mechanismsAppearance

Crack width, stress

Vibration

Noise, vibration level

Comfortability ofvehicle ride, etc.

Displacement,
deformation

Watertightness

Water permeation
through the structure
Crack width

Serviceability

Verification index

Design load to be considered

Force

All loads (maximum value)Stress, force
Deformation,
deformation offoundation structure

Cyclic load

Resistance against
damageForce, deformation, etc.
(maintenance offunctionality)

All loads (maximum value),
accidental loads
Load of a magnitude whose
frequency of occurrence isrelatively highLoad of a magnitude whose
frequency of occurrence isrelatively highLoad of a magnitude whose
frequency of occurrence isrelatively highLoad of a magnitude whose
frequency of occurrence isrelatively highVariable load, etc.

(3) The basic rule when verifying the required performance of a structure is to take into
consideration changes in performance over time during the design life of the structure. In thisSpecification, however, the safety, serviceability and earthquake resistance described in thisSpecification may be verified without taking into account deterioration of the constituent materials
during the design life if the requirements for the verification of durability described in Chapter 8
and the requirements for the verification concerning initial cracks described in Chapter 12 are met.
It is necessary to estimate the degree of safety by assuming structural member details, the accuracyof reinforcement locations, the variability of the mechanical properties of materials used, etc.
(4) In order to rationally verify the performance of a structure, the basic rule is to compare limit
values with response values by using verification indices that can directly express the performance
to be considered. On the other hand, it is a prerequisite that performance requirements such asenvironmental compatibility and landscape compatibility are verified by an appropriate method, if
possible. Landscape compatibility, for example, needs to be verified by using structure models,
perspective drawings, etc., having structural details satisfying the verification criteria for durability,
safety, serviceability and earthquake resistance.

26

Chapter 4 Rules for Performance Verification

4.2

Prerequisite for Verification

The performance verification of a structure in accordance with this Specification
assumes, as a prerequisite, that the structural detail requirements for performanceverification specified here, other structural detail requirements, the standard construction
method requirements and standard placeability requirements in accordance with
Construction Part of this Specification, and the maintenance procedure requirements
specified in Maintenance Part of this Specification are met.

[Commentary] The methods of performance verification described in this specification are basedon structural mechanics of structures and materials, which generally have some assumptions
regarding deformational consistency of concrete and reinforcement and local stress states. Thus,
general requirements for structural details are specified to realize these assumptions. Otherwise,
accuracy of the verification decreases and the range of application is restricted. If verification
methods would be more applicable in future, fewer requirements on structural details would beenough.
In this Specification, safety margin is considered on the basis of the standard construction
method and concrete placeability indicated in Construction Part of this Specification. Actual
construction methods and concrete placeability (expressed in terms of workability, such as filling
ability, pumpability and setting characteristics, and strength during construction) are determined on
the assumptions that the construction plan is drawn up and the materials design is made inaccordance with Construction Part of this Specification so that the quality of concrete is equivalent
to or better than that specified in this Specification. It is also assumed that the maintenanceprocedure requirements specified in Maintenance Part of this Specification are met so that thestructural performance specified in Design Part of this Specification can be kept.

4.3

Verification method(1) The verification of a limit state shall be made by the methods specified in Chapters
8, 9, 10, 11 and 12, after calculating response values by the methods specified in Chapter
7 by use of characteristic values of material strengths and loads, and the safety factors
specified in Section 4.5.
(2) In general, verification shall be made by using Eq.(4.3.1):

i ･Sd／Rd ≦1.0
where

(4.3.1)

Sd : design response value
Rd : design limit value

i: structure factor as per Section 4.5[Commentary] (2) In general, when verifying a limit state, it is necessary to consider the state at
the end of the design life in view of the influence of changes in performance over time and use
Eq.(4.3.1). Eq.(4.3.1) shows the case where the limit value of performance, Rd, is regarded as thelower limit value. If Rd represents the upper limit value, the direction of the inequality sign and thetreatment of safety factors differ from those in Eq.(4.3.1).

27

Standard Specifications for Concrete Structures-2007, Design

4.4

Calculation of Response Values and Limit Values(1) In principle, the function to calculate a response value shall earn the mean value ofit, when loads, material characteristics and stiffness of members are actual values.
(2) In principle, the function to calculate a limit value of performance shall earn themean value of it when material characteristics and stiffness of member are actual values.

[Commentary] Here given is a principle for functions to calculate response values and limit
values. When a new method for calculating limit values of performance is proposed by new
findings, the equation shall conform to this principle, that is, to relate most expected mean values.
In addition, it is required to offer the appropriate member factor associated with accuracy of theequation and reliability of the analytical values.

4.5

Safety Factors(1) Safety factors are material factor, m, load factor, f, structural analysis factor, a,member factor, b, and structure factor, i .
(2) Material factors, m, shall be determined considering the unfavorable deviations ofmaterial strengths from the characteristic values, the difference in material properties
between test specimens and actual structures, the effects of material properties on thespecific limit states, the time dependent variations of material properties, etc.
(3) Load factors, f, shall be determined considering the unfavorable deviations ofloads from the characteristic values, the uncertainties in evaluation of loads, the change
in loads during the service life, the effect of loads on the limit states, etc.
(4) Structural analysis factors, a, shall be determined considering the uncertainties ofcomputational accuracy in determination of response values through structural analysis,
etc. The value of structural factor, a, may be taken as 1.0.
(5) Member factors, b, shall be determined considering the uncertainties incomputation of limit values of performance of members, the effect of dimensional errorsof members, the importance of members among the entire structure when it reaches acertain limit state, etc. The value of member factor, b, is determined corresponding toeach equation for limit value of performance.
(6) Structure factors, i, shall be determined considering the importance of thestructure, as determined by the social impact when the structure would reach the limit
state. The value of structure factor, i, may be in between 1.0 and 1.2.
(7) If a nonlinear analysis method is used for performance verification, safety factors
shall be determined appropriately according to the verification indices used in theanalysis in view of the meaning of the safety factors.
(8) Safety factors used for verification of earthquake resistance described in Chapter
11 shall be determined appropriately according to the verification method in view of themeaning of the safety factors.

28

Chapter 4 Rules for Performance Verification[Commentary] (1) Verification of safety based on the limit state of cross-sectional failure
employs five safety factors - two of them, f and a, are related to calculation of response values,
another two, m and b, are associated with calculation of limit values of performance, and the other,i, is used when comparing the response value with the limit value of performance. The concept ofthese safety factors can be applied to other limit states. Fig. C4.5.1 shows a process for performanceverification using the safety factors described in this Specification.
Construction

Construction
Performance oforiginal concrete(standard cured
specimen)

Design value of
performance ofconcrete instructure

Design value of
performance ofstructure

Verification Design value of
response ofstructure due toloads andactions

Determination of
conditions:Type andmagnitude ofloads and actions

Manufacture
Performance verification (Linear analysis)
Characteristic
values of materials
Design strength of
concreteExtracoefficient

DesignstrengthmbMaterialfactorDesign limit Verification
Design response
values ofof structural
structuralmembermemberiMemberfactor

Structure factor

aDesignvalues ofloads

Structural
analysis factor

fCharacteristic
values ofloads

Load factor

Required average
strength(expected value)

Characteristic
values of materials
Design strength of
concrete

Calculated
values of
response

Designstrengthm

MaterialfactoraVerification

Performance verification(Nonlinear analysis)bDesignvalues ofloads
Structural
analysis factor

fCharacteristic
values ofloads

Load factor

Design valuesof response

Design limit
valuesMemberfactorDurability verification

Chloride ion penetration
Carbonation depth, etc.

MaterialfactorCharacteristic valuesof materials

cCarbonation velocity
coefficient: kChloride ion
diffusion coefficient:
Dk ....

Verification

Designcarbonation
velocitycoefficient: dDesign chloride
ion diffusion
coefficient:
bb
Dk ....
bl

Design value ofcarbonation
depth: yd
Design value ofchloride ion
concentration:
Ck

Verification

i
Structure
factorLimit depth forsteel corrosion: ylim
Limit concentration
for steel corrosion:
Clim

Environmental
conditions

Determination of limit
valuesSafety factors considering accuracies
of design equations for durability
performance of a structure

pSafety factors considering accuracies ofprediction equation for material
characteristics
Prediction values of material
characteristics:
Prediction equation, material test,
accelerated test

Expected values such as properties of adiabatic
temperature rise, shrinkage properties andstrength appearance properties
Temperature analysis

Verification
Characteristic with crack
Stressindex
values ofgenerated bytensilevolume change
strengthof concretecrEnvironmental
conditions:
External constraint
Temperature, moisture

Verification for initial cracks

Fig. C4.5.1

Safety factors used for performance verification
29

Standard Specifications for Concrete Structures-2007, Design(3) The value of load factor, f, may depend upon the type of load, the limit state concerned andthe effect of the load on calculated response values in the target cross-section. It should be notedthat the maximum load does not always create the critical condition, but in some structures, theminimum applied load may become dominant in design.
(4) The function to calculate the response values should earn the mean value of it in principle
according to Section 4.4. The deviation of the response values calculated by the function should betaken into account by the structural analysis factor, a.
(5) The importance of the member should be judged from its role in the entire structure, in sucha manner as primary members are more important than secondary ones. The member factor, b, may
be used to control the safety levels against flexural and shear failure modes separately, and to
specify the member to be failed in a structure. The function to calculate the limit values of
performance should earn the mean value of it in principle according to Section 4.4. The deviation of
the limit values calculated by the function should be taken into account by the member factor, b.
(6) The structure factor, i, which is associated with the importance of the structure, should
account for the social impact of violation of the limit state. This impact could be in view of disastermitigation and the cost of reconstruction or repair.
Table C4.5.1 shows the contents considered by each safety factor for verification of safety
against cross-sectional failure.
Table C4.5.1

Details covered by safety factors

Contents being considered
Limit values of performance
1. Variation of material strength(1) Where can be evaluated by records of material tests(2) Where can not be evaluated by records of material tests(Consider such conditions as lack or inadequacy of therecords, degree of quality control, differences inmaterial strength between test specimen and actual
structure, time-dependent variation, etc.)
2. Degree of influence on limit state
3. Uncertainty in calculation, dimensional errors,
importance of member, and failure mode
Response values
1. Variation of load(1) Where can be evaluated by statistical records of loads(2) Where can not be evaluated by statistical records of loads(Consider such conditions as lack or inadequacy of therecords, variation of load during service life, uncertainty
in evaluation of load, etc.)
2. Degree of influence on limit state
3. Uncertainty in structural analysis
Importance of structure, influence on society when the structure
reaches a limit state

30

Value / Safety factor
Characteristic value, fk
Material factor, γmMember factor, γbCharacteristic value, Fk
Load factor, γf
Structural analysis factor, γaStructure factor, γiChapter 4 Rules for Performance Verification

Table C4.5.2
Safety factor

Standard values of safety factors

Material factor, γmMemberfactor, γm

Structural
analysisfactor, γm

Loadfactor, γm

Structure
factor, γm

1.0 or1.05

1.1 - 1.3

1.0

1.0 - 1.2

1.0 - 1.2

1.0

1.0

-

1.0 - 1.2

1.0 - 1.2

1.3

1.0 or1.05

1.0，1.1 1.3

-

-

1.3

1.05

1.0 - 1.1

1.0

1.0

1.0 - 1.1

1.0

1.0

1.0

1.0

1.0

1.0

Required
performance(Limit state)
Safety (Cross-sectional
failure)*1
SafetyResponse(Cross-sectionalvalue
failure,collapse)*2
Limit
Earthquake
value
resistance (II,III)*2

forconcreteγmfor steelγm

1.3

Safety (Fatigue)*1
Serviceability*1
Earthquake resistance (I)*1
Remark)1.0 - 1.2

*1: Calculated by linear analysis *2: Calculated by non-linear analysis

The value of safety factors should be given for each limit state, and they are not necessarily thesame for different limit states. Although each safety factor covers the uncertainty of individual
event separately, the influence of each safety factor may be considered collectively.
The standard values of safety factors that may be used when performance verification is madeaccording to this Specification together with inspection system in accordance with Construction
Part of this Specification are shown in Table C4.5.2.
(7) Fig. C4.5.2 shows typical safety factors for verification against limit state of cross-sectional
failure when linear analysis is used. When nonlinear analysis is used to determine the limit state ofcross-sectional failure of a structure, indices other than sectional forces may be used for
performance verification. Examples are an average in-plane strain in a shell structure in shear andan average curvature of a member in bending. Here, S is a function of both the design values ofmaterial property and the design values of loads. In this case, it is recommended that the safety
factors be set for the indices and limit values related to failure as shown in Fig. C4.5.3. To
determine design response values, uncertain factors considered by both the structural analysis factor
and the member factor in Table C4.5.1 are taken into consideration. Examples are accuracy andreliability of analysis including setting of boundary conditions, and variability and dimensional
errors of members and structures. When determining limit values, Rd, it is good practice todetermine it conservatively, taking into consideration the uncertain factors considered by themember factor indicated in Table C4.5.1.

31

Standard Specifications for Concrete Structures-2007, Design

Limit value

Response value

Characteristic valuesof material strength

Characteristic valuesof loads

fk ( = m fn )m

Fk ( = f Fn )

fDesign strength ofmaterial

fd = fk / m

Design values of loads

Fd = f Fk

Limit values ofstructural capacity

R (fd)

Response of structuralmemberS (Fd)

b

aDesign limit values ofstructural capacity

Safety factors in the case where linear analysis is used

Characteristic values of materials(strength, ductility, stiffness, etc)

Characteristic valuesof loads

fk

m

Fk

f

Design strength of material

Design values of loads

fd

Response of structure, structural members, materials

b

Fd

S (fd, Fd)aDesign limit values ofstructural capacity

Design response ofstructural member

Rd

Verification

Fig. C4.5.3

Sd = a S(Fd)i Sd / Rd ≦ 1.0

Verification

Fig. C4.5.2

Design response ofstructural member

Rd = R(fd) / b

Sd

i Sd / Rd ≦ 1.0

Safety factors in the case where nonlinear analysis is used

(8) Safety factors used for verification of earthquake resistance are to be determined inaccordance with Chapter 11.

32

Chapter 4 Rules for Performance Verification

4.6

Modification Factors(1) The Specification defines two modification factors namely material modification
factor, m, and load modification factor, f.
(2) Material modification factor, m, shall be determined considering the difference inmaterial strength between characteristic value and specified value.
(3) Load modification factor, f, shall be determined for each limit state considering thedifference in load between characteristic value and specified or nominal value.

[Commentary] When specified or nominal values are defined on material strength and load
instead of characteristic values, the specified or nominal values can be converted into thosecharacteristic values by the modification factors. The value of load modification factor, f, can begiven depending on each limit state. The modification factors are specified as a tentative measure
until specified or nominal values are to be indicated according to the definition of characteristic
values in the Specification.

4.7

Documentation of Design Calculations(1) The design calculations clearly showing required performance and associated limit
states of members or structures for verifying durability, safety, serviceability, earthquake
resistance, etc. shall be preserved with calculation processes of their examination.
(2) The calculated results shall be precise in two significant digits at final stages inprinciple.

[Commentary] (2) The calculated results at final stages above refer to the value obtained fromEq.(4.3.1). In order to report these results with two significant digits, computations for response
values, limit values, stress and strength are generally required to be carried out with threesignificant digits.

4.8

Design Drawing(1) Design drawings shall indicate not only structural and reinforcement steel details
but also basic information on design calculation, construction and maintenanceconditions, etc., listed below. The information in Items 16 to 20 should be indicated forreference purposes.
1) Design life and environmental conditions
2) Characteristic values of loads and combinations of design loads
3) Safety factors
4) Required performance and verification results- Design response values- Design limit values

33

Standard Specifications for Concrete Structures-2007, Design

5) Characteristic values of materials used (concrete, steel)6) Type and quality of steel7) Concrete cover over steel in all members and construction accuracy8) Type of reinforcing bar joints and joint locations or regions in which joints may beprovided
9) Tensioning force at tension end, elongation and tensioning procedure10) Information necessary for construction and maintenance11) Name of structure and place of use
12) Signature of responsible engineer
13) Date of design14) Scales, dimensions and units of measurement15) Name of applied standard16) Type of cement17) Maximum size of coarse aggregate18) Cement content
19) Slump or slump flow of concrete20) Water/cementitious material ratio21) Air content(2) Design drawings shall be stored along with construction records throughout theperiod in which the structure remains functional and in service.

[Commentary] Design drawings may be considered to be the only means through which thedesigner communicates his idea(s) to the agency responsible for construction and maintenance ofthe structure. This Specification requires as a general rule that mixture proportion of concrete shallbe determined so that the requirements of characteristic values of material properties of concrete
indicated in the design drawings are met during construction. To this end, the design drawings must
indicate all characteristic values of concrete determined at the design stage, and these drawings
must be turned over to the construction agency. The characteristic values of concrete mentioned in
Item (1) 5) include material strength, shrinkage strain measured by the JIS test method, shrinkage ofmembers, creep, carbonation rate coefficient, chloride diffusion coefficient and relative dynamic
modulus of elasticity. In view of the cases, however, where field-proven mix proportion of concreteand simplicity of mix design during construction, it is also required that other information including
type of cement, maximum size of coarse aggregate, cement content, slump or slump flow andwater/cementitious material ratio be also indicated in the design drawings for reference purposes. It
is also important to clearly indicate the requirements and other information that may be usefulduring construction such as the timing of formwork and supporting removal, the compressive
strength of post-tensioned prestressed concrete at which prestress may be given, and the thermal
cracking index.
34

Chapter 4 Rules for Performance Verification

For durability enhancement of concrete structures, factors such as the cover to reinforcement
and the quality of concrete cover, cracks assumed at the design stage, are of importance. Details
pertaining to these are also needed for inspection at the end of construction when the structure ishanded over to the management agency for actual operation and also during in-service maintenance.
In order to convey the relevant considerations in detail made at the design stage to the responsible
agency for construction and maintenance of the structure, it is necessary to describe clearly indesign drawings the information on concrete cover over steel, construction accuracy of steel bars
arrangement, design crack widths in all parts. It is further desirable that comprehensive drawings forthe complicated parts be prepared showing the details for arrangement of reinforcement, sheaths,
anchor-bolts, and so on. Such information should be utilized when checking whether the concrete
placed in these parts can be adequately compacted. It is also requested that all other useful
information for construction and maintenance such as calculation details, member force diagrams,
agendas of meetings, data and relevant records selected from design documents to determine thestructural details, are also appropriately preserved as well as the design drawings. It may be usefulto record the following items other than those indicated above, if necessary.
1) List of materials used2) Detail diagrams of concrete cover part3) Detail diagrams where steel bars, sheaths and anchor bolts are complicatedly arranged
4) Order of concrete placement
5) Position of construction joints6) Supporting7) Ground conditions and bearing capacity of supporting piles8) Geological profile and N-value

35

Standard Specifications for Concrete Structures-2007, Design

CHAPTER 5 DESIGN VALUES FOR MATERIALS

5.1

General(1) Quality of concrete or steel is represented by not only compressive or tensile
strength but also other material properties such as other strengths, modulus of elasticity
or deformation characteristics, thermal characteristics, durability and water tightness.
The effect of loading rate on strength and deformation characteristics should beconsidered if necessary.
(2) The characteristic value for material strength f k shall be determined, taking into
account the variation in tested values, such that most of the tested values exceed thischaracteristic value.
(3) The design strength of material f d shall be obtained by dividing the characteristic
value for material strength f k by a material factor  m .
(4) When a specified value for material strength f n is determined independently fromits characteristic value, the value of f k shall be obtained by multiplying the specified
value by a material modification factor  m .

[Commentary] (1) Various types of concrete are used in concrete structures ranging incompressive strength from 18 to 100 N/mm2 even for concrete using ordinary Portland cement.
Concrete could be classified according to its properties – for example, air-entrained concrete,
super-plasticized concrete, self-compacting concrete, expansive concrete, high strength concrete,
ultra high-early-strength concrete, ultra-rapid-hardening concrete, anti-washout concrete and steel
fiber reinforced concrete. When considering the methods of construction, there are varieties ofconcrete such as that cast in bentonite, tremie concrete, prepacked concrete, shotcrete and precast
concrete, in addition to the concrete cast in the conventional manner.
Appropriate type and quality of the concrete are necessary to be applied for concrete used instructures or members, in consideration of its purpose for use, environmental condition, design life,
construction condition and so on.
Reinforcing bars, prestressing steel and rolled sections of structural steel used in composite
steel-concrete construction are the different steels used in concrete structures. Besides these, there
are other steels for the anchorage or connection. Most of these steels are standardized by JIS(Japanese Industrial Standard).
In accordance with needs in structural performance verification, quality of concrete isrepresented by not only compressive strength but also quantities for various material properties.
Material properties can be classified into mechanical properties, such as strength and deformation
characteristics, physical properties, chemical properties and so on.
Strength characteristics are expressed by strengths under static and fatigue loadings incompression, tension, bond, etc. Deformation characteristics are expressed by time-independent
quantities such as modulus of elasticity and Poisson's ratio, and time-dependent quantities such as
creep coefficient and shrinkage strain. There are also mechanical properties expressed using a
relationship between two mechanical variables, such as a stress-strain relationship. Fractureenergy is used to express the crack resistance and toughness in some cases.

36

Chapter 5

Design Values for Materials

Physical properties include thermal characteristics such as coefficient of linear expansion andspecific heat, density, water tightness, air tightness and so on. Among these, the quantitative
treatment of density and thermal characteristics are generalized at present.
Resistance against acid corrosion, decomposition induced by sulfate and so on is considered as
chemical properties.
Durability of concrete is considered to be its resistance to time-dependent deterioration resulting
from various actions, such as weather, intrusion of chemicals and erosion by chemicals. For the
durability of reinforced concrete, resistance to corrosion of reinforcing steel over time is anadditional concern. In regard to steel corrosion, durability performance verification has been carriedout using the resistance to carbonation and chloride ion intrusion of concrete as indices.
Quality of concrete is influenced by not only conditions of material used and mix proportion,
but also construction and environmental conditions at the site. Since these conditions are various,
general values for material properties used in usual design, which are given here, are applicable toconcrete which is made mainly from Portland cement and natural aggregate or artificial lightweightaggregate, cast in atmosphere with normal temperature, and existing under normal environmental
conditions. These values are just standard values, some of which vary little under changes in
conditions but others vary greatly. Therefore, if a reliable value can be obtained under actual
conditions of material used, mix proportion, construction, environment, it is advisable to use it
instead of a value given here.
It is the same for steel as concrete, where the values for material properties other than tensile
strength are used in accordance with needs in structural performance verification.
Loads that act on civil structures are classified into static loads, dynamic loads, and impact loads.
The static load acts throughout the service life such as dead loads. The dynamic loads include
effects of traffic, waves, and earthquakes. The impact loads include explosions and collision of
flying object. The rate of action of these loads is normally expressed as a stress or strain rate.
Loading rates are known to be significantly affecting the failure mode of concrete structures. Also,
the widening variety of structures increases the necessity for investigation into measures againsthigh loading rates. The mechanical properties of materials that make up the concrete structures,i.e., concrete and steel, should therefore preferably be determined according to the stress and strain
rates.
The material property values given in this chapter may be used in the examination of limit states
under normal static and dynamic loads. Where special consideration for strain rate is required,such as in cases of impact loads, values obtained from highly reliable experiments shall be used.
Where the effects of strain rate on the yield stress, tensile strength, and strain at rupture of steel
need to be considered, these values must be determined through reliable experiments.
(2) The characteristic value for material strength f k may generally be obtained using
Eq.(C5.1.1)
f k  f m  k  f m 1  k 

(C5.1.1)

where, f m : mean value of tested values: standard deviation of tested values: coefficient of variation of tested valuesk: coefficient37

Standard Specifications for Concrete Structures-2007, Design

Coefficient k is determined by probability to have tested values less than a characteristic value
and distribution shape of tested values. When the probability of the tested values is less than 5 %and the normal distribution is assumed, the coefficient k becomes 1.64 (See Fig.C5.1.1).
Frequency
Distribution oftested values

頻度

試験値の分布kσ
fk

Fig. C5.1.1

5.2

f

fm

Characteristic values for materials strength

Concrete

5.2.1

Strength(1) Characteristic values for concrete strengths shall, in general, be based on 28-day
tests. They may be based on tests of other appropriate ages depending upon factors
such as, the proposed function of the structure, time of main loading and construction
schedule.
Tests for compressive strength of concrete shall be carried out in accordance with JIS
A1108 ''Method of Test for Compressive Strength of Concrete".
Tests for tensile strength of concrete shall be carried out in accordance with JIS A1113"Method of Test for Splitting Tensile Strength of Concrete"(2) When ready-mixed concrete in accordance with JIS A5308 is used, the nominal
strength specified by the purchaser may be used as the characteristic compressive
strength of concrete f ck .
(3) Characteristic values for bond and bearing strengths of concrete shall be
determined from strengths obtained using appropriate tests.
(4) Characteristic values for tensile, bond and bearing strengths of concrete may beobtained using Eq.(5.2.1) to Eq.(5.2.3) indicated below, based on the characteristic
compressive strength f ck (basic strength for design).
In the case of lightweight aggregate concrete, where all the aggregate is lightweight, if
actual strength data is not available, the design strengths may be taken to be 70% of thedesign strengths for normal concrete. The unit of strength is N/mm2.
Tensile strength f tk  0.23 f ck

23(5.2.l )Bond strength (For deformed bars satisfying the requirements given in JIS G3112),

f bok  0.28 f ck

23(5.2.2 )where f bok  4.2 N/mm2

38

Chapter 5

Design Values for Materials

For plain bars, the design bond strength shall be 40% of that of deformed bars,
provided that semicircular hooks shall be provided at the ends of plain bars.
Bearing strengthf ak    f ck

where， AAa(5.2.3)

A Aa  2: concrete area for distributing bearing stress: bearing area

(5) Flexural cracking strength may be obtained using Eq.(5.2.4)

f bck  k 0b k1b f tk

(5.2.4)

where， k0b  1 

10.85  4.5h lch 

0.55
k1b  4h(5.2.5)(  0.4)(5.2.6)k 0b: coefficient representing the relation between tensile strength andflexural cracking strength on account of tension softening
characteristics of concrete

k1b: coefficient representing reduction in strength on account of otherreasons such as drying and heat of hydrationh: height of member (m)lch: characteristic length (m)(>0.2)= GF Ec f tk2 , where, Ec :Young’s modulus, GF : Fracture energy, ft k :tensile
strength
Fracture energy and Young’s modulus may be obtained as outlined in
Sections 5.2.4 and 5.2.5(6) The material factor of concrete,  c , may be taken as 1.3 ( f ck  80 N/mm2) and 1.0,
when carrying out the examination for the ultimate limit state and the serviceability limit
state, respectively.

[Commentary] (1) When concrete is cured properly, its compressive strength increases with age,
and in normal structures it can be expected that the strength will become greater than the 28-daycompressive strength of cylinders with standard curing. Considering this, the characteristic
strength of concrete for normal structures may be determined using results of 28-day strength ofstandard cylinders.
However, there are the cases in which it is not appropriate for practical application to determine
the characteristic strength of concrete from strength at early age. For example, many of massive
concrete structure, such as underground LNG storage tanks and foundation mats, are firstly
experienced with design load after a very long period has passed after placing concrete, and cementwith low heat of hydration and fly ash are used for massive concrete structures. For these cases,characteristic values may be based on strengths determined at 91 days.
In the case of concrete used in products made in factories, initial strength development is rapid
though the rate of increase of strength after 14 days is likely to be less than that for normal
39

Standard Specifications for Concrete Structures-2007, Design

structures because of use of high-early-strength Portland cement and low water-cement ratio in
concrete and use of accelerated curing such as steam and autoclave curing, etc. In some cases
factory product is subject to earlier service after the required strength has been obtained. Thus it isdesirable that the characteristic strengths for concrete used in products made in factories is based onstrengths determined at 14days or less.
The age at which concrete can be prestressed in prestressed concrete structures depends on thetype of structure and the purpose of construction. A characteristic compressive strength atprestressing may be determined from the strength tested at age when the required strength can beobtained.
As mentioned above, for some types and purposes of structures, it is not reasonable that thecharacteristic value is based on 28-day tests. In such cases, the characteristic value may be basedon tests carried out at any other appropriate age rather than 28days.
Concrete strength depends on factors such as, age at test, curing condition before test, shape andsize of specimen, loading rate, and loading conditions: eccentricity, inclination and roughness ofloading surfaces, etc. In the Specification, the strengths shall be determined by the tests specified
by the Japanese Industrial Standard. Shape and dimension of specimens shall be in accordancewith JIS A 1132 “Method of Making and Curing Concrete Specimens”.
(4) Equation (5.2.1) was obtained for normal concrete having a strength ( f ck ) between 20 and
50 N/mm2, but Eq.(5.2.1) has also been found to be applicable for concretes with f ck less than orequal to 80 N/mm2. Since mechanical behavior of resin concrete, fiber reinforced concrete, ultrahigh strength concrete having strength greater than 100 N/mm2 is different from that of normal
concrete, appropriate characteristic values should be determined through experiments.
Though it has been reported that the bond and bearing strengths of high strength concrete
increase as the compressive strength increases, the data is insufficient and the required characteristic
values for high strength concrete should be determined through appropriate experiments.
Equation (5.2.3) is given for design bearing strength in the case where concrete area for
distributing bearing stress A is greater than bearing area Aa , referring to previous experiments or
requirements reported elsewhere. In Eq.(5.2.3), A is the area whose centroid coincides with that of
Aa and is the center of symmetry of A (See Fig.C5.2.1). When there are many of Aa , each A
shall not be overlapped with each other. Equation (5.2.3) is applicable to concretes having astrength ( f ck ) between 20 and 50 N/mm2. Bearing strength for the same ratio A Aa becomes
smaller as concrete strength becomes higher than that range.
In cases when the area immediately under the bearing surface is reinforced using wire mesh,steel pipe, prestressing steel, etc. the value of  may be increased if the safety is confirmed using
experiments, past experience, etc.
Aa=b1・b2

A=π(r+r1)２
Aa=πr２c1

b1 c 1A=(b1+2c1)・(b2+2c2)

r1

2r
c2

b2

c2

Fig. C5.2.1 Definition of bearing area
40

Chapter 5

Design Values for Materials

Properties of lightweight aggregate concrete depend on the proportion of lightweight aggregate
content in the total, i.e., fine and coarse, aggregates. Now, the specifications given here areapplicable for the case when all the fine and coarse aggregates are lightweight. For this case, forthe same compressive strength the tensile, bond and bearing strengths of lightweight aggregate
concrete are known to be smaller than those of normal concrete. Thus, the strengths of lightweightaggregate concrete may be taken to be 70% of the values for normal concrete.
(5) An accurate estimate of flexural cracking strength is difficult at present, as it depends on thequality of concrete, environmental conditions, and size of member. For this reason, an equation
based on test data (see Fig. C5.2.2) according to which the flexural cracking strength is inversely
proportional to the cube-root of the height of the member ( f bck  0.6 3 h  f tk ) has been used so far.
On the other hand, analysis incorporating tension softening of concrete has revealed that theflexural strength decreases as the specimen size increases, converging at the tensile strength.
Further, it has been qualitatively shown that the apparent flexural cracking strength can be evenlower than the tensile strength if the concrete is dry. However, it is difficult at present toaccurately predict residual stresses induced by drying and heat of hydration in structures.
Accordingly, flexural cracking strength has been calculated taking into account the size effect, as it
can be incorporated analytically by considering the softening properties. The effect of drying andheat of hydration have been treated separately by quantifying them on the basis of past test data.
These can be incorporated into the equation in future, when tools for quantitative evaluation of thedrying and heat of hydration become available.
5

2

GF=100N/m, Ec=30kN/mm , ftk=3N/mm

2fbck (N/mm2)

42

k0bk1bftk

1

0.6h-1/3ftk

0

Fig. C5.2.2

k0bftk

3

0.5

1.0

1.5 2.0
h (m)

2.5

3.0

Size effect of flexural cracking strength(6) When the response of high-strength concrete (f'ck ≥ 60 N/mm2) such as the limit state ofcross-sectional failure in a wide range including the nonlinear range needs to be considered,conventional practice is to use a greater value of the material factor γc than the value used fornormal-strength concrete. However, when the concrete construction is carried out in accordancewith the provisions of the Standard Specifications for Concrete Structures “Materials andConstruction”, the same value for the material factor,  c , may be used for all concretes in the rangeof f ck  80 N/mm2.

41

Standard Specifications for Concrete Structures-2007, Design

5.2.2

Design fatigue strength(1) The characteristic value for fatigue strength of concrete shall be determined fromfatigue strength obtained by experiments carried out considering the type of concrete,
exposure condition of the structure, and others.
(2) Material factor of concrete,  c , used in the examination of the limit state of fatigue
shall be 1.3.
(3) Design fatigue strengths f rd for concrete in compression, flexural compression,
tension and flexural tension, as a function of fatigue life N and stresses due topermanent loads  p , may be obtained using Eq.(5.2.7).

 log N 
f rd  k1 f f d 1   p / f d 1 
K 

(5.2.7)

where， N  2  10 6

f d : design strength of concrete, where material factor of concrete,  c , is 1.3.
The upper limit of f d shall be the design strength for f ck =50 N/mm2(i) K shall be taken as 10 for normal concrete continuously or often saturated withwater and lightweight aggregate concrete, and shall be taken as 17 for other generalcases.
(ii) In general, k1 f may be determined as follows:
For compression and flexural compression, k1 f =0.85
For tension and flexural tension, k1 f =l.0(iii) Although p is the stress due to permanent loads, it shall be taken as zero in thecase of reversed cyclic loading.

[Commentary] (2) The value of  c may be decreased if fatigue failure will not cause theultimate state of the structure.

(3) On the basis of previously obtained experimental data on compressive fatigue strength ofnormal concrete, an approximate relationship can be expressed by Eq.(C5.2.1), which consists of
the ratio of minimum stress to static strength ( S min ), the ratio of maximum stress to static strength( S max ), ratio of stress range to static strength S r ( S r  S max  S min ) , and the fatigue life N , for N
not greater than 2×106.
log N  17

1  S maxSr  171 S
1  S min
1

min 


(C5.2.1)

If the characteristic value f ck is used instead of f d , a modified form of the Eq.(5.2.7) can beobtained. The modified equation gives a conservative estimate for most of the experimental results
where k1 f is unity and K is 17. However, k1 f in Eq.(5.2.7) is determined conservatively to be
0.85 considering reduction in strength due to permanent loads, etc. Due to insufficient data forf ck above 50 N/mm2, Eq. (5.2.7) should be used only when f ck is 50 N/mm2 or less. However for
42

Chapter 5

Design Values for Materials

f ck above 50 N/mm , the design fatigue strength at 50 N/mm2 may be used.
2

Fatigue strength of concrete in flexural tension or tension has been reported to have a greater
scatter compared with that in compression. However, a modified equation of Eq.(5.2.7) with acharacteristic value instead of design static strength f d can predict conservatively most of the data
similarly to the case of compression.
It has been established that the compressive fatigue strength of concrete, immersed in water orotherwise continuously wet, is approximately two thirds of that of concrete dried in air. Thus, thedesign fatigue strength should be specified depending on exposure conditions. It is reported that thecompressive fatigue strength of lightweight aggregate concrete does not differ from that of normal
concrete. On the other hand, according to another report, the former is about 10~25 % less thanthe latter. The lightweight aggregate concrete may be considered to include more water due to thegreat absorption by the lightweight aggregate. In the Specification, the compressive fatigue
strength of lightweight aggregate concrete has been assumed to be equal to that of continuously wet
normal concrete.
The design fatigue strength of other special concretes shall be determined experimentally toensure that the safety level is similar to that of normal concrete.
In spite of no report on fatigue strength in the case of reversed cyclic loading, compressive andtensile fatigue strengths are determined as stress range repeated in only compression and tensionside, respectively.
In the case where the required fatigue life, N , exceeds 2106 cycles, the design fatigue strength
should be determined experimentally, because sufficient data is not available. However, Eq.
(3.2.7) may still be used in the examination of the fatigue limit state, as the equation is considered
to provide a conservative estimate for N exceeding 2106.

5.2.3

Stress-strain curve(1) An appropriate curve shall be assumed to express the stress-strain behavior of
concrete depending upon the purpose of examination.
(2) An idealized stress-strain curve given in Fig.3.2.1 may generally be used for
examination of the ultimate limit state of failure of members subjected to flexural moment
or to flexure and axial forces. The stress-strain curve in Fig.3.2.1 may also be used forlightweight aggregate concrete, for the examination mentioned above.

k1  1  0.003 f ck

k1 f cd

 
 cu

c


155  f ck
30000

 0.85  0.0035
0.0025   cu

The unit of f’ck is N/mm2.
Equation for the curved line is:

0

0.002
c

Fig.5.2.1

 c'  k1 f cd' 

cu

 c'


' 
  2  c 
0.002 0.002 Stress-strain curve of concrete

43

Standard Specifications for Concrete Structures-2007, Design(3) The stress-strain curve for concrete may be assumed to be linear for examination of
the serviceability limit states. In this case, the Young’s modulus shall be determined inaccordance with Section 3.2.5.
(4) Since the stress-strain curve under biaxial or tri-axial stress differs greatly from thatin Fig.3.2.1, the effect of such stresses shall be taken into consideration for examinationof ultimate limit state. For examination of serviceability limit states, the concrete may be
assumed as elastic. Values of the modulus of elasticity and Poisson's ratio may be takenfrom those given in Sections 5.2.5 and 5.2.6.
(5) Stress strain envelop curve in compression shall include the softening branch after
peak stress. Stress hysteresis shall consider both residual plastic strain and stiffness
degradation on loading and reloading path.
(6) In the analysis of linear members in (5), stress-strain relationship in tension may beneglected. In cases when the compressive strength is less than 50N/mm2, thestress-strain relationship given in Fig 5.2.2 may generally be used.

Fig.5.2.2 Simplified hysteresis model of concrete c'  E 0 K  c'   'p   0

E0 

2 f

(4.1.1)'cd

 'peak' 
 '   K  exp   0 .73 'max  1  exp   1 .25 'max   
 peak  peak   


'
'
 2 .86   'peak {1  exp(  0 .35 'max )} 'p   max(4.1.2)

 peak

(4.1.3)Whereε'peak : strain corresponding to compressive strength( in general, a value of 0.002 may
be used)ε'max : maximum value of experienced compressive strain
ε'p : plastic strain

44

Chapter 5

Design Values for Materials

K : residual rate of elastic stiffness(7) When multi-directional cracks are considered for planar member in (5), it may be
assumed that only the crack which is almost perpendicular to the direction of principle
tensile stress contribute to deformation. Stress strain relationship in Fig 5.2.2 may be
used assuming that the compressive zone is parallel to the direction of crack. In thetensile zone perpendicular to direction of crack, tension stiffening effect due to bond on
average stress strain relationship shall be considered after cracking. If concrete fails incompression prior to the yielding of re-bar, such as the case of large reinforcement ratio,degradation of compressive strength and stiffness due to the deformation in the direction
perpendicular to the direction of crack propagation shall be accounted for.
(8) When the reinforcement ratio in orthogonal directions is same for planar member in(5), shear stress transfer on crack surface may be neglected. Relationship between shear
stress and shear strain on crack surface shall be considered, when reinforcement ratios inorthogonal directions differ by more than 2 times, or the loading direction change greatly
during an earthquake.

[Commentary] (1), (2), (3) and (4) Even for ordinary concrete, the stress-strain curve varies
greatly depending upon the type and age of concrete, applied stress condition, loading rate andhistory, etc. There are, however, cases such as the ultimate strength of a linear member, which are
not much affected by the shape of the stress-strain curve. In such cases, an appropriate
stress-strain relationship such as that given in Fig 5.2.1, or a rectangle which has been usedconventionally, may be assumed. However, considering the fact that the difference between thecylinder strength and the strength obtained from estimates based on the load-carrying capacity ofmembers increases as the strength increases, k1 has been taken to depend on f ck as shown in Fig.
C5.2.3. Also, considering the tendency of brittle failure in high strength concrete, the ultimate
strain has also been reduced. It should be noted that Fig. 5.2.1 should be used as a model only forcalculating the ultimate load-carrying capacity under bending and axial forces. Since thestress-strain relationship has a significant effect on the deformation, the full stress-strain curve
including the descending portion showed in Fig. 5.2.2 should be used when making a detailed
assessment of the deformation at the ultimate state. In such cases, compressive strain of concrete
is not uniformly distributed in the specimen but localized in the descending zone. It is therefore
advisable to indicate the element size, length of specimen, and the size of strain localization, which
determine the stress-strain curve.
1.0

0.00400.9

0.0035

k1 0.8ε'cu 0.0030

0.7
0.00250.6
0.5

0.0020

30

40

50
60
f'ck(N/mm2)70

Fig. C5.2.3

80

30

40

50
60
f'ck(N/mm2)

Relations between k1 ,  'cu and f ck'

45

70

80

Standard Specifications for Concrete Structures-2007, Design

Though the present specification allows the use of the stress-strain curve in Fig.3.2.1 forlightweight aggregate concrete, the actual curve is slightly different from that of normal concrete,
and therefore, an appropriate curve should be used in the examination for deformation and ductility
in the case of lightweight aggregate concrete. In general, lightweight aggregate concrete ischaracterized by features such as, almost a linear stress-strain curve up to high levels of stress, asmall initial tangential modulus of stiffness, a difference in secant modulus at one third point ofcompressive strength compared to normal concrete, and a sudden reduction in stress after peakstress.
The stress-strain curves given here are some commonly used examples. Concrete surrounded byhoops and spiral reinforcement is especially known to exhibit greater compressive strength andultimate strain due to the confining effect of such reinforcement. When actual values of theseparameters are available from appropriate experiments, etc. they may also be used.
(5)(6) Uni-axial material model of concrete can be distinguished with three parts: compression,
tension and recontact after cracking. It is ideal that hysteresis energy absorption can be evaluated in
response analysis considering the hysteretic behavior in all models.
In general, the effect of hysteresis loop of concrete in compression on response behavior issmall for linear members in contrast with planar members. Therefore, the hysteretic damping at
unloading and reloading in compression may be neglected. This assumption gives safety side
evaluation because the response deformation is overestimated. Moreover, even if the tensile stress isneglected, the effect to the response of structures is small although concrete carries the tensile stressafter cracking due to the bond with re-bar, because nonlinear region is only limited in a certain
portion of linear member.
When no special examination is conducted, a simplified material model described in Eqs.
(5.2.8)-(5.2.11) and in Fig. 5.2.2 may be applied in all cross section of linear member in whichstress level under the constant axial force is less than about 10 % of uni-axial compressive strengthof concrete. Applicability of the relation has been confirmed for the concrete with compressive
strength less than about 50 N/mm2.
For cracked concrete, the compressive stress is transmitted on closing of cracks under repeatedcyclic loading. In real structures, crack contact gradually begins before the cracks are completely
closed and stiffness gradually increases. On the other hand, a rapid change of stiffness is assumed ina simplified Eq. (5.2.8) and high frequency component of acceleration often generate to the axial
direction of the member in dynamic response analysis. A simplified model can, however, be used,which does not consider the complex nonlinearity at recontact of crack, since the influence to the
response values in the seismic performance verifications are negligibly small.
Strength to axial direction and deformation capacity of concrete increase due to confinement
stress in the parallel and perpendicular direction of member axis from the re-bar arranged laterally
and/or placed at outer portion in cross section. Therefore, it is desirable to apply the different stressstrain relationship at each part in cross section considering the difference of confinement effectaccording to lateral re-bar arrangement and so on. Eqs. (5.2.8)-(5.2.11), however, show the stressstrain relationship neglecting confinement effect, because it gives safety side evaluation for thegeneral columns subjected to small axial force. Though uni-axial stress strain relationship changes
with the increase in confinement stress of lateral re-bar, it has been confirmed that the residual rateof the elastic stiffness becomes large by higher confinement stress and the relationship between
maximum value of experienced compressive strain and plastic strain are not influence. If theresidual rate of elastic stiffness is appropriately defined according to the confinement stress, it ispossible to represent the change of maximum stress, corresponding strain increment and thehysteresis under unloading and reloading.
46

Chapter 5

Design Values for Materials

When the response values of Seismic Performance 2 and 3 are computed for the members
subjected to large axial force, it is recommended to consider the confinement effect because Eqs.
(5.2.8)-(5.2.11) underestimate the member performance and it sometimes results in uneconomical
design. Three dimensional analysis considering multi-axial stress field can give response value withhigher accuracy, if material model including confinement effect is used. It is possible to estimate theresponse values using a simplified stress strain relationship of confined concrete based on theexperimental results.
(7) For the planar members and shell structures, the strain hardly localizes in contrast withlinear members and cracks distribute over wide area. The effect that stress transfer due to bondrestraints deformation of re-bar affects to the structural response greatly. Therefore, in order toenhance the accuracy of estimated response values, accurate modeling of stress strain relationship in
tension is required.
Fig (C5.2.4) is an example of uni-axial averaged stress strain relationship applied to tension
field of reinforced concrete with sufficiently arranged re-bars. This example includes the bondeffect with re-bar and is considered that concrete between cracks transmit tensile stress even after
cracking. In this case, the effect of bond action should be simultaneously considered in the re-bar
model in tension to form a counterpart with concrete model in tension. The yield stress of averaged
stress strain relationship of re-bar in concrete is lower than that of bare bar due to the effect of bondaction. In addition, it is desirable to consider the gradual increment of stiffness at recontact of
cracks and absorption of hysteresis energy.

Figure C5.2.4

An example of stress strain relationship in tension of concrete47

Standard Specifications for Concrete Structures-2007, Design

5.2.4

Tension softening properties(1) Fracture energy, G F , for normal concrete may be obtained using Eq.(5.2.12).

G F  10d max   f ck
13

where, d max

f ck

13

(N/m)

(5.2.12): maximum size of aggregate (mm): characteristic compressive strength (N/mm2)(2) An idealized curve given in Fig.5.2.3 may be used for the tension softening part.

Tensile stress (σ/ftk)

引張応力(σ/ ftk)

1.0
0.8
0.6
0.4
(0.75, 0.25)

0.2
0

1

2

3

4

ひび割れ幅（ω×fCrackwidth (ω·tkftk/ /GGF）
F)

Fig. 5.2.3

5Tension softening curve[Commentary] Verification for safety of reinforced concrete may generally be carried out by
assuming concrete to be a completely brittle material under tension. However, since performanceverification for members, where the occurrence and propagation of cracking governs, cannot be
carried out in a rational manner using conventional models, it may be necessary to take into
consideration a fracture process zone at the crack tip where micro cracks accumulate. In a fracture
process zone, which is located between the elastic zone having no cracks and the completely
cracked portion, the transferred tensile stress decreases as the ‘crack width’, i.e., the total width ofminute cracks in the zone, increases. This is the so-called tension softening. A tension softening
curve expresses the relationship between the transferred stress and the crack width, and the area
below the curve corresponds to the fracture energy, which is equal to the energy required to form aunit area of completely opened crack. It is reported that by incorporating the tension softening
properties in analysis, the fracture phenomenon in concrete associated with propagation of cracks
can be understood, and the size effect in the apparent strength of members can be rationallyexplained.
150
dmax
30mm
25mm
20mm
15mm

GF(N/m)

125
100
75
50
20

30

40
50
60
fck (N/mm2)

Fig. C5.2.5

70

Fracture energy
48

80

Chapter 5

Design Values for Materials

Equation (5.2.12) and Fig. 5.2.3 have been obtained on the basis of experimental data available
in literature. Figure C5.2.5 shows the fracture energy determined using Eq. (5.2.12).

5.2.5

Young’s modulus(1) The Young’s modulus of concrete shall be obtained in accordance with JIS A 1149
"Test method for static modulus of elasticity of concrete."(2) In general, the value of the Young’s modulus for concrete E c may be taken to beequal to that shown in Table 5.2.1.
Table 5.2.1

Young’s modulus of concrete2

18 24 30
f’ck（kN/mm ）Normal concrete
22 25 28
Ec （kN/mm2）
Lightweight aggregate
13 15 16
concrete** All aggregates are lightweight

40
31
19

50
33
-

60
35
-

70
37
-

80
38
-

[Commentary] (2) The values given in Table 5.2.l may be applied for computation of elastic
deformation and statically indeterminate force(s) at serviceability limit states. In the case of
repeated loading or when the applied stress level is low, the values in Table 5.2.l may be preferablyincreased by 10 %, as the Young’s modulus in such cases is closer to the initial modulus of elasticity.
Each value in Table 5.2.l is the average from a survey of test results from across the nation, andindividual values vary considerably depending upon the type and quality of aggregates, and theregion.

The relative effect of the Young’s modulus of concrete on the safety of the structure is small
compared to other characteristic values. However, in cases where the affect of the value of theYoung’s modulus on the design calculations is large, it is desirable that an investigation into thedesign conditions is undertaken and, if necessary, the measured value determined using the actual
materials shall be used.

3.2.6

Poisson's ratio

Poisson's ratio of concrete may, in general, be taken to be 0.2 within elastic range.
However, it shall be taken to be zero when cracking due to tension is allowed.

3.2.7

Thermal characteristics(l) The thermal characteristics of concrete shall be decided on the basis of experiments
or previous available data.
(2) In general, the coefficient of thermal expansion for concrete may be taken as 10×
10 /°C.
-6[Commentary] (1) In general, thermal characteristics of concrete are greatly influenced bycharacteristics of aggregate, which constitute most of the volume of the concrete. Even for
concrete with the same mix proportion, the thermal characteristics vary considerably, depending on
49

Standard Specifications for Concrete Structures-2007, Designlevel of saturation and temperature.
For normal concrete, the values for the thermal characteristics may be taken to be equal to thoseshown in Table C5.2.2.
Thermal characteristics of lightweight aggregate concrete vary considerably depending on theabove-mentioned factors. For reference, some values of heat conductivity, on the basis of previous
experiments are given in Table C5.2.3. It is reported that the specific heat of lightweight aggregate
is 1.6 ~1.8 kJ/kg°C, compared with 1.0~1.3 kJ/kg°C for normal concrete, and that the coefficient ofheat diffusion of lightweight aggregate concrete is 0.0014 to 0.0020 m2/h, compared with 0.0028 to
0.0040 m2/h for normal concrete.
Equation (C5.2.2) shows the relation between thermal characteristics – the coefficient of heat
conductivity,  c , coefficient of heat diffusion, hc2 , and specific heat, C c and the including
density  . When one of the four quantities is unknown, it may be estimated using the other three.
The quantities  c , hc2 and C c are also affected by the level of saturation of concrete, therefore,
saturation effect should be appropriately considered.

hc2   c Cc   (C5.2.2)

Table C5.2.1

Thermal characteristics of normal concrete

Thermalconductivity
Specific heat
Thermal diffusivity

Table C5.2.2

1.05 kJ/kg°C
0.003 m2/h

Thermal conductivity of lightweight aggregate concrete ( kJ/mh°C)

Unit weight（kg/m3）
1500
1600
1700
1800
1900

5.2.8

9.2 kJ/mh°C

dry condition

wet condition

2.1
2.3
2.5
2.9
3.3

4.6
4.8
5.0
5.9

Shrinkage(1) Shrinkage of concrete shall be determined, considering the humidity around thestructure, shape and dimension of members, mix proportion of concrete, etc.
(2) For computation of statically indeterminate forces using the elastic theory, theshrinkage strain of concrete may be taken to be equal to 15010-6. However, when thisvalue is used, effect of creep shall not be added.

[Commentary] (1) Shrinkage of concrete, which includes drying shrinkage, autogenous
shrinkage and carbonation shrinkage, is affected by properties of the aggregate and cement,
compaction of concrete and curing conditions, as well as temperature and humidity aroundstructures, shape and dimension of cross-sections of members and mix proportion of concrete.
The properties of aggregate may vary regionally, and shrinkage may reach as great as 1,000 × 10−6.
50Chapter 5

Design Values for Materials

As a general rule, therefore, the shrinkage strain of concrete used for verification purposes must be
determined on the basis of the values obtained from shrinkage strain tests of the concrete to be usedor past performance data. If no such data are available, the value of shrinkage strain to be used to
calculate the response of a structure may be determined by multiplying the value calculated from Eq.
(C5.2.4), Eq. (C5.2.9) or Eq. (C5.2.14) by 1.5. The reason is as follows. It has been reported that intested conducted in accordance with JIS A 1129 (10 × 10 × 40 cm specimens, seven days of water
curing followed by six months of dry curing), few concrete specimens showed a shrinkage greaterthan 1,000 × 10−6. To this shrinkage, the autogenous shrinkage occurring before the age of sevendays and an estimated shrinkage that is thought to occur after the first six months (200 × 10−6)
were added. Hence, as a final value, a shrinkage strain of about 1,200 × 10−6 is allowed for. Since
the maximum final value of shrinkage strain obtained from an equation like Eq. E5.2.4 is about 800
× 10−6, the value is increased by multiplying by 1.5.
Environmental humidity and member size strongly affect the magnitude and rate of shrinkage
strain, which may normally be estimated using Eq. (C5.2.3) for normal concrete with a compressive
strength of up to 55 N/mm2 (up to 70 N/mm2 when W C is reduced to increase the strength). Here,Eq. (C5.2.3) is for the concrete using normal aggregates which don’t greatly increase the shrinkageof the concrete.







 cs' t , t0   1  exp  0.108t  t0 0.56   sh'(C 5.2.3)

where， sh  50  781  expRH 100  38 log e W  5log e V S 10 2

 sh'(C 5.2.4): final value of shrinkage strain ( 10-5)

 cs' t , t0  : shrinkage strain of concrete from age of t0 to t (  105 )RH : relative humidity (%) (45%≤ RH ≤80%)W: unit water content (kg/m3) (130 kg/m3≤ W ≤230 kg/m3)

V: volume (mm3)S: surface area in contact with outside air (mm2)V S: volume-surface ratio (mm) (100 mm≤ V S ≤300 mm)

t0 and t : temperature adjusted age (days) of concrete at the beginning of drying and duringdrying, values corrected by Eq.(C5.2.5) should be used.
n


4000
t0 and t   ti  exp 13.65 273  T ti  T 0 i 1
(C5.2.5)

ti : number of days when the temperature is T (°C)
T0

: 1°C

The range indicated above for the variables is the range over which the variables were varied in
the experiments used in deriving Eq.(C5.2.3). The equation (Eq.(C5.2.3)) for predicting shrinkage
is derived for concrete made using ordinary Portland cement. It is known that the shrinkage ofconcrete is not significantly affected by the cement type, while it varies depending on the
mix-proportion of the concrete. Equation (C5.2.3) has also been verified to be applicable toconcrete using high-early-strength cement.
Equation (C5.2.3) has been driven using experiments carried out at 20°C. When concrete isconstantly subjected to high or low temperatures, the shrinkage strain shall be determined based on
51

Standard Specifications for Concrete Structures-2007, Design

experimental results, because the shrinkage behavior may be different from that observed in thenormal range of temperature (0~40°C).
Equation (C5.2.3) may be used for the cases where drying begins between the age of 3 to 90
days. It is applicable to concretes having a W C between 40 to 65%, and having a compressive
strength of up to 55 N/mm2 (up to 70 N/mm2 when W C is reduced to increase the strength).
It has been pointed out that, in high strength concrete, autogenous shrinkage resulting fromhydration of cement may not be ignored. In the case of high strength concrete with a compressive
strength exceeding 55 N/mm2, i.e., the range where Eq. (C5.2.3) is not applicable, Eq. (C5.2.6) may
be used to determine the magnitude and rate of development of shrinkage strain, incorporating theeffects of the environmental humidity and member size. These parameters considerably affect thestrain and strain rate. Though Eq. (C5.2.6) has been derived using data up to 120 N/mm2, it may
be used for concrete having a compressive strength up to 80 N/mm2, which is covered by thepresent specification. For cases when both Equations (C5.2.3) and (C5.2.6) are applicable, the onethat yields a more conservative estimate should be used.

 cs t , t0    ds t , t0    as t , t0 

(C5.2.6)

where,  cs t , to  : shrinkage strain of concrete from age of t0 to t (  106 ) cs t , to  : dry shrinkage strain of concrete from age of t0 to t (  106 ) ds (t , t0 )  ds   (t  to )  (t  to )(C5.2.7)

 : term representing the time dependency of dry shrinkage

4W V / S
100  0.7to(C5.2.8)

 ds : final value of dry shrinkage strain (  106 ) ds  ds  ds
1    to(C5.2.9)

 (1  RH 100)W(C5.2.10)

 500 1  150 exp f c(28)   104 15 exp(0.007 f c(28))  0.25W W: unit water content (kg/m3) (130 kg/m3≤ W ≤230 kg/m3)

V S :volume-surface ratio (mm) (100 mm≤ V S ≤300 mm)

RH : relative humidity (%) (40%≤ RH ≤90%)f c(28) : compressive strength of concrete at age of 28 days (N/mm2)( f c(28) ≤80 N/mm2)

: coefficient representing the influence of the cement typeordinary or low-heat cement (  =11)
high-early-strength cement (  =15)

52

(C5.2.11)

Chapter 5

t 0 and t

Design Values for Materials: temperature adjusted age (days) of concrete at the beginning of drying andduring drying; values corrected by Eq.(C5.2.5) should be used.
(1day≤ t0 ≤98days, t0 =98days for t0 >98) as t, to  : autogenous shrinkage strain of concrete from age of t0 to t (  106 ). In
general, the final value of autogenous shrinkage strain after age of t0 shownin Table C5.2.3 may be used.
Table C5.2.3

Final values of autogenous shrinkage strain after age of to (10-6)

t0 (day)Compressive strength2
at 28days (N/mm )
1
3
7
100
230
110
50
80
160
80
40
60
150
90
50
The compressive strength is obtained after 28days curing in water. The
accuracy in prediction of autogenous shrinkage is ±40%. Only Portland
cement was used as binding material.
 t, to  is estimated as a function of time, the equation for predicting
In cases where  as
autogenous shrinkage strain (Eq.(C5.2.12) and Eq.(C5.2.13)) may be used.

 as t , to    as t    as to  as t     as'  1  exp  at  t s b

(C5.2.12)

(C5.2.13)

 as t  : autogenous shrinkage strain of concrete from the start of setting to age of t (  106 ): coefficient representing the influence of the cement and admixtures type (  may beunity for the case where only the ordinary Portland cement is used) as : final value of autogenous shrinkage strain (  106 ) as   3070 exp 7.2W C 

(C5.2.14)

W C: water-cement ratiots: start of setting (days)a, b: coefficient representing the characteristic of progress of autogenous shrinkage. The
values shown in Table C5.2.4 may be used.

53

Standard Specifications for Concrete Structures-2007, Design

Table C5.2.4

Coefficient a and b in Eq.(C5.2.13)

W/ C
a
b
0.20
1.2
0.4
0.23
1.5
0.4
0.30
0.6
0.5
0.40
0.1
0.7
over 0.50
0.03
0.8
Values in this table are for concrete in which only Portland cement
was used as binding material.
t , ts and t0 : temperature adjusted age (days) of concrete; values corrected by Eq.(C5.2.5)

should be used.
Despite active study by several researchers on autogenous shrinkage of concrete, sufficientexperimental data is still not available. The estimated autogenous shrinkage values given in Table
C5.2.3 and the Eq. (C5.2.13) for estimating autogenous shrinkage have been determined fromexperiments using concrete containing Portland cement as the only binding material. It is clarified
that the type of binder and water-binder ratio significantly affects the autogenous shrinkage ofconcrete. When a different type of binder is used, autogenous shrinkage of concrete shall be
determined based on experimental results.
Apart from Eqs. (C5.2.3) and (C5.2.6), the shrinkage strain of concrete can be predicted using
those given by Bazant, ACI Committee 209, and CEB/FIP Model Code (1990). These are widely
applicable and can be used depending on the purpose of prediction.
When calculating the stress of concrete incorporating the shrinkage at ages less than 1 day,accurate evaluation should be made for not only the shrinkage at such ages but also physicalproperties of concrete, such as modulus of elasticity and creep.
Since the method of determining shrinkage strain by the method described above is complicated,
and, mix proportions of the concrete may not be known at the design stage, the values given in
Table C5.2.5 may be used for normal members made using normal strength concrete. If neither test
data nor past performance data on the shrinkage strain of the concrete to be used are available, it isrecommended that the value shown in Table E5.2.5 be multiplied by 1.5.
Table C5.2.5 Shrinkage strain of concreteAge of concrete*
Environmenta
l condition3
less
4 to 728
monththan 3
days
days
s
days
Outdoor
400
350
230
200
Indoor
730
620
380
260
* The age at which the concrete is subjected to drying

1 year120
130Here, “Normal strength concrete” refers to concrete having a unit water content between 160 to
180 kg/m3, cement content between 350 to 400 kg/m3, and a compressive strength of up to 55
N/mm2 (up to 70 N/mm2 when the strength is increased by reducing the W/C). “Normal members”
here refer to those having a volume-surface ratio, V/S, of around 150mm. It is therefore desirable
that the shrinkage strain of concrete should be estimated by different manner when using othertypes of concrete. The value of V/S is a major factor in determining the shrinkage strain. When the
V/S differs from the value stated above, it can be incorporated by Eq. (C5.2.3). General civil
54Chapter 5

Design Values for Materials

structures are situated outdoors. In addition to measurements in real structures, the values in Table
3.2.2 for outdoor conditions were established to correspond to environments with an annual mean
relative humidity of 65%, considering that Japan’s climate is such that the annual mean relative
humidity ranges between 60 and 70%. As the shrinkage strain is strongly affected by the relative
humidity, at the design state, if an environment whose humidity conditions are widely different
from those stated above is assumed, it is desirable that calculations for the shrinkage be carried out
appropriately. Indoor relative humidity may be assumed to be 40% or less in air-conditioned areas
and 50% in non air-conditioned areas. The values given in Table 3.2.2 for indoor conditions were
established for a case with a relative humidity of 40%. These may be corrected to adapt to theconditions where the structure is to be situated. Note that the ages given in Table 3.2.2 denote theages at which the concrete is subjected to drying. For prestressed concrete, for instance, theserefer to the ages of applying prestress when the prestress losses due to shrinkage are considered.
The values given in Table C5.2.5, Eq. (C5.2.3) and Eq. (C5.2.6) are shrinkage strain values ofconcrete without reinforcement. The restraining effect of steel embedded in concrete should,
therefore, be appropriately considered. Shrinkage strain, when longitudinal bars are symmetricallyarranged at a reinforcement ratio of 1%, is given in Table C5.2.6. If neither test data nor past
performance data on the shrinkage strain of the concrete to be used are available, it is recommended
that the value shown in Table E5.2.6 be multiplied by 1.5.
Shrinkage strain of normal concrete (10-6) (reinforcement ratio of 1%)
Age of concrete*
Environmental
less
4 to 728
3
condition
1 yearthan 3days
days
monthsdays
Outdoor
340
290
180
160
120
Indoor
620
520
310
210
120
* The age at which the concrete is subjected to drying

Table C5.2.6

Shrinkage strain of lightweight aggregate concrete is greater than that of normal weight concrete
because of the smaller stiffness of lightweight aggregate than that of normal aggregate, but the innerconcrete is harder to dry because of influences of water contained inside lightweight aggregate forgeneral civil structures where member size is relatively large. According to some experimental
results using small specimens, the shrinkage strain in lightweight aggregate concrete is greater thanthat of normal concrete, but reports from some other experiments indicate that the two are aboutsimilar or the former is smaller than the latter. The values in Table C5.2.5 may be used forshrinkage strain of lightweight aggregate concrete as well as normal concrete.
(2) Forces induced by shrinkage of concrete in statically indeterminate structures, such as, arigid frame and an arch, are usually calculated by elastic theory, assuming that the member
contracts uniformly in the longitudinal direction. It has been confirmed that the actual force instatically indeterminate structures is much smaller than that obtained by elastic theory because of
the effect of creep. Considering this, shrinkage strain may be reduced for the calculation of
statically indeterminate forces. When this value is used, effect of creep shall not be added. Thisvalue may be taken as 150 × 10−6 for normal-weight ordinary-aggregate concrete made with acharacteristic compressive strength of up to about 55 N/mm2.

55

Standard Specifications for Concrete Structures-2007, Design

5.2.9

Creep

(1) Creep strain of concrete may generally be obtained using Eq.(3.2.9), assuming that
it is proportional to the elastic strain caused by an applied stress.

 Ect
 cc     cp

(3.2.9)
where，  cc:compressive creep strain of concrete:creep factor

 cp

:

applied compressive stress

E ct

:

Young’s modulus at age of loading(2) In principle, creep coefficients of concrete shall be determined, considering theeffect of factors such as, humidity around the structure, shape and dimensions of crosssection of the member, mix proportion of concrete, age of concrete when stress isapplied, etc.

[Commentary] (1) Creep strain of concrete can be considered to be in proportion to the elasticstrain induced by an applied compressive stress in concrete, provided that this is not greater thanabout 40 % of the compressive strength. If the applied compressive stress is larger than that, it is
not appropriate to assume that the creep strain is proportional to the elastic strain due to the appliedstress.
(2) Besides the temperature and humidity around the structure, shape and size of member, mix
proportion of concrete and age of concrete at loading, creep of concrete is affected by factors suchas, properties of aggregate, type of cement, and compaction and curing condition of concrete. The
design value for creep coefficient of concrete, thus, should be determined on the basis of results ofprevious tests and measurements from actual structures.
In the absence of experiments, creep coefficient may be obtained as given below.
The creep strain per unit stress,  cc t , t , to   'cp , for normal strength concrete having acompressive strength of up to 55 N/mm2 (up to 70 N/mm2 in the case the W C is reduced toincrease the strength), may generally be determined using Eq. (C5.2.15), when the concrete is
subjected to drying and loading at temperature adjusted ages of t and t ' , respectively.







 cc t , t , to   cp  1  exp  0.09t  t 0.6   cr

(C5.2.15)

   dc
where,  cr   bc

(C5.2.16)

 bc  15C  W 2.0 W C 2.4 log e t 0.67(C5.2.17)

  4500C  W 1.4 W C 4.2 log e V / S / 10 2.2 1  RH 100 0.36 to 0.30
 dc

(C5.2.18)

 cr: final value of creep strain per unit stress (  1010 /(N/mm2)) bc: final value of basic creep strain per unit stress (  1010 /(N/mm2)) dc: final value of drying creep strain per unit stress (  1010 /(N/mm2))C: unit cement content (kg/m3) (260 kg/m3≤ C ≤500 kg/m3)
56

Chapter 5

Design Values for Materials: unit water content (kg/m3) (130 kg/m3≤ W ≤230 kg/m3)

W

W C :

water-cement ratio (40%≤ W C ≤65%)

RH : relative humidity (%) (45%≤ RH ≤80%)
V: volume (mm3)S: surface area in contact with outside air (mm2):V S

volume -surface ratio (mm) (100 mm≤ V S ≤300 mm)

t0 , t ' and t : temperature adjusted age (days) of concrete at the beginning of drying, at the
beginning of loading, and during loading, respectively; values corrected by Eq.
(C5.2.19) should be used.
n


4000
for t0 , t’ and t    t i  exp13.65 273  T t i  T 0 i 1
(C5.2.19)

 t i : number of days when the temperature is T (°C)
T0

: 1°C

Equation (C5.2.15) for predicting creep has been given for concrete made using ordinary
Portland cement. Though the effect of cement type on the creep factor is relatively small, thecreep strain is known to vary depending on the mix proportions of concrete. The effect of cement
type should, therefore, be considered in an appropriate manner depending on the requirements.
Comparison with past experimental data shows that Eq. (C5.2.15) is applicable also to cases whenhigh-early-strength cement is used. The values given in Table 3.2.3 may therefore be used forhigh-early-strength cement.
Since Eq.(C5.2.15) assumes the temperature after loading to be around 20C, it is applicable tonormal conditions (normal temperatures) in Japan. As the creep strains at high or low
temperatures may be different from those at normal temperatures, the creep strains in the case ofstructures continuously exposed to high or low temperatures should be determined using separate
experiments carried out under appropriate conditions.
As in the case of Eq.(C5.2.3) for shrinkage, Eq.(C5.2.15) is applicable to concrete with astrength of up to 55 N/mm2 (up to 70 N/mm2 when the W C is reduced to increase thecompressive strength). In the case of high strength concrete (with a compressive strength
exceeding 55 N/mm2), Eq.(C5.2.20) may be used to predict the creep.

 cc t , t , to   cp 
where,f c(t )4W 1  RH 100  350
log e t  t   1
12  f c(t )(C5.2.20): compressive strength of concrete at the loading age t ' (N/mm2)( f c(t )  80 N/mm2)

t ' and t : temperature adjusted age (days) at the beginning of loading and duringloading, respectively; values corrected by Eq.(3.2.19) should be used.
W: unit water content (kg/m3) (130 kg/m3  W  230 kg/m3)

RH :relative humidity (%) (40%  RH  90%)

Since Eq.(C5.2.20) has been derived using compressive strength data of up to 120 N/mm2, it canbe applied to concrete with a compressive strength of up to 80 N/mm2, the upper limit of the scope
57

Standard Specifications for Concrete Structures-2007, Designof the present Specification. The scope for application of Eq.(C5.2.20) for conditions other thancompressive strength is the same as that of Eq. (C5.2.15). For the range of strength range where
both Eqs.(C5.2.15) and (C5.2.20) are applicable, the one that leads to a more conservative value
should be used.
Apart from the equations given above, the creep strain can also be predicted using otherequations, such as those given by Bazant, ACI Committee 209, and CEB/FIP Model Code (1990),
which are effective in predicting creep under complex conditions. When the applied stress isvariable, the principle of superposition may be applied, and the creep strain assumed to be linearly
proportional to the applied stress, provided the stress level is lower than 40% of the compressive
strength of concrete.
Since the method of determining creep coefficient by the method described above iscomplicated, and, mix proportions of the concrete may not be known at the design stage, the values
given in Table C5.2.7 or Table C5.2.8 may be used. When creep strain is obtained using Eq.(3.2.9)
using the creep coefficients shown in Table C5.2.7 or Table C5.2.8, the value of E ct at 28days
shall be used.
Table C5.2.7

Creep coefficients for normal weight concrete

OutdoorIndoorAge of concrete at which prestress is introduced
or load is applied
4 to 7
14
28
3
1
days
days
days
months
year
2.7
1.7
1.5
1.3
1.1
2.4
1.7
1.5
1.3
1.1

Table C5.2.8

Creep coefficients for lightweight concrete

Environmenta
l condition

Environment
al condition
OutdoorIndoorAge of concrete at which prestress is introduced
or load is applied
4 to 71428
3 months
1 year
days
days
days
2.0
1.3
1.1
1.0
0.8
1.8
1.3
1.1
1.0
0.8

The creep coefficient given in Tables C5.2.7 and Table C5.2.8 have been established on thebasis of the values calculated using Eq.(C5.2.15) for normal members, and are applicable tounreinforced concrete with a compressive strength of up to 55 N/mm2 (up to 70 N/mm2 when the
W C is reduced to increase the strength). Tables C5.2.9 and C5.2.10 give the creep coefficientfor members with a reinforcement ratio of 1%, with the longitudinal bars being provided
symmetrically.
Table C5.2.9

Creep coefficient for normal concrete (reinforcement ratio 1%)
Age of concrete at which prestress is introduced or load
is applied
Environmental
4 to 714
28
3
condition
1 year
days
days
days
monthsOutdoor
2.1
1.4
1.2
1.1
0.9
Indoor
1.9
1.4
1.2
1.1
0.9

58

Chapter 5

Design Values for Materials

Table C5.2.10

Creep coefficient for lightweight concrete (reinforcement ratio 1%)
Age of concrete at which prestress is introduced or load
is applied
Environmental
4 to 714
28
3
condition
1 year
days
days
days
monthsOutdoor
1.6
1.1
0.9
0.8
0.7
Indoor
1.4
1.1
0.9
0.8
0.7

Similar to the case of shrinkage, “normal members” here refer to members made of concrete
proportioned with a unit water content, W, between 160 to 180 kg/m3 and cement content, C,
between 350 to 400 kg/m3. The applied compressive stress should be lower than 40% of thecompressive strength, and the volume-surface ratio, V/S, is around 150mm. The values areapplicable to an outdoor temperature and relative humidity of 15C and 65%, respectively, andindoor temperature and relative humidity of 20C and 40%, respectively. The values of the creep
coefficient should be calculated separately when the proportion of concrete mixture or otherconditions differ widely from those mentioned above.
The outdoor mentioned here means a situation in which structure is exposed to open air. The
outdoor conditions correspond to environments with an annual mean relative humidity of 65%,
considering that Japan’s climate is such that the annual mean relative humidity ranges between 60
and 70%. ‘Indoor’ refers to a condition when the structure is protected from open air, and where
the relative humidity is approximately 50 %. When cooling in summer and heating in winter isprovided, humidity may not become greater than 40 %. The values in Table C5.2.7, therefore,
have been given for humidity of 40 % as a standard.
As the average temperature in Japan, except for the Hokkaido and Okinawa, is about 15 C,temperatures of 15 C for outdoor and 20 C for indoor have been taken as a standard.
The creep coefficient given here may be used to compute loss of prestress and to calculate
statically indeterminate forces, where the structural system varies during and after construction.
The above equations and values for creep coefficient are applicable to normal concrete forstructural use. Creep in high strength concrete, concrete under temperatures higher than 40 C,and concrete under high levels of stress should be considered separately.
In addition to the factors that affect the creep characteristics of normal concrete, in the case oflightweight aggregate concrete, these characteristics are also known to depend greatly on the type ofthe lightweight aggregate used and its ratio to ordinary aggregates in concrete. According to themeasurement carried out using small specimens, it has been reported that creep strains inlightweight aggregate concrete are about the same as or greater than those in normal concrete.
However, creep coefficient in lightweight aggregate concrete have been confirmed to be between 60
and 85 % of those of normal concrete, as the modulus of elasticity of the former is much smaller
than that of the latter. The creep coefficient for lightweight aggregate concrete may, thus, beassumed to be 75% of those for normal concrete, and, the values given in Table C5.2.8 may be used.
When calculating the creep strain using Eq.(5.2.13), the modulus of elasticity at the age ofloading should be estimated from the value at 28 days, using the equation given in CEB/FIP Model
Code (1990) or other appropriate equation.

59

Standard Specifications for Concrete Structures-2007, Design

5.2.10Influence of low temperature(1) The characteristic value of concrete strength at low temperatures shall be
determined with appropriate consideration of temperature and moisture content on thebasis of experimental results.
(2) The characteristic value of compressive strength at low temperatures may be
estimated by adding the increments in the strength determined by the temperature andmoisture content.
(3) Tensile strength and modulus of elasticity of concrete at low temperatures may be
estimated on the basis of the compressive strength at low temperatures.

[Commentary] (1) to (3) The compressive strength of concrete at low temperatures may be
determined by adding the compressive strength and the increment in strength due to the effect of
low temperature and moisture content. According to past studies, in the temperature range
between 0 and -100C, the compressive strength increases parabolically as the temperature drops,
while it increases linearly as the moisture content increases. The increment in the compressive
strength at -60C may be taken to be approximately 60 N/mm2 for moist-cured concrete and 45
N/mm2 for concrete air-cured at 20C and 60% RH. As the mean humidity in Japan isapproximately 65%, the increment in the compressive strength is likely to fall in this range.

Since it has been found that the tensile strength at low temperatures is linearly related to aradical of the compressive strength at low temperatures with the index of the root ranging between
3/4 and 1, provided the temperature ranges between 0 and -100 C. The tensile strength may
therefore be estimated from the compressive strength at low temperatures using Eq. (3.2.1).
Equation (3.2.1) approximately gives the lower limit of experimental data in the past.
As stated above, concrete shows a significant increase in strength at low temperatures, whichleads to an associate increase in the load-carrying capacity of members. However, it is safer not toconsider this increase in strength at low temperatures, in cases when normal temperatures may also
be experienced during the design service life. Further, in cases when thermal stress due to dropand gradient in temperature is of concern, it is important to consider appropriately the temperatureand the level of saturation, as it considerably affects the rigidity and tensile strength of members.
Since using an excessively low Young’s modulus leads to an underestimation of thermal stresses,
it is advisable to determine the Young’s modulus considering the temperature and level of saturation.
At low temperatures, the Young’s modulus of concrete has been found to vary linearly withcompressive strength. An appropriate form of the stress-strain curve for concrete at low
temperatures may be assumed considering the temperature and level of saturation, depending on the
purpose of investigation. Poisson’s ratio in the elastic range may normally be assumed to be 0.2,
as in the case of normal temperatures. However, it should be taken as zero when cracking isallowed in tension. Variation of the thermal characteristics of concrete with temperature should be
accounted for.

5.2.11

Carbonation rate

The characteristic value of carbonation rate,  k , shall be generally defined based upon
experimental or past data.

60

Chapter 5

Design Values for Materials[Commentary] The carbonation rate is a proportional constant when it is assumed that the depthof carbonation varies linearly with the square-root of the exposure period.

The carbonation rate defined by selected material and mix proportion must satisfy characteristic
value of carbonation rate k for the verification: p p   k(C5.2.21)

where,
p: estimated value of carbonation rate (mm /` year ).

p: safety factor to account for the accuracy in determining
between 1.0 and 1.3.

p

. Generally, it may be taken to be

The carbonation rate may be obtained using the following equation with effective water - binder
ratio and binder type.
 p  a  b W / B(C5.2.225)

a , b : constants determined from results of actual experiments associated with binder type

W / B : effective water - binder ratio.

Strictly speaking, the constants a and b in Eq. (C5.2.22) also depend on the environmental
conditions, so the effect of the environment on these parameters shall be appropriately taken into
account, especially in cases where the conditions are particularly severe from the point of view ofcarbonation. The following regression equation was obtained based on the experimental data of 17
cases by the “Research Subcommittee on Fly Ash” using ordinary portland and moderate heat
portland cements.

  3.57  9.0W / B (mm / year)(C 6.4.1)

Where
W/B : effective water binder ratio W /(C p  k  Ad )W : unit water content of concrete (kg/m3)
B : unit effective binder content of concrete (kg/m3)
3

C p : portland cement content (kgs) per m of concrete
3

Ad : mineral admixture content (kgs) per m of concretek : constant representing the efficiency of the mineral admixture used.
for fly ash, k=0.
for ground granulated blast furnace slag, k=0.7.
On the basis of data from several sources and regression analysis, the “JSCE Research
Subcommittee on Fly Ash” concluded that the ratio between the carbonation depth and the61Standard Specifications for Concrete Structures-2007, Design

square-root of the exposed age (in years) has a linear relationship with the water-binder ratio. The
carbonation rate is basically the slope of this straight line. In their experiments, cylindrical concrete
specimens (diameter 15cm and height 30cm) were exposed outdoor after an initial 14-day period ofcuring under water. The carbonation depth in the experiments was determined by spraying
phenolphthalein solution on the surface after cutting through the specimen. The procedure followedby the Research Subcommittee mentioned above may be used as a reference when carrying out
carbonation related studies.

5.2.12

Diffusion coefficient of chloride ions in concrete

The diffusion coefficient of chloride ions in concrete, Dk , shall be generally defined
based upon experimental or past data.

[Commentary] The diffusion coefficient is a proportional constant in Fick’s laws of diffusion,
expressing the speed of diffusion. The diffusion coefficient used in Eq. (8.3.6) in Chapter 8, hasbeen determined with the basic assumption that the penetration of chloride ions in concrete is a
one-dimensional process. The diffusion coefficient of concrete must be determined to prevent
corrosion of the reinforcing bars caused by the ingress of chloride ions.

The diffusion coefficient of chloride ions in concrete determined by selected materials and mix
proportion must satisfy diffusion coefficient Dk for the verification:

 p D p  Dk

(C5.2.24)

where,
Dp: estimated value (cm2/ year) of diffusion coefficient of concrete.

p: safety factor to account for the accuracy in determining
be between 1.0 and 1.3.

Dp

. Generally it may be taken toSome regressive equations have been proposed for the prediction of the diffusion coefficient of
concrete based on the investigation results of chloride concentration distribution in actual structures.
The following are two examples of such equation.
(a) When normal portland cement is used;log D p  3.9(W / C ) 2  7.2(W / C )  2.5(C 5.2.25)(b) When blast furnace slag cement is used;log D p  3.0(W / C ) 2  5.4(W / C )  2.2(C 5.2.26)

For estimating the diffusion coefficient based on the results of the distribution of chloride ionsin concrete from actual structure inspections or exposure tests, the boundary condition in terms of
the surface chloride concentration is assumed and the apparent diffusion coefficient of chloride ionsestimated subsequently. In short, the estimated apparent diffusion coefficient depends on theassumed surface chloride concentration.
For estimating the diffusion coefficient based on the experiment, test method for effective
diffusion coefficient of chloride ion in concrete by migration (JSCE-G571-2003), test method for
62

Chapter 5

Design Values for Materials

apparent diffusion coefficient of chloride ion in concrete by submergence in salt water(JSCE-G572-2003), Measurement method for distribution of total chloride ion in concrete structure(JSCE-G573-2003) may be referred.

5.2.13

Relative dynamic modulus of elasticity for freezing-thawing action

Relative dynamic modulus of elasticity for freezing-thawing action shall be generally
determined by JIS A 1148 (A method) “The Freezing-Thawing Test Method of Concrete(Freezing-Thawing Test Method of Concrete Underwater).”[Commentary] The relative dynamic modulus of elasticity of concrete is defined as the ratio (inpercentage) between the one-dimensional resonant frequencies measured after and before
deterioration of the specimen in the test carried out in accordance with the provisions of JIS A 1127
“Testing Method for Dynamic Modulus of Elasticity, Dynamic Shear Modulus, and Dynamic
Poisson’s Ratio of Concrete by Resonance Vibration.” However, if actual freezing and thawing
conditions are more severe than the condition stipulated in JIS A 1148 (A method), or, if thestructure is designed for a very long service life, the test conditions in terms of the freezing andthawing temperatures, the time durations for the freezing and thawing cycles, etc. should beappropriately modified. For normal concrete with the air content of fresh concrete is between 4%
and 7% , the relative dynamic modulus of elasticity is sufficient to ensure that the water to cement(or binder) ratio is less than that stipulated in Table C5.2.11.

Table C5.2.11. Water-cement ratio (%) to satisfy the relative dynamic modulus of elasticity infreezing and thawing

Water-cement ratio (%)

Relative dynamic
modulus ofelasticity (%)

65

60

55

45

60

70

85

90

1) The value of relative dynamic modulus of elasticity of concrete having water-cement ratio
between the listed values can be obtained by the linear interpolation.
2) When water-cement ratio is lower than 45%, the value of relative dynamic modulus ofelasticity becomes 90%.

63

Standard Specifications for Concrete Structures-2007, Design

5.2.14

Concrete properties for verification of initial cracking(1) Concrete properties associated initial cracking resistance shall be determined based
upon experimental or past data.
(2) The values representing thermal properties to be used in thermal analysis, i.e.,thermal conductivity, thermal diffusivity and specific heat, shall be adequately determinedconsidering the mix proportion of concrete used.
(3) The adiabatic temperature rise of concrete shall be adequately determinedconsidering such factors as the materials and mix proportion of concrete used andconcrete temperature at placing.

[Commentary] (2) The thermal properties of cement paste vary depending on the progress ofhydration and the water content. The thermal properties of concrete, however, may be assumed tobe constant because the thermal properties of aggregate, which accounts for a major part of concrete
volume, are constant. Thermal constants of concrete generally depend on the mix proportion of
concrete, especially on such factors as the property and unit content of aggregate, and the moisture
content of concrete. Therefore, the constants are recommended to be determined considering theeffects of these factors. The constants may be obtained in 5.2.7.

For concrete to be used in ordinary concrete structures, the thermal conductivity, specific heatand thermal diffusivity may be taken as 2.6-2.8 W/mC, 1.05-1.26 kJ/kgC and 0.83-1.1E-6 m2/s,
respectively.
Once the thermal conductivity and density are determined, the other constants can be estimatedby the following equations.
h2c=3.34×10-7·λc(C5.2.27)

Cc=3.03×103/ρ

(C5.2.28)(3) The design value of adiabatic temperature rise of concrete is expressed by Eq. (C5.2.29)
unless either chemical admixtures or admixtures that are highly effective for retarding hydration areused.
Q(t)=Q∞(1-e-γt)(C5.2.29)

where, Q: ultimate adiabatic temperature rise to be determined by testing, γ : constant on rate of
temperature rise to be determined by testing, t : age (days), Q(t) : adiabatic temperature rise at anage of t (C). Methods for estimating Q∞ and r in cases where typical cements are used aredescribed in Chapter 4 of “Design of Concrete Structure.”

5.3

Reinforcing steel

5.3.l

Strength(1) The characteristic value of the tensile yield strength of reinforcing steel f yk andthat of the tensile strength f uk shall be determined based on strengths obtained bytensile tests, carried out in accordance with JIS Z2241 "Method of Tensile Test for Metallic

64

Chapter 5

Design Values for Materials

Materials."(2) For reinforcing steel in accordance with JIS, the characteristic values f yk andf uk may be regarded as the lower-limit values specified in JIS. In general, for design oflimit state, the nominal cross-sectional area may be used as the area of reinforcing steel.
(3) The characteristic yield strength of reinforcing steel in compression
taken to be equal to the tensile yield strength f yk .
(4) The characteristic yield strength of reinforcing steel in shear
obtained using Eq.(5.3.1).

f vyk  f yk

3

f yk may be

f vyk

may be(5.3.1)(5) Material factor for steel  s , used for the examination of the ultimate limit state,shall be taken as given below:
For reinforcing bars and prestressing steel

1.0

For other steel

1.05

For examining the fatigue limit state, a value of 1.05 may be used.
For examining the serviceability limit state, a value of 1.0 may be used.

[Commentary] (2) The characteristic tensile yield strength and the tensile strength of reinforcing
steel shall be determined based on the strengths obtained by tensile tests, in the same manner thatthe characteristic compressive strength and the compressive strength of concrete are determinedfrom appropriate experiments. Past results have shown that the characteristic values are generally
equal to or a little greater than the lower limit values specified in JIS. Therefore, the lower limit
values specified in JIS may be taken as the characteristic values.

In order to use the test method specified in JIS Z 2241 "Method of Tensile Test for Metallic
Materials", determination of the cross-sectional area of reinforcing steel is required. Cross-sectional
area used for the calculation of strength in accordance with JIS varies with the type of reinforcing
steel. The nominal cross-sectional area specified in JIS may be used for purposes of design. As for
JIS Z 2241, strength of reinforcing bars is calculated using the nominal cross-sectional area, andthat of prestressing bars is calculated using the larger of the actual or the nominal cross-sectional
area. This method of calculation yields conservative results. There is no difficulty in the case ofprestressing steel wire or wire strand, as the strength is given in terms of that of a single wire. On
the other hand, the strength of structural steel should be calculated using the original cross-sectional
area. When the cross-sectional area determined using nominal thickness is applied to design, thestrength may be overestimated, compared to the actual strength, due to differences of dimension.
However, it may be assumed that practical design is not greatly affected by this problem.
When threads are cut on the surface of a prestressing bar by the rolling, for large bars having anominal diameter greater than or equal to 26 mm, the tensile strength in the threaded portion ishardly decreased due to this plastic working. On the other hand, for smaller prestressing bars with astandard diameter is not greater than 23 mm, the tensile strength of the threaded portion decreases
slightly. However, except for bars whose nominal diameter is 13 mm or smaller, the decrease in thetensile strength in the threaded portion is within 5 % of the strength of the original bar and may beneglected.
(3) The behavior of reinforcing steel during the elastic to plastic deformation in a compression
65

Standard Specifications for Concrete Structures-2007, Design

test is basically the same as that observed in a tensile test. Though the tensile yield strength
calculated in accordance with the provisions of JIS Z 2241 "Method of Tensile Test for Metallic
Materials", where the original cross-sectional area is used, is not the true value of the stress, theeffect of which is not significant for consideration of limit state, and therefore, the characteristic
value of the yield strength in compression has been taken to be the same as that in tension.
(4) The yield strength of reinforcing steel in shear may be obtained by applying Von Mises'
yield criterion.
(5) When operations such as threading and cutting, threaten to harmfully affect the strength ofthe original material, such effects should be appropriately accounted for.

5.3.2

Design fatigue strength(1) The characteristic fatigue strength of reinforcing steel shall be determined based on
the fatigue strength obtained from tests considering the type of steel, surface
configuration, size, method for jointing, magnitude and frequency of stress application,
environmental conditions, etc.
(2) The design fatigue strength of a deformed bar f srd may be obtained using
Eq.(5.3.2) as a function of the fatigue life N and the stress  sp in the deformed bar due topermanent load.

f srd  190

10 a   sp   s (N/mm2)
1 
k 
N 
f ud 

(5.3.2)for N  2  106
where, f ud : design tensile strength of reinforcing bar, which may be obtained byassuming that the martial factor is 1.05.

s: material factor of reinforcing bar, which may be taken as 1.05.

(i) In principle, the values of a and k should be determined experimentally.
(ii) When the fatigue life N is less than or equal to 2×106 cycles, the values of a and k
may be obtained using Eq.(5.3.3).

a  k 0 f 0.81  0.003 
k 0 f  0.12
where, (5.3.3): diameter of the reinforcing bar

k0 f : a factor depending on the shape of lug and may generally be taken as 1.0(3) In the case of reinforcing bars with gas pressure welding joints, the design fatigue
strength may be assumed to be 70% of that of the original reinforcing bar. In the case ofreinforcing bars made by welding of bars, or having bent parts, the design fatigue
strength may be assumed to be 50% of that of the original reinforcing bar.

[Commentary](1) In principle, the fatigue strength shall be determined experimentally because
66Chapter 5

Design Values for Materials

the fatigue strength of reinforcing steel is affected by material properties, shapes, dimensions andmany other factors.
In prestressed concrete structures, design that does not permit cracks to occur has been quiteprevalent and, therefore, the effect of variable stresses in prestressed concrete structures is relatively
small.
Consequently, it was considered that the fatigue did not have a great influence on the behaviorof prestressed concrete structures. In the case of prestressed reinforced concrete structures
mentioned in 15.2 (3), however, the stress variability of prestressing steel is relatively large. Fatigue
resulting from such variable stress should, therefore, be investigated.
The fatigue strength of prestressing steel should be determined by fatigue tests usingprestressing steel and anchorage elements to be used in the project. Where no test data or reliablereferences are available, the fatigue strength may generally be determined by Eqs.(C5.3.1) and(C5.3.2).
Regarding the prestressing steel, there is tendency that the fatigue strength of anchorage is lower
than that of the steel itself, therefore, especially for unbonded prestressing steel and the out-cablesystem, it is necessary to examine the fatigue characteristics of anchorage.
For prestressing wire and wire strand
10 ar   pp  s
f prd  280 k 1 
f pud N 

(N/mm2)(C5.3.1)(N/mm2)(C5.3.2)

For prestressing bar
f prd  270

10 ar   pp 
1 
 s
f pud N k 

where, f prd : design fatigue strength of prestressing steelN: fatigue life pp : stress of a prestressing steel due to permanent loading
f pud : design tensile strength of prestressing steel
ar and k :values shown in Table C5.3.1 may be used in general s : material factor of prestressing steel, which may be 1.05 in generalarkTable C5.3.1 ar and k
Prestressing wire
Prestressing bar
and wire strand
1.14
0.96
0.19
0.16

The fatigue strength of a structural steel is affected by residual stresses and stress concentrationof a welded portion, because structural steel is generally welded or connected by high tension bolts
for the assemblage of structural members. As for steel plate, since a lot of fatigue tests have been
carried out, the fatigue strength may be determined by considering test results obtained.

67

Standard Specifications for Concrete Structures-2007, Design(2) The fatigue strength of a deformed bar is affected by diameter of the bar, shape of lug,surface configuration, etc. Equation (5.3.2) is obtained by arranging the results of fatigue tests thathave been carried out in Japan. Repeated loading cycles of almost all these data are not greaterthan 2x106 cycles. When the arc at the base of a lug does not exist and the intersectional angle
between the direction of the lug and the longitudinal direction of the bar is more than or equal to 60
degrees, the value of k0 f in Eq.(5.3.3), in general, may be regarded as 1.00. The value ofk 0 f may be taken as 1.05 for the case of absence of the arc and the intersectional angle of less than

60 degrees, and k0 f may be taken as 1.10 for the case of presence of the arc. Since the numberof fatigue test data, with repeated loading cycles are more than 2x106 cycles, is not sufficient topropose an equation for design fatigue strength, it is advisable to confirm fatigue strength by tests
for the case of repeated loading cycles of more than 2x106 cycles. The value of a and k inEq.(5.3.3) ,for repeated loading cycles of more than 2x106 cycles, generally becomes on the safe
side and, therefore, the value given by Eq.(5.3.3) may be used as it is for the examining limit state.
In general, material factor,  s , may be taken as 1.05. The value of  s may be decreased if
the fatigue failure of reinforcing bar will not cause the ultimate state of the structure.
(3) As for the joint of reinforcing bars, there are many kinds of mechanical joints besides gas
pressure welding joint. Since there are a lot of connecting methods for mechanical joints, it isadvisable to determine the fatigue strength of each mechanical joint by confirming the fatigue
characteristics by tests.
It is well known that fatigue strengths of reinforcing bars decrease when they are welded orworked by machine. According to previous researches on this problem, various decreasing rates infatigue strength have been reported and are not constant. However, it is prevalently consideredthat the fatigue strengths of reinforcing bars welded or worked by machine may decrease to almost
50 % of that of the original straight reinforcing bar. It is actually quite obvious that the welding
for connecting reinforcing bars induces considerable decrease in the fatigue strength. Hence, if
actual fatigue strength is not confirmed by tests, the design fatigue strength may be considered to be
50 % of the fatigue strength of the original straight reinforcing bar.

68

Chapter 5

5.3.3

Design Values for Materials

Stress-strain curve(1) The stress-strain curve of reinforcing steel shall be assumed to have a suitable form
for the purpose of the examination.
(2) As for the examination of ultimate limit state, the stress-strain curve represented in
Fig.5.3.1 may be generally used.

  0.93 f yd



0.93 f yd

f yd

  f yd

0.8 f yd0.84 f yd

  E・p   E・p   E・s 0(a) Stress-strain curvefor reinforcing bar andstructural steel

0

0.015



(b) Stress-strain curve forprestressing wire, wire
strands and steel bar No.1

  0.8 f yd

0(c) Stress-strain
curve forprestressing steel
bar No.2

Figure 5.3.1 Stress-strain curve of reinforcing steel(3) In the seismic performance verifications under cyclic loading, stress strain
relationship shall appropriately consider yielding, strain hardening, Bauschinger effectand absorption of energy during hysteresis. Behavior in compression and tension may betaken to be identical.
(4) Material modeling of re-bar in (3) shall be used with the stress-strain relationshipcorresponding to the one of concrete in tension zone in consideration of the bond effectwith concrete. Especially for analysis of planar members, relationship between average
stress and average strain shall be used corresponding to stress strain relationship ofconcrete in tension zone(5) In general, stress strain relationship in Fig 5.3.2 may be used in (3).

Figure 5.3.2

Hysteresis model of re-bar

69

Standard Specifications for Concrete Structures-2007, Design(σ/σs - a)(ε/εs + a - 1) - a(1 - a) = 0（5.3.4）a = Es/(E - EB)（5.3.5）EB = σs/εB（5.3.6）EB = -(E/6)･log1010oεs（5.3.7）

Where os：Summation of experienced strain on skeleton curve part
Then, Opposite loop from tension to compression is as the symmetric form.

[Commentary] (1) and (2) The stress-strain curve of reinforcing steel is widely different
according to kinds of reinforcing steel, chemical composition, manufacturing methods, etc. For
example, the ratio of yield strength to tensile strength ranges from 65 % to 80 % for reinforcing bars,
from 85 % to 95 % for prestressing steel and from 55 % to 80 % for structural steel without
tempering. Therefore, it is necessary to assume a suitable form for the stress-strain curve
corresponding to the purpose of the examination. However, according to the contents of theexaminations, there are some cases where the difference of the stress-strain curve does not have agreat influence on calculated results for design. The stress-strain curve given in Fig.5.3.1, in
general, may be used for the examinations of stress distribution and ultimate strength of crosssection of a structural member.

(3)-(5) The average stress and average strain relationship of re-bar in cracked concrete isdifferent from the one of bare bar. The reason is that the re-bar remains in elastic state due to thebond effect everywhere else besides the vicinity of the crack plane even if re-bar yields at the crack
plane. The yielding portion at crack plane extends with the increase in stress so that the elastic andplastic portion in the element is not constant. Therefore, the average stress and average strain
relationship of the re-bar in concrete does not exhibit a yield plateau as in a bare bar. The yielding
stress of average stress and average strain relationship in cracked concrete is lower than the yieldstress of bare bar due to the bond stress between re-bar and concrete. The decrease of the yieldstress in the relationship should be considered in the re-bar model because tensile stiffness after
cracking still remains in material model in concrete used in planar member. These models greatly
influence the response values for planar members and shell structures.
When no special examination is conducted for hysteresis process, a simplified material model
described in Eqs. (5.3.4)-(5.3.7) and in Fig. 5.3.2 may be applied for the member in which stresslevel under the constant axial force is less than about 10 % of uni-axial compressive strength of
concrete and diameter of re-bar is sufficiently small as compared with the cross section of member.
The yield stress of re-bar after yielding under reversed loading become lower values, which is
known as the Bauschinger effect. Equations (5.3.4)-(5.3.7) give the hysteresis loop including theeffect, where the equations represents the curve from the stress reversed point (s, s) as the curve
crossing the origin. Opposite loops from tension to compression are assumed to be the symmetric.
It is specified that tensile stress of concrete may be neglected for linear member, because theinfluence on the structural response is small. When this assumption is applied, a simplified bi-linear
model for the skeleton curve of stress and strain relationship may be used and the yield stress of
re-bar in concrete may be same as one of bare bar. This model assumes that the strain hardening
occurs just after the yielding. The reason why the strain hardening is considered in 'Seismic
Performance Verification' though its effect is not considered in 'Structural Performance Verification'is that the effect of strain hardening on the estimation of member deformation after yielding is verylarge and it is important to exhibit the ductility for member having strain gradient. The bi-linear
model connecting initial yield stress point with tensile strength point is adopted, since the bond70

Chapter 5

Design Values for Materials

between concrete and re-bar is lost in large deformation region.
In large deformation region, main bar deforms in lateral direction under axial force and load
carrying capacity in axial direction is lost with spalling of cover concrete. Therefore, it may reflect
to analysis the occurrence of re-bar buckling and the residual compressive stress after swelling-out
of main re-bar considering arrangement of lateral re-bar, diameter of main re-bar and material
strength and so on. The effect of swelling-out of main re-bar is not small for the specimen that inwhich diameter is large in comparison with cross section size. However, in real structures, since thediameter in general is small in comparison with cross section size, the effect of swelling-out of main
re-bar show a tendency to be relatively small in comparison with test specimen. Equations(5.3.4)-(5.3.7) are not considered the effect of buckling, because load carrying mechanism of main
re-bar with swelling to lateral direction has been studying. Structural analysis factor should be set aslarge value, since the response value of deformation is estimated as a smaller value when the effectof swelling-out is neglected.
It is possible to take smaller value than the standard value specified in 4.5, for the structural
analysis factor of response value of displacement, when the effect of swelling-out is considered inmaterial model. It is necessary to set the structural analysis factor and the member factor judging
the accuracy of modeling.

5.3.4

Young’s modulus(1) It is a principle that the Young’s modulus of reinforcing steels shall be determinedbased on results of the stress-strain curve obtained by the tensile test specified in JIS Z
2241 "Method of Tensile Test for Metallic Materials".
(2) The Young’s modulus of reinforcing steels, which are reinforcing bars, structuralsteel and prestressing steel, in general, may be taken as 200kN/mm2.

[Commentary] The Young’s modulus of reinforcing steel varies according to some factors, suchas measuring methods employed. The value generally ranges from 190~210kN/mm2. The valueof the Young’s modulus for reinforcing bar and structural steel, which is different from that ofprestressing steel, has been used. However, the difference in the value of the Young’s modulus ofreinforcing steel, in general, has only small influence on the calculated results concerning stress
distribution of cross section and deformation of a structural member. Therefore, the value of
200kN/mm2 may be used for all types of reinforcing steel. When it is necessary to calculate
exactly the deformation of a structural member or the elongation of prestressing steel for the control
of prestressing force, it is advisable to use the actual value obtained by tests.

5.3.5

Poisson's ratio

Poisson's ratio for reinforcing steel, in general, may be taken as 0.3.

[Commentary] Poisson's ratio for reinforcing steel varies according to some factors, such asmeasuring methods employed. However, the difference in the value, in general, does not have agreat influence on the calculation for design. Therefore, the traditional value that has been
employed may be used.

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Standard Specifications for Concrete Structures-2007, Design

5.3.6

Coefficient of thermal expansion

The coefficient of thermal expansion for reinforcing steel, in general, may be regarded
as the same value as that of concrete.

[Commentary] Although the coefficient of thermal expansion for reinforcing steel in steel
structures and composite beams consisting of steel and concrete is, in general, 12x10-6/°C, thecoefficient of thermal expansion for reinforcing steel contained in concrete may be taken as thesame value as that of concrete.

5.3.7

Relaxation ratio of prestressing steel(1) The relaxation ratio of prestressing steel shall be three times the value of 1000
hours test obtained by the relaxation test.
(2) The apparent relaxation ratio of prestressing steel  , in order to calculate the loss
in prestress, in general, may be regarded as the values given in Table3.3.1
Table 5.3.1

Apparent relaxation ratio of prestressing steel, Kind of prestressing steel

Apparent relaxation ratio ofprestressing steel, Prestressing wire and wire strand

5%

Prestressing bar

3%

Low-relaxation prestressing steel

1.5 %[Commentary] (1) The relaxation ratio of prestressing steel is the value represented by thepercentage of the decrease in tensile stress under constant strain to the initial tensile stressintroduced in prestressing steel. As for the testing method for the relaxation of prestressing steel,the provision of 10 hours test is specified in JIS G 3536 "Uncoated Stress-Relieved Steel Wire andStrand for Prestressed Concrete" and JIS G 3109 "Steel Bar for Prestressed Concrete". However,the purpose of this testing method is to confirm the quality of material. In order to determine therelaxation ratio for design, this testing method is not suitable and it is necessary to carry out along-term relaxation test. Therefore, it is advisable to carry out the long-term test in accordancewith the JSCE standard "Test Method for Long Term Relaxation of Prestressing Steel". The JSCE
test method, however, is applicable only for the condition of constant temperature within normal
temperature ranging from 5°C to 35°C and constant strain in prestressing steel. When relaxation
tests are carried out under the condition beyond normal temperature, it is necessary to examinevarious factors affecting test results, such as the level of the initial load, the loading method, themethod for heating or cooling, the measuring method for temperature, and the range of variation oftemperatures.

When relaxation tests are not carried out, the relaxation ratio may be determined according to
the assumptions (i) and (ii) below.
(i) When the ratios of the initial tensile stress to the tensile strength of prestressing steel are
50 % and 75 %, the relaxation ratios of prestressing steel may be regarded as the values given in
Table C5.3.2.

72

Chapter 5

Design Values for Materials

Table C5.3.2 Relaxation ratio  0 corresponding to initial tensile stressSpecified value for the initial
tensile stress divided by tensile
strength
0.50
0.75
 01 = 3 % 02 = 15%
 01 = 1%
 02 = 7%
 01 = 1%
 02 = 4%

Kind of prestressing steel
Prestressing wire and wire strand
Prestressing bar
Low-relaxation prestressing steel(ii) When the ratio of the initial tensile stress to the tensile strength exists between 0.50 and 0.75,
the relaxation ratio may be assumed as shown in Fig.C3.3.1

純リラクセーション率 γ0（％）

γ02

γ01+0.64(γ02－γ01)
次二γ01+0.36(γ02－γ01)

放

物

線

γ01+0.16(γ02－γ01)
γ01+0.04(γ02－γ01)
γ01
0.50

Fig. C5.3.1

0.55

0.60

0.65

0.70

0.75

Relationship between initial tensile stress and relaxation ratio(2) The apparent relaxation ratio that is used for the design of concrete structures and members,
in principle, shall be determined based on the relaxation ratio of prestressing steel,  0 , inconsideration of the influence of both drying shrinkage and creep of concrete. The apparent
relaxation ratio of prestressing steel, in general, may be obtained by Eq.(C 5.3.3).
   0 1  2  pcs  pi 

(C5.3.3)

where,  pcs : decrease in tensile stress of prestressing bar due to the shrinkage and the creepof concrete pi: tensile stress of prestressing bar just after prestressing

The apparent relaxation ratio of prestressing steel  , for calculating the decrease in prestressstresses, in general, may be taken as the values given in Table 5.3.1.
However, the apparent relaxation ratio is influenced by the longitudinal compressive stress ofconcrete at the position of prestressing steel caused by permanent load, even though the initial
tensile stresses of prestressing steel introduced in a structure are identical with those of otherstructures.
The apparent relaxation ratio becomes small or large when the longitudinal compressive stressbecomes large or small, respectively. The value of the apparent relaxation ratio of prestressing73

Standard Specifications for Concrete Structures-2007, Design

steel with low relaxation is calculated by Eq. (C5.3.3), assuming that the ratio of the initial tensilestress to the tensile strength is equal to 0.7 and using the similar relaxation ratio to those of normal
prestressing steel wires and wire strands.
The prestressing steels with low relaxation explained here are the prestressing steel wires andwire strands whose relaxation ratios are definitely low. It means that the prestressing steels whose
relaxation ratio after 1000 hours test in accordance with the testing method of the JSCE standard isless than or equal to 2.5 %.

5.3.8

Influence of low temperature

The characteristic values of tensile yield strength and tensile strength of steel at low
temperatures shall be established on the basis of respective test strengths.

[Commentary] At low temperatures, steel should not be used unless the required quality is
confirmed, even if it conforms to JIS. Though the tensile yield strength and tensile strength ofsteel increase as the temperature drops, the values for normal temperatures may be used as thecharacteristic values regardless of the effect of temperature. According to past study, electric steel
reinforcement has strength properties comparable to those of blast-furnace steel, provided the bar
diameter is 32mm or less.

The elongation of reinforcing steel in air of both blast-furnace steel and electric steel tends todecrease at low temperatures, but the losses are not appreciable down to around -100C, whencompared with those at normal temperatures. According to past experiments, the elongation ofprestressing steel in air tends to decrease at low temperatures, but at -120C or higher, it meets the
JIS requirements for normal temperatures. However, prestressing steel constantly subjected totension with a high stress is sensitive to flaws particularly at low temperatures. It is, therefore,
necessary to exercise care not to make deleterious flaws in prestressing steel.
The stress-strain curves of reinforcing steel and prestressing steel at low temperatures should bedetermined based on testing in general. Where the temperature can rise to the normal range during
the design service life, the curves for normal temperatures should be used.
Though the modulus of elasticity tends to increase at low temperatures, the rate of increase ismarginal. The modulus for normal temperatures may be used. Poisson’s ratio and thermal
expansion coefficient for normal temperatures are also applicable to low temperatures.
The use of gas pressure welded joints and ark welded joints of reinforcing steel should be
avoided in low temperatures, as the elongation of even blast-furnace steel can abruptly decrease at a
range below temperatures between -50 to -100C. The low temperature performance ofcold-swaged joints with sleeves depends on the sleeve material and swaging method. The quality ofjoints should, therefore, be confirmed beforehand.
A wide variety of anchorage elements for prestressing steel are available for various methods.
Their performance at low temperatures should be confirmed by testing to meet the requirements.

74

Chapter 6

Load

CHAPTER 6

6.1

LOAD

General(1) Structures shall be designed for appropriate combinations of loads likely to act
during the construction stage and the design life of the structure with consideration oflimit states for performance requirements being considered.
(2) Design load shall be obtained by multiplying characteristic value of load byappropriate load factor.
(3) Combinations of design loads shall be determined according to the limit states forthe required performance of the structure, as shown in Table 6.1.1.
Table 6.1.1
Required performance
Durability
SafetyCombinations of design loads

Limit state
Every limit state
Cross-sectional failure

Combination to be considered
Permanent load + variable load
Permanent load + Primary variable load + Secondary variable load
Permanent load + Accidental load + Secondary variable load

Fatigue

Permanent load + Variable load

Serviceability

Every limit state

Permanent load + Variable load

Earthquake resistanceEvery limit state

Permanent load + Accidental load + Secondary variable load[Commentary] (1) Loads can be generally divided into permanent loads, variable loads, andaccidental loads, according to their frequency of occurrence, the duration of action and the extent ofvariation.
Permanent loads act continuously on the structure, and the variation is rare or the magnitude ofvariation is negligible compared to the average. Dead load, earth pressure, water pressure, load
produced by prestressing, shrinkage and creep of concrete should, in principle, be considered aspermanent loads.
Variable loads are act frequently on the structure, and the variations in the magnitude cannot be
neglected compared to the average. Live loads, loads produced by change in temperature, windloads and snow loads should be considered as variable loads.
Accidental loads occur rarely during the design life of the structure, but once an accidental load
act on the structure, serious damage will happen. Earthquake loads, collision loads, loads by strong
wind, etc. should be considered as accidental loads.
Appropriate combinations shall be selected from permanent loads, primary variable loads,
secondary variable loads, and accidental loads according to the limit states for performancerequirements to be considered during the construction stage and the design life of the structure.
Design loads shall be appropriately determined for each limit state.
(2) Although a combination of loads may be defined as a design load in some cases, design
loads shall be determined for individual type of load in the Specification.
(3) Examining the limit states for verification of safety and earthquake resistance, it is practicalto distinguish a set of primary variable loads from secondary variable loads. In general, different
75Standard Specifications for Concrete Structures-2007, Design

combinations of primary variable loads are compared to make a selection. Only one accidental load
may be considered when accidental loads are taken to be part of a load combination. When bothaccidental and variable loads are included in the combination of loads, only the secondary variableloads need to be considered. In general, permanent loads do not change over time. Permanent loads,
therefore, are always combined with other types of loads, and variable loads are combined either as
primary variable loads or as secondary variable loads. It must be noted that accidental loads arenever combined as secondary load. When secondary variable loads are combined with primaryvariable loads, the probability that the maximum expected value of the secondary variable loads
occurs concurrently with the maximum expected value of the primary variable loads is generally
thought to be low. It is therefore desirable that characteristic values of secondary variable loads be
determined appropriately (e.g., reduction of characteristic value).
In performance verification of safety of the structure, the resultant design member force cangenerally be given by Eq. C6.1.1.
Distinction between primary and subsidiary variable loads is not necessary in the performanceverification of serviceability and durability because combinations of loads are specified
corresponding to cracking, deformation, and other limit states.
S d    ap S p ( fp  Fp )    ar S r ( fr  Fr )    aa S a ( fa  Fa )(C6.1.1)

where
S d : Design member force

S p , S r , S a : Functions to calculate member force resultants due to permanent loads, primaryvariable loads, and secondary variable load, respectively
Fp , Fr , Fa : Characteristic values of permanent loads, primary variable loads, and secondary

variable load, respectively
 fp ,  fr ,  fa : Load factors for permanent loads, primary variable loads, and secondary variableloads, respectively
 ap ,  ar ,  aa : Structural analysis factors for permanent loads, primary variable loads, andsecondary variable loads, respectively

76

Chapter 6

6.2

Load

Characteristic Values of Loads(1) The characteristic values of load shall be determined respectively for each of thelimit states, for which verification is carried out.
(2) The characteristic values of permanent load, primary variable load, and accidentalload used for verification of safety shall be calculated from the expected maximum valuesof these loads during construction and the design life of the structure. In cases where theminimum value of the load governs the design, the expected minimum value for the load
shall be adopted. The characteristic values of secondary variable loads shall be
determined in accordance with the combination of primary variable loads and accidentalloads. The characteristic values of loads used for verification of safety against fatigue
shall be determined considering varieties in the loads expected to occur during thedesign life of the structure.
(3) The characteristic values of loads used for verification of serviceability shall becalculated using the loads that frequently occur during construction and the design life of
the structure. The values shall be appropriately chosen depending upon the limit state
and the combination of loads being considered.
(4) The characteristic values of loads to be used for the verification of earthquake
resistance shall be determined considering the predetermined level of earthquake
resistance provided that the value must not be greater than the maximum expected value
during the design life of the structure.
(5) The characteristic values of loads to be used for the verification of durability shallbe calculated using the loads that frequently occur during construction and the design
life of the structure.
(6) When specified or nominal values of loads are given instead of characteristic
values, the characteristic value of loads for performance verification shall be determinedby multiplying the specified or nominal values by the load modification factor, f.

[Commentary] (2) Although the maximum or minimum loads during the return period more thanthe design life of the structure should be essentially employed as the characteristic value ofpermanent load, primary variable load, and accidental loads that are used for the verification ofsafety, measured data concerning the maximum or minimum loads are not necessarily sufficient todetermine the characteristic values. Therefore, in the Specification, it is determined that the
expected values for the maximum or minimum loads are regarded as the characteristic values of theloads.
Secondary variable loads are additionally taken into account in combination with primaryvariable loads or accidental loads. Therefore, the characteristic value of the secondary variable load
may be smaller than the value of the same load being treated as primary variable load.
(3) The characteristic values of loads that “frequently occur”, which are used for theverification of serviceability, means that the loads with the values would not cause the limit state
regarding cracking, deformation, etc.. Therefore, they shall be determined according to thecharacteristics of the structure, the type of load, and the limit state to be considered.

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Standard Specifications for Concrete Structures-2007, Design

6.3

Load Factors
Values given in Table 6.3.1 may be used as load factors for calculating design loads.

Table 6.3.1
Required performance
Durability

Load factors

Limit state
Every kind of limit state

Kind of load
Load factor
Every kind of load
1.0
Permanent load
1.0～1.2*
Primary variable load
1.1～1.2
Cross-sectional failure
SafetySecondary variable load
1.0
Accidental load
1.0
Fatigue
Every kind of load
1.0Serviceability
Every kind of limit state
Every kind of load
1.0
Seismic resistanceEvery kind of limit state
Every kind of load
1.0*
In cases when the minimum value of the permanent load other than dead load governs the design, theload factor for the permanent load may be taken to be between 0.9 and 1.0.

[Commentary] Although the load factor is required when verifying the safety of the structure,load factors are formally introduced in verification of serviceability and seismic performance since
the design load was defined as in Section 6.1(2).
Variations in the unit weight of the material used and the cross-sectional dimensions of thestructure could cause some variation in the self-weight (dead load), which is one of the componentsof the permanent loads acting on a structure. Though small, such variations need to be accounted
for through appropriate load factors. The load factor for self-weight, whose variation is likely to besmall, can be taken to lie between 1.0 and 1.1, when verifying safety of the structure. The loadfactor for the dead load can be set to 1.0 because an increase in the dead load generally causes anincrease in the load bearing capacity of the structure. Here, ‘dead load’ refers to the total weight ofmembers contributing to the load bearing capacity of the structure, and is calculated using the unit
weights as shown in Table 6.4.1.
Loads on account of external fittings such as railings, pavement and ballast load, may beconsidered as additional dead loads and a part of the permanent loads. However, because of themore variable nature of the unit weights and the possibility of major changes in this component in
the future, the load factors for such loads, should be taken to vary between 1.1 and 1.2.
The load factor for prestressing forces may be taken to be 1.0, as discussed in Chapter 15.
The load factor for accidental loads, which occurs infrequently during the design life of thestructure, may be taken as 1.0, provided that its characteristic value does not fall into a dangerous
decision.

78

Chapter 6

6.4

Kind of Load

6.4.1

GeneralLoad

In performance verification, the following kinds of loads shall be considered as a
general rule.
- Dead load
- Live load
- Earth pressure- Hydrostatic water pressure- Fluid dynamic force- Wave action- Prestress- Wind load
- Snow load
- Shrinkage and creep of concrete- Effect of temperature- Effect of earthquake- Loads during construction stage- Others[Commentary] In this Specification, a load is defined as every action causing stress ordeformation in the members or structure. The loads consist of physical forces acting on the
structure concentratedly or distributedly, deformation in the structure and actions causing
confinement in the structure.

79

Standard Specifications for Concrete Structures-2007, Design

6.4.2

Dead load

Calculation of the nominal values of dead loads shall be made on the basis of thedimensions of the members given in drawings and specifications. The unit weight ofmaterials used shall be taken from the values given in Table 6.4.1, unless the actual
weights of the members are available, in which case they can be used.
The nominal values of dead loads shall be divided into two components - fixed deadloads and additional dead loads. The load modification factors to obtain characteristic
values from nominal values, in general, may be taken as 1.0 for fixed dead loads. The load
modification factors for the additional dead loads shall be determined considering thevariation in the magnitude of loads.
Table 6.4.1
Material
Steel, Cast steel, Forged steel
Cast iron
Aluminum
Reinforced concrete
Prestressed concrete

Unit weights of materials

Unit weight(kN/m3)77
71
27.5
24.0-24.5
24.5

Material
Concrete
Cement mortar
Wooden material
Bituminous material
Asphalt pavement

Unit weight(kN/m3)22.5-23.0
21.0
8
11
22.5

[Commentary] Dead load can be defined as load caused by the self-weight of constituent
materials and attached to a structure. In principle, the characteristic values of dead loads should bedetermined using actual data, which shows some extent of variation in unit weights. However, since
the scatter in unit weights of materials is not very large, the nominal values of dead loads of thestructure may be determined using the dimensions given in drawings and specifications.
Since the unit weight of lightweight concrete generally varies according to the type and mix
proportion of aggregates used, the values of the unit weight of lightweight concrete shall be
determined considering these factors.

6.4.3

Live load

The characteristic values of live loads shall be determined taking into consideration
the characteristics of the variation in the magnitude of loads.
For the examination of fatigue failure, the loads that have adequate magnitude andcorresponding equivalent repeated cycles shall be determined in consideration of all ofvariable loads during the design life of structures.

[Commentary] The term "live load" refers to the load of an automobile, train, crowd of people,
etc., moving on a structure plus the resulting dynamic response such as impact and braking loads. A
dynamic response due to live loads may be replaced with a static load by evaluating the ratio ofincrease from a static response appropriately. If there are standard-specified values of live loads as
for railway bridges and road bridges, the characteristic values are determined by multiplying themby load modification factors, f, according to the verification item.

80

Chapter 6

6.4.4

Load

Earth pressure(1) Earth pressure acting on a structure shall be determined by taking into
consideration overburden thickness, mass of soil, loosening of soil, construction
methods, etc.
(2) Earth pressure is classified into vertical earth pressure and lateral earth pressure.
Lateral earth pressure consists of static earth pressure, active earth pressure and passive
earth pressure. The earth pressure to be used in performance verification shall be
determined depending on the type and stiffness of structure, the limit state being
considered according to the type of soil. In that case, changes over time in the state of
the structure and the ground should be taken into account.
(3) When nominal values of earth pressures are already determined, the characteristic
values of earth pressures shall be obtained by multiplying these nominal values by theload modification factor, f.

[Commentary] Earth pressure is classified into vertical earth pressure and lateral earth pressure.
Lateral earth pressure consists of static earth pressure, active earth pressure and passive earthpressure. Vertical earth pressure and static earth pressure may be estimated taking into
consideration the conditions of the ground around the structure. Active and passive earth pressures
are interaction due to the deformation of the structure as shown in Fig. C6.4.1, being indirect loads.
Earth pressures due to surcharge on the ground shall be determined considering the distribution ofsurcharge and overburden thickness.

Static earth pressure
静止土圧Lateral earthpressure
側方土圧

Active earth pressure
主働土圧Passive earth pressure

受働土圧

O

Fig. C6.4.1

Deformationof structure

壁体変位

Lateral earth pressure as interaction with a structure

Active earth pressure and passive earth pressure are earth pressures that occur when a structureis deformed. Because of differences in the behavior of the structure, therefore, the two types ofearth pressure need to be distinguished when considering earth pressure. Earth pressure in general,
including vertical earth pressure and static earth pressure, may also change because of not only
deformation of the structure but also changes over time in the state of the ground. It is desirable,
therefore, that earth pressure assumed at the design stage be determined by taking into
consideration changes over time in the state of the ground and the structure. Expected earthpressure changes include earth pressure changes due to the aging of the structure, earth pressure81Standard Specifications for Concrete Structures-2007, Designchanges due to changes of soil over time, earth pressure changes due to coupling effect withgroundwater and earth pressure changes due to excavation or other earth-disturbing work carriedout in the vicinity of the structure. Design earth pressure should be preferably determined in viewof these earth pressure changes over time. Since, however, it is still difficult at present to calculatethese changes, it is recommended that design earth pressure be determined on the basis ofexperiment results or measurement data. If that is not possible, design earth pressure may be
determined on the basis of basic theories such as Coulomb's earth pressure theory or Rankine's
earth pressure theory.

6.4.5

Water pressure, fluid dynamic force and wave pressure(1) Loads on account of hydrostatic pressure, dynamic water pressure during
earthquake, fluid dynamic force, and wave pressure shall be determined depending upon
the type of structure, environmental conditions, geometries, which are shape and size ofstructural members, etc.
(2) The characteristic values of forces on account of dynamic water pressure during
earthquake shall be determined taking into consideration the shape of the structure, thewater depth, etc.
(3) The characteristic values of force on account of wave pressure shall be determinedtaking into consideration the location and shape of the structure and the wave properties.

[Commentary] (1) The characteristic values of hydrostatic pressure, pw, acting on the structure incontact with water or below the ground water level shall, in general, be obtained using Eq. C6.4.1.
pw  w0  h(C6.4.1)

where, pw : characteristic value of hydrostatic pressure (kN/m2)
h : water depth (m), to be determined according to considered limit states
w0 : unit weight of water (kN/m3)
However, in the case of structures below the groundwater level, static water pressures may beappropriately reduced from values given by the above equation when it is obvious frominvestigation on pore water pressures, etc, that the actual distribution of hydrostatic pressures isdifferent from that calculated by Eq.C6.4.1. As for structures in contact with liquids other thanwater, the hydrostatic pressures acting on the structures may be estimated using Eq.C6.4.1,
replacing the unit weight of water by the unit weight of that liquid.
The characteristic values of fluid dynamic force due to flow of water, Pw, shall be obtainedusing Eq. C6.4.2.
Pw 1
ρ  v 2  Cv  A
2(C6.4.2)

where, Pw : characteristic values of fluid dynamic force (N) : density of water (1000 kg/m3)
 : speed of flow (in m/s), to be determined in accordance with the considered limit
states82

Chapter 6

Load

Cv : coefficient of resistance, or resistance factor, depending on the cross section of thestructure
A : projected cross-sectional area of the member perpendicular to the direction of flow
(m2)

6.4.6

Prestress

The characteristic values of prestressing loads shall be determined according to
Chapter 10.

6.4.7

Wind load(1) Wind loads shall be determined keeping in view the type of structure,environmental conditions, and geometries, which are shape and size of structuralmembers.
(2) Dynamic effects duet to wind shall also be taken into account in case of structuresand members are flexible.

[Commentary] (1) The characteristic values of wind loads, W, shall, in general, be obtainedusing Eq. C6.4.3.
W

1
  v v2  C  A
2(C6.4.3)

where, W : characteristic values of wind loads (N) : density of air, which may be taken to be 1.25 kg/m3
s : design wind speed (m/s), to be determined according to intended limit states
C : coefficient of drag, depending on the shape of cross- section of structural member
A : projected cross-sectional area of the member perpendicular to the direction of wind(m2)
Design wind speed shall be defined for each limit state taking into account recorded data ofwind speed, the design life of the structure, and the return period of a certain wind speed. In general,design wind speed may be determined on the basis of the 10-minute average wind speed at the
ground surface or at that at a height of 10 m above the sea water surface with appropriate
corrections for effects of the elevation of the site, the horizontal and vertical length of the structure,
the ground surface roughness, the shielding and convergence effect caused by nearby features, windspeed variations in time and space, etc.
Table C6.4.1 may be used to determine the coefficient of drag for the different cross-sectional
shapes of a structural member.
(2) Wind-induced vibrations should be accounted for in the case of flexible structures andmembers, such as suspension bridges and cable-stayed bridges, and of slender members such as
hangers.

83

Standard Specifications for Concrete Structures-2007, Design

Table C6.4.1
Shape of cross section

Coefficient of dragShape of cross section

Coefficient

CoefficientWind direction
2
Circular section

Flat plate,

1.2

r

1
Rectangular section

1.5(1.1)d
2.1(1.5)

2.2
Square section

or othersection similar
to

1.8

2.7

1
Rectangular section
0.7

2.3(2.1)

1.5

1Square section

Rectangular section
0.5(diagonal direction)

6.4.8

Snow load

The characteristic values of snow loads shall be determined according to the locationand characteristics of the structure and the environmental conditions in the region.

[Commentary] In cases where the snow loads need to be considered, the characteristic values ofthe snow loads, SN, should be determined on the basis of actual data on snow fall, etc. in the region.
SN may in general be obtained using Eq. C6.4.4.

SN  ws  z  I(C6.4.4)

where, SN : characteristic values of the snow loads (N/m2)
ws : unit design weight of snow (N/m3)
z : design depth of snow above the ground (m)I : factor considering the gradient, as defined below:

I  1  30    30
In cases when <30o and 60o, I should be taken as 1.0 and 0.0, respectively.

 : gradient of the surface of the structure where snow falls (o)Unit weight of snow varies greatly due to properties of snow and conditions of snow fall. Since
the depth of snow varies greatly by the region, and is also related to snow removal procedures,
which may be carried out, it is desirable that snow loads should be determined on the basis of not
only the observed snowfall data in the region, but also the maintenance of the structure and the84Chapter 6

Loaddesign life of the structure.

6.4.9

Effect of shrinkage and creep of concrete(1) The characteristic values of shrinkage and creep of concrete shall be determinedtaking into consideration material properties, environmental conditions, geometries,
which are shape and size of the structural member. The values are given in Section 5.2.8
and 5.2.9.
(2) In design for statically indeterminate structures, such as rigid frames and arches,
the shrinkage and creep of concrete may, in general, be assumed to be uniform
throughout the cross section of members.

[Commentary] In general, the influence of shrinkage and creep of concrete may be considered inverification for serviceability and safety against fatigue failure. In the case of staticallyindeterminate structures, the deformation of a member under the influence of shrinkage or creep ofconcrete generates statically indeterminate forces. The influence of such forces, therefore, must be
taken into consideration. Also, in the case of statically determinate structures, the influence of suchforces needs to be taken into account if deformation is restrained or shrinkage deformation varies
considerably in a cross section.

6.4.10Effect of temperature(1) The effect of temperature shall be determined according to the type of thestructures, environmental conditions and the geometries, which are shape and size ofstructural members.
(2) In the design of statically indeterminate structures, such as rigid frames andarches, any increase and/or decrease in temperature may, in general, be assumed to beuniform throughout a cross-section of members. If it is clear that the temperature cannot
be assumed to be uniform, the difference in temperature among members or parts thereof
shall be appropriately accounted for. The characteristic values of increase and decreasein temperature shall be defined based on the differences between the annual averagetemperatures and the highest or lowest value of the monthly average temperatures.

[Commentary] The difference between the annual average temperatures and the highest or
lowest values of the monthly average temperatures in Japan lies between -15°C and 15°C, as
represented in Table C6.4.2. These values, i.e. -15 °C and 15 °C, have thus, been recommended foruse as the characteristic values of increase and decrease in temperature, in general.

85

Standard Specifications for Concrete Structures-2007, Design

Table C6.4.2

DistrictThe
highestvalue
Thelowestvalue

Regional differences between annual average temperature and monthly
average temperature (ºC)

KyusyuShikoku

Chugoku

Kinki

Chubu
Pacific
General
coast

Kanto

TohokuHokkaido
Pacific
General
coast

+11.5

+11.5

+12.5

+12.5

+13.0

+12.0

+12.5

+14.0

+14.0

+13.0

+15.0

-11.5

-11.0

-11.5

-12.0

-13.0

-11.5

-12.0

-13.0

-13.5

-13.0

-15.5

InlandTemperature differences occur between members exposed to and those not exposed directly tosunlight. If the statically indeterminate forces caused by these differences in such structures cannot
be neglected, the characteristic values of temperature difference shall be determined taking into
consideration the location of the structure and climate conditions around the structure. The effect oftemperature difference between inside and outside of the structure should be taken into account in
the cases of such as low- or high-temperature storages.
In some cases the temperature at the time of completion of the structure does not coincide withthe annual average temperature. When the structure completed in summer or winter, the variationsof temperatures are different from those given here at the initial stage. However, thermal stresses
vary up and down around the annual average temperatures because of creep of concrete. Therefore,
it is not necessary to consider the variation of temperatures at the construction stage. Calculationsof camber, extent of expansion and contraction, etc. should, however, be based on the temperature
at the construction stage.

6.4.11

Influence of earthquake(1) To allow for the influence of earthquakes, all ground motions and all loads
generated by the ground motions shall be considered.
(2) As for the direction of ground motion, ground motions in only two orthogonal
horizontal directions shall be considered. Depending on the characteristics of thestructure under consideration, however, it may also be necessary to consider the groundmotion in the vertical direction.
(3) As a general rule, ground motions used for the purpose of seismic performanceverification shall be expressed in the form of time-history acceleration waveform.
(4) Ground motions shall be defined at the engineering bedrock surface at theconstruction site.
(5) As a general rule, ground motions shall be defined in view of such factors as thelevel of seismic activity at and around the construction site, hypocenter characteristics
and the propagation characteristics of ground motions from the hypocenter to theconstruction site so that the influence on the structure is exaggerated. In general, groundmotions may be defined on the basis of two or more observed earthquake waveforms orby methods that takes into consideration the crust failure process in the hypocentralarea.
(6) For Level 1 ground motions, it may be assumed that the return period occurs
86Chapter 6

Loadseveral times during the life of the structure.
(7) In the case of Level 2 ground motions, of the two types of ground motions listed
below, the one with greater influence on the structure may be adopted. The groundmotions to be considered shall be the strongest ground motion expected at theconstruction site.
(i) Ground motions caused by an inland active fault directly under or near theconstruction site(ii) Ground motions due to a large-scale near-coast plate boundary earthquake[Commentary] (1) In general, to evaluate the influence of earthquakes, the following factors aretaken into consideration:1) Mass of the structure and the mass of the load2) Dynamic interaction between the structure and the ground3) Dynamic water pressure during earthquake4) Liquefaction of the ground and ground flow caused by liquefaction
From the factors listed above, necessary factors need to be selected according to the type ofstructure, structural conditions, environmental conditions around the structure to be constructed, etc.
Masses that generate inertia forces because of earthquake-induced shaking include the mass loadedon the structure as well as the mass of the structure itself. Generally, in view of the case where theloaded mass acts simultaneously with earthquake loading, permanent loads and secondary variableloads need to be taken into consideration.
The dynamic interaction between the structure and the ground results from the difference in the
dynamic response characteristics between them. Structures that require the consideration of thisinteraction include bridge abutments, retaining walls, underground structures and foundation
structures such as piles and caissons.
In the case of fluid-containing structures such as tanks, dynamic water pressures caused by theloaded mass and dynamic water pressure resulting from sloshing of the fluid during earthquake
need to be taken into consideration.
As for the liquefaction of ground, the basic rule in seismic design is to take measures to preventliquefaction. If taking such control measures is technically difficult or highly uneconomical, it isnecessary to design the structure by giving careful consideration to the influence of liquefaction onseismic performance of the structure. If the ground surface is inclined or if uneven earth pressure isalways acting, liquefaction might cause ground flow. The influence of this, therefore, needs totaken into consideration.
(2) In general, seismic force is dominated by horizontal ground motions. When seismic
performance is verified, therefore, only horizontal ground motions needs to be considered.
Although horizontal ground motions act in any direction, seismic performance of the structure may
be verified independently in two horizontal directions. In the case, however, of a curved bridge, astructure subjected to torsion or a column acted upon by a highly eccentric axial force, multi-axis
response may result even if ground motion is unidirectional. In such cases, the influence ofmulti-directional inputs of the ground motions should be considered.
If it is judged that the influence of the vertical component of ground motions cannot be ignored
87

Standard Specifications for Concrete Structures-2007, Designin connection with Seismic Performance Grade 2 and 3 because of the type and shape of structure,
its stiffness distribution, etc., it is necessary to perform verification against seismic force in thevertical direction. The magnitude of the earthquake input may be taken as 1/2 to 2/3 of thehorizontal input on the basis of the records on past earthquakes.
(3) In order to properly evaluate the level of safety of a concrete structure during an earthquake,
it is necessary to perform a nonlinear dynamic response analysis using time-history ground motion
waveform data as inputs. Ground motion waveforms can be expressed with displacement, velocity
and acceleration. Since, however, it is common practice to give an input by acceleration waveformin vibration equations, it is required that a waveform input expressing ground motions be given in
the form of time-history acceleration waveform.
(4) In order to properly evaluate the influence of the surface layers of the ground at theconstruction site of a structure, it is required that ground motions to be used for the verification ofseismic performance be defined at the depth of engineering bedrock surface. The engineering
bedrock surface may be taken as the top surface of a continuous layer of the ground with a shear
wave velocity (in the case of infinitesimal strain) of about 400 m/s or more (generally, an SPT
N-value of 50 or more for sandy soil and 30 or more for cohesive soil).
(5) to (7) As a general rule, ground motions to be used for verification purposes must be
determined in view of such factors as the level of seismic activity at and around the construction
site, hypocenter characteristics, and propagation characteristics of ground motions from the
hypocenter to the construction site. The preparation of such a time-history acceleration waveform,
however, is a laborious task requiring, for example, detailed surveys on the state of the ground at
the construction site, surveys on the location and activity level of active faults, and surveys on theinfluence of plate boundary earthquakes. An alternative is to use a number of ground motion
waveforms of past earthquakes, but it is not possible to judge whether the ground motions underconsideration is appropriate for use in seismic performance verification. If ground motions at theconstruction site cannot be defined appropriately, the simulated waveform of ground motions
containing vibration components that exaggerates the influence on the structure be used.
One way to concretely define acceleration waveforms of Level 1 and Level 2 ground motions
on the basis of past records is a probabilistic prediction method. The return period as an index forthe intensity of ground motions is used to evaluate variability of the distance-attenuation
relationship by which the intensity of ground motions is evaluated by assuming a logarithmic
normal distribution, and the probability of the occurrence of an earthquake is determined as that ofa Poisson process event. In order to clearly define earthquakes corresponding to Level 1 and Level
2 ground motions, this Specification requires that ground motions be expressed in terms of the
return period, and indicates rough values as stipulated above.
As examples of simulated ground motion waveforms, Fig. C6.4.2 shows a Level 1 groundmotion waveform, and Fig. C6.4.3 and Fig. C6.4.4 show ground motion waveforms of Level 2
inland earthquakes (Nos.1 and 2) and Level 2 plate boundary (ocean trench) earthquakes (Nos.1
and 2). Fig. C6.4.5 and Fig. C6.4.6 show absolute acceleration response spectra (damping constant,h = 0.05) of Level 2 ground motion waveforms. These are examples of ground motions at theengineering bedrock surface (free surface).
The ground motion waveform No.1 due to inland earthquake (Fig. C6.4.3 (a)) was determinedon the basis of inland earthquake records by the following procedure described below.
- Acceleration response spectra of many observation records are converted by using the
distance-attenuation relationship to ones directly above a fault, and modifications are made sothat the probability of non-exceedance among those samples becomes 90%.

88

Chapter 6

Load- To determine the phase characteristics to be used when making a time-history acceleration
waveform, the asperity and the failure starting point were varied parametrically in a
40km×20km fault plane and the phase characteristics were defined in view of the failure
process of the fault, and a waveform was synthesized.
The ground motion waveform No.2 due to inland earthquake (Fig. C6.4.3 (b)) was defined by
calculating the ground motion (NS component) at the free bedrock surface from the data recorded
by a strong motion seismograph at Kobe Port Island (installation point: GL = -83m) during the
Hyogoken Nanbu Earthquake of 1995.
The ground motion waveform No.1 due to plate boundary (ocean trench) earthquake (Fig.
C6.4.4 (a)) was defined by the following procedure described below.
- The acceleration response spectrum of the observation record is corrected so that themagnitude of the earthquake became 8 (M8) or so and the epicentral distance became about 40
to 50km by using the distance-attenuation relationship.
- Phase characteristics were defined by an empirical method by using ones corresponding to amagnitude 8 (M8) earthquake and an epicentral distance of 50km, and a waveform wassynthesized.
The ground motion waveform No.2 due to plate boundary (ocean trench) earthquake (Fig.
C6.4.4 (b)) was determined by calculation as a simulated ground motion waveform at a free
bedrock surface near a fault (epicentral distance: about 50km) based on the fault model of theassumed Tokai Earthquake (moment magnitude: MW = 8.0) proposed by the Central Disaster
Prevention Council, Japan.

Acceleration(gal)
加速度(gal)It is generally known that the magnitude of ground motions varies locally. If the influence ofthe level of seismic activity, the distance from the hypocenter, etc., in the region concerned can beevaluated appropriately, waveforms obtained by multiplying these acceleration waveforms by anappropriate reduction factor may be used.
200

Max. acceleration = 137 gal
0

-200

0

20

40

時間（秒）

60

80

Time (s)Fig. C6.4.2

Example of time-history acceleration waveform of Level 1 ground motion89

Acceleration(gal)
加速度(gal)Standard Specifications for Concrete Structures-2007, Design
800
600
400
200
0
-200
-400
-600
-800

Max. acceleration = 749 gal

0

20

40

60

時間（秒）

80

Time (s)(a) No.1
加速度(gal)Acceleration
(gal)

800
600
400
200
0
-200
-400
-600
-800

0

Max. acceleration = 700 gal

20

40

時間（秒）

60

80

Time (s)Fig. C6.4.3(b) No.2
Example of time-history acceleration waveform of Level 2 ground motion

Acceleration(gal)
加速度(gal)(due to inland earthquake)400

Max. acceleration = 322 gal

200
0
-200
-400

0

20

40

時間（秒）

60

80

Time (s)加速度(gal)Acceleration(gal)(a) No.1
400

Max. acceleration = 347 gal

200
0
-200
-400

0

20

40

時間（秒）

60

80

Time (s)Fig. C6.4.4(b) No.2
Example of time-history acceleration waveform of Level 2 ground motion(due to ocean trench earthquake)

90

Absoluteacceleration response (gal)
絶対加速度応答(gal)

Chapter 6

Fig. C6.4.5

Load

内陸型
Inland No.1
1000
海洋型
Ocean trench
No.1

500

100
50
0.05

Target spectra of acceleration response
図中の直線は目標加速度応答スペクトル

0.1

0.5
1
周期（秒）
Period (s)5Acceleration response spectra of Inland Earthquake No.1 and Ocean Trench

Absolute
acceleration response (gal)
絶対加速度応答(gal)Earthquake No.1 (damping constant, h = 0.05)

Fig. C6.4.6

Inland No.2

1000
500
Ocean trench No.2

100
50
0.05

0.1

0.5
1
周期（秒）
Period (s)5Acceleration response spectra of Inland Earthquake No.2 and Ocean Trench
Earthquake No.2 (damping constant, h = 0.05)

6.4.12

Loads during construction stage

The following loads shall be considered to act on the structure, or part of it, during
construction: dead load on account of self weight of the structure, loads on account ofconstruction equipments, wind loads, and earthquake loads. The actual values of theseloads should be chosen in consideration to the method of construction, the structural
system during construction, length of construction period.

[Commentary] Loads during the construction stage are loads that act on the structure during
construction. If loads during the construction stage are different from those after the completion, it
is necessary to determine the loads during the construction stage appropriately with consideration
91

Standard Specifications for Concrete Structures-2007, Designof the structural system under construction and the construction method.
Wind loads and earthquake loads during the construction stage may be reduced from thecharacteristic values determined according to 6.4.7 and 6.4.11, in consideration with length of
construction period and importance of the structure.

6.4.13

Other loads

In cases when it is necessary to consider other loads than those specified above, thecharacteristic values of such loads shall be determined in accordance with the actual
situation of loads.

[Commentary] Impact load is one of the other loads mentioned in this clause. In the case of
impact by automobiles, the loads may be evaluated and taken to act in a manner similar to staticload. In the case of impact by flying objects, on the other hand, the particular failure mode of thestructure should be taken into consideration. In the former case, performance verification against
safety can be done by converting the impact loads to static loads considering the mechanicalequivalence. In the latter case, three special limit states caused by impact of flying objects should
be considered: incomplete penetration, backside peeling (i.e., concrete bursting on the back side of
impact) and complete penetration. Characteristic values of velocity, weight and size of the flying
objects shall be determined when carrying out the performance verification.
In some structures, the ground conditions may be changed due to ground settlement after thecompletion of the structure, resulting in movement and rotation of supporting points of thestatically indeterminate structures. Such effects shall be considered appropriately.

92Chapter 7

Calculation of Response Values

CHAPTER 7 CALCULATION OF RESPONSE VALUES

7.1

General(1) Response value calculation shall involve modeling the structure to be constructedaccording to the shape of the structure, support conditions, the state of loads and thelimit states to be considered, perform a structural analysis by using an analysis model ofproven reliability and accuracy and calculating response values such as sectional force,
deflection, stress, strain, crack width, etc., according to verification indices.
(2) The structure shall be modeled appropriately according to the analysis method
used for verification.
(3) Loads shall be modeled appropriately according to the load characteristics and theinfluence on different types of limit states to be taken into consideration. Loads may bemodeled equivalently or conservatively by, for example, simplifying the state of load
distribution or replacing dynamic loads with static loads.
(4) In response value calculation, loads shall be considered so that response values
are verified under the least favorable conditions.
(5) Sectional forces such as bending moment, shear force, axial force and torsional
moment and deflection shall be calculated in accordance with an appropriate analyticaltheory according to each limit state.

[Commentary] (1) Dealing with matters related to the response value calculation methods used
for the verification of the limit states related to each required performance attribute specified in
Chapter 4, this chapter describes modeling, the selection of structural analysis methods, andmethods of calculating design response values. Many limit values for the limit states related to eachrequired performance attribute are given as constraints, while design response values are obtained
as a result of design work. The calculation of design response values, therefore, is important inensuring the reliability of verification results. In order to ensure the reliability of verification results,
therefore, response values must be calculated in strict accordance with the intent of this chapter.
When calculating response values by using a sophisticated analysis method such as a nonlinear
analysis method, it is necessary to ensure the required quality and accuracy by referring to the
Design: Appendix, Part 3, of this Specification, etc.
(2) Fiber modeling used to be a widely used approach to structural modeling, but modeling by
the finite element method also has become a commonly used approach because of recent advancesin numerical analysis technology. In the finite element method, the shape of the structure to beanalyzed can be modeled with considerably high accuracy by using two-dimensional or
three-dimensional elements. The method, however, also poses some problems such as the need forhuge computing capacity. It is also necessary to keep in mind that the accuracy of obtained response
values varies among different analysis methods.
(3)(4) If response values of a structure are calculated by replacing dynamic influences such as
the impact of vehicles, wind and earthquakes with static loads, load distribution patterns and thestructure must be modeled so that static response values are equivalent to or more conservative than
dynamic response values. Response values concerned vary depending on the type of load. When theinfluence of an earthquake is evaluated, post-yielding displacement is usually used as an index for
response values, and a nonlinear analysis approach is required. Because not only earthquake
93

Standard Specifications for Concrete Structures-2007, Design

response acceleration but also the relationship between the period characteristics of the structure
and loads are important factors affecting response displacement, it is necessary to model the loads
and the structure appropriately.
(5) An analysis theory can be broadly classified either as a linear (material linearity) theory or anonlinear theory depending on whether the assumed stress–strain relationship for the material underconsideration is linear and either as a first-order theory or a second-order theory depending onwhether the secondary effect (geometric nonlinearity) of deformation is ignored. Linear analysis isperformed according to the first-order theory of material linearity, and combination cases areanalyzed by nonlinear analysis Analytical theories applicable to the limit state of a mechanism
include plastic analysis assuming a rigid-plastic body, etc.
In a verification, it is not always necessary to apply the same structural model or analyticaltheory to all limit states. Structural models and analytical theories suitable for different limit states
may be used. In such cases, settings need to be determined appropriately by giving consideration to
the influence on response values and accuracy. It is also necessary to select an appropriate structural
analysis factor (γa) according to the analytical theory used for response value calculation.

7.2

Modeling

7.2.1

General(1) Modeling shall involve determining the extent of the region to be analyzed and thedimensionality of analysis and modeling structural members according to the load
response characteristics of the structure under consideration.
(2) In modeling, the extent of the region to be analyzed consisting of the structure ofinterest, ground and boundary elements, etc., shall be defined according to the extent of
the region in which response occurs.
(3) If an analysis region including ground is defined, modeling shall be performed sothat the influence of such coverage can be evaluated appropriately.

[Commentary] When modeling a structure, it is necessary to define an analysis region so that theregion in which load response occurs is covered. If the influence of such coverage is small or ifsuch influence can be allowed for by boundary conditions, the analysis region may be divided into
structural elements for modeling purposes.
For example, if the influence of an earthquake is to be considered, the analysis region is theentire structural system including the foundation and the surrounding soil because the response of astructure during an earthquake is strongly affected by the surrounding soil, etc. Depending on thetype and characteristics of structure and ground, however, the dynamic interaction between the
structure and the soil can be ignored or modeled appropriately. In such cases, it is possible to model
the structure and the soil separately and perform an analysis of the structure separately. If theinfluence of the surrounding soil is expressed simply with soil springs, etc., only the structure isincluded in the analysis region, and soil springs are treated as boundary elements.
Even when the influence of earthquakes is not taken into consideration, if there is a need todefine an analysis region including soil, modeling must be done by an appropriate method byreferring to the soil modeling during an earthquake described in Section 7.3.4.

94

Chapter 7

7.2.2

Calculation of Response Values

Modeling of structure(1) A structure shall be modeled two-dimensionally or three-dimensionally as an
assembly of structural members in view of its shape, etc.
(2) Structures may be analyzed assuming them to be made of simplified elements suchas slabs, beams, frames, arches, shells and their combinations.
(3) Members should be modeled as linear or planar members.
(4) Linear members or planar members shall be modeled by use of finite elements orfibers.

[Commentary] (1) Structures should be modeled as an assembly of member models in whichcolumns and beams are modeled as linear members and members with planar spread such as wall or
floor are modeled as planer members such as slab or shell. Strictly speaking, structures should bemodeled three dimensionally, because it is composed of members connected in three dimensions.
Two dimensional modeling of the structure may, however, be applied if only the response behavior
in a two dimensional plane is considered according to the direction of input earthquake groundmotion and characteristics of structural response.
(2) A structural analysis of a structure may be performed by assuming a simplified structural
analysis model consisting of slabs, beams, columns, rigid frames, arches, shells or their
combinations. Such structural analyses and related verifications should be performed as specified in
the Design: Standards, Part 1, of this Specification.
(3) and (4) There are a number of methods for modeling a structure. Modeling is also closely
related to analytical theories. It is therefore necessary to take the applicability of analytical theories
into consideration when selecting a modeling method. Modeling methods can be broadly classified
into two types: the method of modeling a structural member as a set of infinitesimal elements andthe method of modeling a structural member as a single element. In the finite element method, acomplex problem is solved by approximation by dividing the region to be analyzed into
infinitesimal elements and expressing the solution in each region with a relatively simple function.
From the point of view of modeling, all methods can be deemed to fall into the category of thefinite element method. Some models, however, such as mass system modeling is usually
distinguished from the finite element method. In this Specification, the method of modeling a
structure as a system consisting of two- and three-dimensional element regions is defined as finite
element modeling, and the method of modeling a structure as a system consisting of
one-dimensional element regions is defined as fiber modeling.
Finite elements that have two-dimensional element regions can be classified into triangularplane elements, quadrilateral plane elements and planar shell elements. Planar elements can be used
for modeling in a two-dimensional analytic space, and planar shell elements enables modeling in athree-dimensional analytic space. Finite elements that have three-dimensional element regions,which can be classified into solid elements such as pentahedrons and hexahedrons, cylindrical shellelements and curved shell elements, can be used for modeling in a three-dimensional analytic space.
In the finite element method, the stress–strain relationship is applied as a constitutive law.
One-dimensional element regions, which can be classified as linear elements (trusses and beams),
can be used for modeling in a three-dimensional analytic space. For beam elements, for example,
various relationships such as the moment–rotation angle relationship, moment–curvature
relationship and the stress–strain relationship can be used as constitutive laws. A beam model inwhich a beam element is divided into infinitesimal fibers so that various relationships such as thestress–strain relationship can be used as constitutive laws is generally referred to as a fiber model.
95

Standard Specifications for Concrete Structures-2007, Design

When a structural boundary or member-to-member joint is to be modeled, spring elements or joint
elements are widely used.
Rod members can be modeled by use of fibers or finite elements. Because different response
values can be calculated with different models, it is necessary to perform modeling by anappropriate method, taking into consideration response values to be used for verification. In general,
however, modeling by using beam element is effective, since the computation time becomes shorterand accuracy does not decrease much. Also, planar members should be generally modeled by using
finite elements, but they can also be modeled by use of linear members if an appropriate method isused.

7.2.2.1

Modeling of members by use of finite elements(1) Members of a structure shall be modeled by using an appropriate set of finite
elements according to the response characteristics of the structure.
(2) The dimensions of elements shall be determined appropriately in view of the limit
states to be taken into consideration and the compatibility with the material models used.
(3) I a planar member region where in-plane force is predominant over out-of-plane
force and the distribution of stress is mostly uniform, relatively large elements that are
several times as wide as they are thick may be used.
(4) When evaluating the influence of earthquakes, etc., in a region of a member where
deformation is concentrated such as an end region of a member where the maximum
bending moment acts, the longitudinal dimension of any element should not be greaterthan the effective depth of the member and should be around 20 cm.

[Commentary] (1) Although all members can be modeled if solid elements are used, it isnecessary to fully understand the characteristics of the elements used. If the deformation of a bar
member is limited to a two-dimensional analytic space, modeling by use of planar elements is agood approach. If flexural deformation is dominant and shear deformation can be ignored, the useof linear elements usually reduces computing time. Modeling by use of linear elements must be
performed in accordance with Section 7.2.2.2. If the deformation of a planar member is dominatedby out-of-plane deformation, laminar shell elements may be used for the superposition of planar
elements capable of resisting planar stress in the direction of plate thickness. In general, laminarshell elements reduce computing time. If the deformation of a member is limited to
two-dimensional deformation, modeling by use of planar elements is acceptable.
(2) and (3) In the finite element method, usually the stiffness method, in which a displacement
function is given, is used. If first-order elements are used, the displacement interpolation function
becomes a first-order equation. Consequently, the deformation of the member of interest is
polylinearly approximated, and the deformation of the member might be underestimated (i.e.,
stiffness might be overestimated) depending on the degree of refinement of meshing. In such cases,
it is necessary to think of meshing refinement or the use of higher-order elements. Prior to element
decomposition, therefore, it must be ascertained that the deformation of the member can beinterpolated with a sufficient level of accuracy.
The element decomposition scheme and element dimensions need to be determined in view ofthe following:1) In element decomposition, effort should be made to avoid random meshing as much as
96

Chapter 7

Calculation of Response Values

possible. The aspect ratio of elements should be made as close as possible to 1:1, and utmost effort
should be made to avoid flat elements. For example, if a low-order displacement function is used incases where localized deformation occurs in the member of interest, the localization behavior of
deformation might be affected. As another example, in the case of a material model using failureenergy, analytical results might be affected because of a difference in the method of equivalent
length determination.
2) Element decomposition should be performed taking into consideration concrete cover andreinforcement patterns. For example, if reinforcement is modeled in a single element in a
distributed reinforcement model, element decomposition needs to be performed so that the locationof the reinforcement roughly coincides with the center of gravity of the element. If reinforcement ismodeled in multiple elements, element decomposition needs to be performed so that the location of
the reinforcement roughly coincides with the center of gravity of the elements in which thereinforcement is distributed.
3) Element decomposition should be performed in view of the expected stress gradients.
(2) When concrete strain exceed the strain corresponding to the compressive strength due to thelarge deformation of member, the concentrated region of progressive compressive deformation(softening region) appears in the part of the member. It is recognized that the size of the softening
region is almost equal to the size of concrete cylinder for compressive test (20cm). On the contrary,elastic recovery occurs due to the stress release in the neighborhood of softening region. Therefore,
when element size is larger than the softening region, the analysis can not reasonably predict the
deformational behavior of real member. Since the stress strain relationship described in this chapter
was obtained from the specimen with size almost equal to that of concrete cylinder specimen, it isnecessary to modify the stress strain relationship of concrete in softening region when the element
size differs significantly. It is, however, confirmed that the influence on the response is small if theelement size is 0.5 to 2.0 times the size of concrete cylinder.
If the structure under consideration is large, it is generally difficult to handle element
dimensions of 20 cm or so in analysis because of limitations related to analytic capacity andanalysis time. If the structure under consideration is small, element dimensions of 20 cm or so may
make the mesh too coarse. In such cases, by using a model allows for failure energy in dealing withthe stress–stress relationship for concrete, it can be made possible to freely set element dimensions.
If the finite element method is used as a nonlinear analysis method, it is advisable to refer to the
Design: Appendix, Part 3, of this Specification.

7.2.2.2

Modeling of members by use of linear elements(1) Bar members shall be modeled as linear elements with axial stiffness and flexural
stiffness. In general, shear deformation may be ignored.
(2) Mechanical characteristics of a bar member shall be either determined directly fromthe stress–strain relationship for the material or allowed for by defining a mechanicalmodel reflecting the dimensions of the member and the mechanical characteristics of thematerial.
(3) In general, a mechanical model of a bar member shall be capable of evaluating themechanical characteristics listed below, and the skeleton curve may be expressed by atrilinear model that takes into consideration the softening gradient after the maximum
load-carrying capacity point is reached, which is determined by drawing a line from the97

Standard Specifications for Concrete Structures-2007, Design

origin through (i) to (ii).
(4) If the out-of-plane deformation of bar members or planar members whose shear
deformation cannot be ignored or the in-plane deformation of planar members is modeledwith linear elements, appropriate mechanical characteristics shall be set, and a fibermodel capable of dealing with shear deformation shall be used.

[Commentary] (1) In a linear analysis of a statically determinate member, sectional forces can becalculated from the equilibrium of forces. In an analysis of a statically indeterminate member,
however, the compatibility of deformation is necessary, so modeling that allows for axial stiffness
and flexural stiffness is needed. In such cases, nonlinearity must be taken into consideration if stressredistribution is expected. If the correlation between axial force and moment can be ignored, axial
stiffness may be ignored.
(2) In order to reproduce the dynamic response behavior of a structure, it is necessary to use amodel capable of accurately expressing the mechanical characteristics of the structural members.
There are two methods of modeling the mechanical characteristics of a bar member: modelingbased on the moment–curvature relationship derived numerically by dividing the cross section into
infinitesimal regions and applying the stress–strain relationship for the material to each
infinitesimal region and modeling based on the relationship empirically determined fromexperiment results. A fiber model in which the stress–strain relationship for the material used isapplied to beam elements automatically takes into account the moment–curvature relationship andthe axial force–axial strain relationship in the numerical algorithm. Because such a fiber model iscapable of allowing for the influence of changes in axial force, it is useful and has been widely usedin recent years. When using a fiber model, it is necessary to set element dimensions in view of theitems specified in Section 7.2.2.1 and the following items:
1) When based on the stiffness method, element dimensions in the direction of the member axis
must be set so that the equilibrium of forces among the elements is maintained.
2) If the cross section of a member is divided, the strain gradient becomes large when themember is acted upon by flexural moment. The accuracy of analysis decreases if the peripheral
zone of the cross section is divided. It is therefore necessary to set element dimensions in view ofsuch factors as the shape of the cross section, reinforcement patterns and axial force. In general, it isrecommended that the peripheral zone be divided, in view of the location of the center of gravity of
the longitudinal reinforcement, so that element width is not greater than the concrete cover.
Preferably, it should be ascertained that solutions do not vary even when the number ofcross-sectional segments is varied to some extent.
It is also possible to model the moment–curvature relationship derived from cross-sectional
analysis and use the model thus obtained as a mechanical model. When dividing a cross section, it
is necessary to take into consideration items similar to the considerations in fiber modeling.
The applicability of a mechanical model of a bar member derived empirically from experimentresults is in many cases guaranteed only within a limited range of member dimensions or material
characteristics. It is therefore necessary to use such a model after carefully considering the scope of
application of the mechanical model. If a mechanical model of a bar member is defined in terms of
the relationship between flexural moment and the average curvature of the hinge, the averagecurvature of the hinge must be set at a value corresponding to the determined hinge length, and thedetermined hinge length and the average curvature need to be used as a pair.
(3) An example of skeleton envelope curves of reinforced concrete linear members is shown in
Fig.C7.2.1. This skeleton curve was defined with reference to study results based on pastexperimental results including results related to flexural failure type members. When no special
98Chapter 7

Calculation of Response Values

investigation is conducted, skeleton envelope curve may be defined based on the following method.
In the case of prestressed concrete members, the yielding point of a member may be evaluated as
90% of the maximum load carrying capacity point of a member when no special investigation isconducted. In steel frame reinforced concrete members, skeleton envelope curve may be defined
converting steel frame into re-bars, on condition that the ends of steel frame have sufficientdevelopment length in concrete.
bending moment (M)Maximum Capacity Point
The point corresponding toultimate displacement

Mm
My(Mn）

Yielding pointof a member

cFigure C7.2.1

y

m

n

rotational angleof members ()Example of skeleton envelope curves of linear member model(i) Yielding Point of Member
Bending moment (My): Bending moment at the yielding of tensile re-bars
Rotational angle of member (y) : It may be calculated by Eq.(C7.2.1)
y =δy0 /La(C7.2.1)

where, δy0 : displacement of member body at the yielding point of member
La : shear span
When the effects of the pullout of longitudinal re-bars from the member joints are large,
rotational angle at the end of a member (y1) due to the pullout of longitudinal re-bars should be
added to rotational angle of member. y1 may be calculated by Eqs. (C7.2.2) - (C7.2.4).
y1 = Ly / (d - xy)(C7.2.2)

Ly = 7.4･y(6+3500y)/(f'’fcd)2/3
 = 1 + 0.9 e 0.45(1-Cs/)(C7.2.3)(C7.2.4)

where, Ly: pullout of longitudinal re-bars from the joint of members at the yielding point ofmember(mm)d : effective depth(mm)xy : neutral axis at the yielding point of member(mm)y : yielding strain of tensile re-bar
 : diameter of tensile re-bar(mm)99Standard Specifications for Concrete Structures-2007, Design

cs : space of re-bars(mm)f ’fcd : compressive strength of concrete at the joint of members(N/mm2)．
(ii)Maximum Load Carrying Capacity Point
Bending moment (Mm): The maximum bending moment calculated by using the provision
6.2.1(2) specified in 'Structural Performance Verification'. However, member factor should be taken
as 1.0.
Rotational angle of member (m): It may be calculated by Eqs.(C7.2.5) - (C7.2.9).
m = m0 / La

(C7.2.5)

m0 = mb + mp(C7.2.6)mp=mp(La－Lp/2)(C7.2.7)

mp＝(0.021kw0pw+0.013)/(0.79pt+0.153)(C7.2.8)

here, 0.021kw0pw+0.013 ≤ 0.04，0.79pt+0.153 ≥ 0.78
Lp = 0.5d + 0.05La(C7.2.9)

where, m0 :displacement of member body at the maximum load carrying capacity pointmb: displacement due to the flexural deformation except the plastic hingemp: displacement due to the flexural deformation at the plastic hingemp: rotational angle at the plastic hinge
pw: lateral reinforcement ratio(%)
pt: tensile reinforcement ratio(%)
kw0: factor to consider the strength of lateral re-bars, it should be taken as 0.85 forSD295, 1.0 for SD345, 1.15 for SD390
Lp: length of plastic hinge
d: effective depth of section
When the effects of the pullout of longitudinal re-bars from the member joints are large,
rotational angle at the end of a member (m1) due to the pullout of longitudinal re-bars should be
added to rotational angle of member. m1 added to Eq.(C7.2.5) may be calculated by Eq.(C7.2.10).
m1=(130mp - 0.47) y1(C7.2.10)

here, 1.0 ≤ 130mp -0.47 ≤ 4.7(iii) Softening region after the maximum load-carrying capacity
In the verification of Seismic Performance 2 and 3, the mechanical behaviors of members insoftening range beyond the maximum capacity point should be modeled. At present, it is difficult toaccurately evaluate the softening region after the maximum load-carrying capacity point is reached.
For this reason, the method of reducing skeleton curve values at a uniform ratio (usually 0.1) is
100

Chapter 7 Calculation of Response Values

permitted. It is recommended that in large-axial-force cases or in cases where shear capacity is close
to flexural capacity, the value of  be made smaller.
 M  Mm Δθ  η n Mm 

(C7.2.11)

where, Δθ: increase in rotation angle from θm: Usually, 0.1 may be used.
Mm: maximum bending moment
Mn: Usually, My may be used.
(4) In general, shear deformation of bar members and out-of-plane shear deformation of planar
members are small enough to be ignored. If shear deformation cannot be ignored, recommended
practice is to use linear elements capable of allowing for shear deformation such as Timoshenko
beams or take a finite element modeling approach. It is desirable that the out-of-plane deformationof a planar member be modeled by use of finite elements because the influence of shear
deformation cannot be ignored. When taking a fiber modeling approach, it is necessary to define theshear force–shear deformation relationship appropriately and use linear elements capable ofallowing for shear deformation.
(5) In order to model the response of structures accurately during an earthquake, the mechanicalmodels of members should consider the load hysteresis properties. In the case of reinforced
concrete members, Clough model or Takeda model which is classified as stiffness degrading typeare used. In the case of prestressed concrete members, Takeda model that considers the effects of
the amount of PC steels and re-bars to the unloading stiffness is used. In the case of steel frame
reinforced concrete members, modified Takeda model is used. When stiffness decreasing typemodels are used for reinforced concrete members, unloading stiffness may be determined with
Eq.(C7.2.12).

k r  k max
y

(C7.2.12)

where, k r : unloading stiffnessk : yielding stiffness

 max : response rotational angle of member y : rotational angle of member at the yielding of a member : stiffness decreasing rate（in general, 0.5)101

Standard Specifications for Concrete Structures-2007, Design
Mm
My

θm

θy

k
θy

kr
θm

My
Mm

Fig. C7.2.2

7.3

Hysteresis model of bar member

Structural Analysis

7.3.1 General(1) In structural analysis, a structural analysis method that meets the load andstructural modeling needs and makes verification indices available shall be used. If
verification indices cannot be obtained directly from structural analysis, a structural
analysis method that enables conversion to verification indices by an appropriate method
may be used.
(2) An analysis of a structural member shall give consideration to the influence of
nonlinearity according to response. A structural member may be regarded as a linear
member if it is evident that the nonlinearity of the member does not affect verification
indices such as sectional forces or that conservative and rational evaluation results are
obtained.

[Commentary] (1) Structural analysis must be made by using an analysis method selectedaccording to the load and structural modeling needs. In order to verify the performance of astructure, it is desirable that verification index values be obtained directly from structural analysis,
and it is necessary, wherever possible, to select a structural analysis method that makes it possible toobtain verification index values directly. If, however, verification index response values cannot be
obtained directly from structural analysis, it is necessary to convert the index response values
obtained from the analysis to design response values of verification indices by an appropriate
method.
(2) 1) Because the stiffness of a concrete member varies depending on such factors as cracking,it is necessary to appropriately evaluate the nonlinearity of the member material. In general, themechanical models of materials indicated in Chapter 5 may be used for material nonlinearity
modeling. The nonlinearity of a structure or a member includes geometric nonlinearity besides
material nonlinearity. If geometric nonlinearity cannot be ignored, an analysis theory that makes it
possible to allow for the influence of geometric nonlinearity must be applied.
If the influence of the nonlinearity of a member on response values that can be used asverification indices such as sectional forces can be ignored, the stiffness of the member may bedeemed to be elastic.
2) Analysis methods other than linear analysis include exact nonlinear analysis that takes into
consideration material and geometric nonlinearity, equivalent linear analysis that approximately
102

Chapter 7 Calculation of Response Values

evaluates the influence of nonlinearity by conducting a linear analysis using a member stiffness
reduced from elastic stiffness, and plastic analysis applied to beams, slabs, etc.
The moment redistribution method applied to statically indeterminate structures such ascontinuous beams, rigid frames and continuous slabs is a practical sectional force calculation
method based on the plastic analysis method. For slabs, there are yield line theory, which gives anupper bound, lower bound theory, which gives a lower bound, and the strip method. When applying
a method other than these linear analysis methods, it is necessary to select an appropriate value ofthe structural analysis factor γa.
3) When conducing an analysis of a member that takes into consideration nonlinear
characteristics including the plastic range of the member as when verifying the failure or collapse ofa structure or calculating design response values to be used for verification with respect to the
influence of an earthquake, it is necessary either to determine a nonlinear model or restoring force
model of the member by using a nonlinear hysteresis model as a material model or to use anonlinear model or restoring force model based on previous study results.
When safety from failure is to be verified by using a discretization method such as finite
element analysis based on nonlinear theory, the safety of a structure or member can be verified byusing verification indices other than sectional forces or sectional capacity. In such cases, it isrecommended that verification be made by setting indices suitable for the type of failure and thelimit state and comparing the obtained design response values and design limit values. For example,
in the verification of bending-dominated failure or shear failure involving an extensive damage
region (e.g., shell structure), indices based on such deformation as element plastic strain or element
rotation angle can be used. Indices that can be used for highly localized failure modes include
indices related to shear force calculated from element stresses, the progress of cracking or the stateof material damage. In all cases, the structural analysis factor γa needs to be determined through theexperimental verification of the scope of application and accuracy.

7.3.2

Structural analysis related to safety verification

7.3.2.1 Structural analysis for verification of cross-sectional failure(1) As a general rule, the structural analysis for the verification of the cross-sectional
failure of a member shall take into consideration the influence of the nonlinearity of themember. If the influence of the nonlinearity of a member on the design response values
such as sectional forces can be ignored, design response values may be calculated byassuming the linearity of the member. In such cases, the structural analysis factor a of 1.0
shall be used.
(2) As a general rule, when the nonlinearity of a member is considered, the effect ofmaterial nonlinearity shall be considered, and the effect of geometric nonlinearity shallalso be taken into consideration on an as-needed basis.
(3) If sectional forces are calculated through linear analysis, the effect of nonlinearity
may be evaluated by a simple method on condition that detailed structural requirements
are met.

[Commentary] (1) In general, deformation properties of a member in the limit state ofcross-sectional failure are nonlinear. When calculating deformation in the limit state ofcross-sectional failure, therefore, it is essential that nonlinearity be taken into consideration. It is103

Standard Specifications for Concrete Structures-2007, Design

also rational to use nonlinear analysis when calculating sectional forces.
If, however, the ultimate strain of concrete in the modeled stress–strain curve for concrete
shown in Chapter 5 is used as the design limit value for the limit state of cross-sectional failure for a
flexural failure type member, it is good practice to apply, for example, the equivalent linear analysis
method, which approximates the effect of nonlinearity by using stiffness equivalent to the stiffness
at the stress level under consideration, because the influence of the nonlinearity of the member on
response values is small if an appropriate value of flexural stiffness of the member is used. In suchcases, the structural analysis factor γa of 1.0 may be used to calculate design response values in thelimit state of cross-sectional failure.
If the design limit value in the limit state of cross-sectional failure is greater than the ultimate
strain mentioned above, appropriate verification indices such as compressive strain in concrete,curvature and the joint translation angle must be set and the design limit value verified by applying
a nonlinear analysis method such as the incremental analysis method. In this case, the nonlinearityof the member concerned must be in accordance with Section 7.3.4.
If, however, sectional forces are used as verification indices for a statically determinate structuresuch as a girder or a cantilever beam, the stiffness of the member may be assumed, for convenience,
to be elastic because changes in sectional forces due to the stiffness of a member are usually small.
(2) In the limit state of cross-sectional failure, as a general rule, the effect of material
nonlinearity is to be taken into consideration. Since, however, it may not be possible to ignore
geometric nonlinearity depending on structural configuration as the amount of member deformation
increases, it is also required that the effect of geometric nonlinearity be taken into consideration on
an as-needed basis.
(3) By specifying structural details by using the linear analysis method, the method of allowing
for the nonlinearity of a member or structure easily is permitted. Simple methods include thoselisted below. In this case, the structural analysis factor γa of 1.0 may be used.
1) If linear analysis is used, plastic rotation capacity needs to be secured because moment
redistribution may occur in reality. As a general rule, the steel ratio in all cross sections must be
75% or less of the balanced steel ratio.
2) When designing for flexural moment at supports or joints in continuous beams and slabs,
frames, etc. moment redistribution may be considered according to values obtained using linear
analyses. Flexural moment to be thus redistributed shall be within 15% of the values obtained bylinear analysis, and the flexural moment at any cross section shall not be smaller than 70% of thevalues before redistribution. In such cases, it shall be ensured, or checked, that the reinforcement at
any cross section does not exceed 50% of the balanced reinforcement ratio.
3) Member forces associated with imposed deformations due to temperature changes, drying
shrinkage and creep in ordinary conditions may be neglected. In such cases, the ratios ofreinforcement at any cross section shall not exceed 50% of the balanced strain reinforcement ratios.
If, however, the structural system during construction differs from the completed structural system,changes in member forces due to creep shall be taken into account.
If sectional forces are calculated through nonlinear analysis, sectional forces reflecting theinfluence of those factors can be obtained because such influence has been allowed for in structural
analysis. If, however, sectional forces are calculated through nonlinear analysis, the influence of
those factors is not taken into account in structural analysis. When calculating design response
values for the verification of cross-sectional failure, therefore, response values due to those types offorced deformation may be ignored on condition that a certain level of plastic rotation capacity of104

Chapter 7 Calculation of Response Values

the member under consideration is secured. This Specification requires, therefore, that the steel ratio
be 50% or less of the balanced steel ratio in all cross sections. This requirement does not need to be
met if verification is made through nonlinear analysis.
If, however, the structural system under construction differs from the completed structural
system for reasons associated with the construction method used, changes in member forces,
particularly due to creep, may be unignorably large. In such cases, appropriate consideration tochanges in member forces due to creep is required. If the influence of temperature changes, etc.,that do not result from weather conditions on design response values related to failure verification
cannot be ignored, it is recommended that design response values be determined in view of thedecrease in stiffness of the member due to cracking, etc., on the basis of experimental results or awell-grounded theory.

7.3.2.2

Structural analysis for verification of fatigue failure(1) As a general rule, the structural analysis for the verification of the fatigue failure ofa member shall take into consideration the influence of the nonlinearity of the member
according to structural characteristics. If, however, the influence of the nonlinearity of themember on design response values can be ignored, design response values may be
calculated by assuming the linearity of the member. In such cases the structural analysis
factor a of 1.0 shall be used.
(2) As a general rule, when the nonlinearity of a member is considered, the effect ofstiffness reduction due to cracking shall be taken into consideration. As a general rule,the influence of normal temperature changes, shrinkage, creep, etc., shall be taken into
account when calculating response values.

[Commentary] (1) Design response values used for fatigue failure verification needs to be
calculated taking into consideration such factors as changes in the stiffness of the structural member
under consideration due to loads and other influences during the design service life.
Under normal service conditions, a structural member usually shows nonlinearity. It is therefore
required that calculation be made taking into consideration the influence of stiffness reduction due
to cracking of the member. Although there are various analysis methods that take into account the
influence of member stiffness reduction, it is good practice to apply an equivalent linear analysis
method that uses stiffness equivalent to that at a particular stress level. In such cases, the structural
analysis factor γa of 1.0 may be used.
(2) In the verification of fatigue failure, the state of stress under normal service conditions is
considered. Sectional forces, therefore, due to such factors as normal temperature changes,
shrinkage and creep cannot be ignored. In the verification of fatigue failure, it is also necessary totake into account the state of stress under permanent loads. This is why it is required, as a generalrule, that the influence of normal temperature changes, shrinkage and creep be taken into
consideration.

7.3.2.3 Structural analysis for verification of structural safety(1) As a general rule, the structural analysis for the verification of the stability of astructure shall take into consideration the stiffness of the ground and the foundation.

105

Standard Specifications for Concrete Structures-2007, Design(2) As a general rule, in the structural analysis for the verification of the displacement,
deformation and mechanism of a structure, an analysis method takes into consideration
the influence of the nonlinearity of the structural members and the ground. As a generalrule, material nonlinearity and geometric nonlinearity shall be taken into consideration aspart of the nonlinearity of structural members.

[Commentary] (1) The verification of the stability of a structure is to be verified by conducting a
structural analysis using a model capable of estimating the behavior of the entire structure including
the structural elements and the ground. For the verification of the stability of a structure under the
influence of the deformation of the foundation structure, it is necessary to conduct a structural
analysis using a model capable of allowing for structural deformation caused by the ground.
(2) When verifying the limit state of the displacement, deformation and mechanism of astructure, it is necessary to conduct a structural analysis, taking into consideration the post-peakrange of the structure or its members. In this case, since reinforced concrete members are subject tobuckling of the longitudinal reinforcement, spalling of cover concrete, etc., it is necessary to
conduct a structural analysis by using a material model or member model capable of allowing forthe influence of these factors. This structural analysis may be conducted by using the method
described in Section 7.3.4.
In the limit state of displacement, deformation or the mechanism of a structure, usually its
members undergo large displacement and deformation. As a general rule, therefore, it is requiredthat the influence of geometric nonlinearity be taken into account in addition to material
nonlinearity.

7.3.3 Structural analysis for verification of serviceability(1) As a general rule, appearance verification using crack width or material stress shalltake into consideration the influence of stiffness reduction due to cracking. If, however,
the influence of the nonlinearity of the member under consideration can be ignored,
design response values may be calculated by assuming the nonlinearity of the member. In
such cases, the structural analysis factor a of shall be used. As a general rule, response
values shall be calculated taking into account the influence of such factors as normal
temperature changes, shrinkage and creep.
(2) If the comfortability of a structure is to be verified by using displacement or
deformation, as a general rule, the influence of stiffness reduction due to cracking andshrinkage and creep occurring during the design service life shall be taken into
consideration.
(3) Structural analysis for the verification of vibration shall be conducted by a method
appropriate for the type of structure concerned.
(4) As a general rule, structural analysis used in a study on stress limits shall take into
consideration the influence of stiffness reduction due to cracking, shrinkage and creep.

[Commentary] (1) For members that are expected to have cracks at the serviceability limit state,
the reduction in the stiffness of the cross-section due to cracking should be accounted for, whencalculating member forces caused by changes in ambient temperature and shrinkage. This ensures
rationality because the more realistic structural behavior is considered in design and106

Chapter 7 Calculation of Response Values

over-reinforcement of the section is avoided. For calculating decreases in the stiffness of a member
due to cracking, it is good practice to determine stiffness experimentally or according towell-grounded theoretical analysis. As an approximation approach, stiffness may be determined inaccordance with Section 7.5.4 in consideration of the influence of shrinkage and creep.
There are many types of concrete cracks. Cracks considered in this section are mechanicallycaused cracks, particularly cracks caused by bending moment, axial force, shear force or torsional
moment.
Cracking verification is to be made under normal service conditions. If there are differences
between the structural system being constructed and the completed structural system, it is necessary
to take their influence into consideration when calculating sectional forces. In general, in the stateof stress under service conditions, the effect of sectional forces under the influence of such factors
as normal temperature changes, shrinkage and creep cannot be ignored. As a general rule, therefore,
it is required that the influence of those factors be taken into consideration. To allow for the
influence of temperature change, shrinkage and creep, the values indicated in Chapter 5 may beused.
(2) During normal use, loads vary widely. As a result, crack patterns vary among members
depending on the loads to be verified, and displacement and deformation vary with stiffness. Whenevaluating displacement and deformation as verification indices, therefore, it is necessary to take
into consideration the influence of stiffness reduction due to cracking according to the loads
concerned.
In general, structural members are classified broadly into those that are subject to cracking andthose that are not subject to cracking. For members that are not subject to flexural cracking, elastic
theory is applied assuming a fully effective cross section. For members that are subject to flexural
cracking, an analysis method that appropriately allows for stiffness reduction due to cracking is to
be used. The influence of stiffness reduction due to cracking may be allowed for by using themethod described in Section 7.4.5. Since, however, that method calculates the stiffness of a member
under virgin loading, if the limit state to be verified is one under cyclic loading during normal use, it
may be necessary to use the stiffness of a member under repeated loading.
When considering displacement and deformation, it is necessary to take into consideration theinfluence of the shrinkage and creep of concrete besides cracking.
(3) The structural analysis method used for vibration verification must be one appropriate forthe type and characteristics of the structure under consideration. Vibration-related studies have been
underway from the viewpoints of the determination of basic characteristics, prediction methods, etc.,
but generation and propagation mechanism are very complicated. It is therefore necessary to use ananalytical method in conjunction with available measurement results obtained under similar
conditions.
(4) Studies related to stress limits involve the verification that response values meet the limit
requirements for permanent in-service loads and the maximum loads of variable loads. Because
structural members are normally subject to cracking, it is required as a general rule that the
influence of stiffness reduction due to cracking be taken into consideration. It is also required thatthe influence of shrinkage and creep be taken into account.

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Standard Specifications for Concrete Structures-2007, Design

7.3.4 Structural analysis for earthquake resistance evaluation
7.3.4.1 General(1) As a general rule, structural analysis used for the verification of earthquake
resistance shall be conducted by using a time history response analysis method thatallows for the influence of the nonlinearity of the member under consideration and theground. If a structural analysis method with proven accuracy of analysis is used, thestructural analysis factor of 1.0 may be used.
(2) In general, when the nonlinearity of a member is considered, the influence ofmaterial nonlinearity shall be considered. The influence of geometric nonlinearity shallalso be taken into consideration on an as-needed basis.
(3) If the analysis region for structural analysis to evaluate earthquake resistanceincludes ground, a structure–soil coupled analysis shall be conducted, and modelingshall be performed as stipulated in Section 7.3.4.3. However, if dynamic interaction
between the structure and the ground can be neglected or it can be appropriately
modeled, the structure may be analyzed independently in accordance with 7.2.4.2.
(4) The integrating time interval shall be determined considering both the accuracy of
the response values and the stability of response analysis, depending upon the method
adopted for time integration.
(5) Viscous damping of structures should, in principle, be neglected. However, it may
be accounted for when carrying out the verification of the structures in elastic region.

[Commentary] (1) Recently, numerical simulation technique has been developed notably, andreliability of analytical results has also been improved sufficiently through comparisons withseveral kinds of experimental results. Therefore, it is in principal in this specification that time
history response analysis is performed to estimate response values. When it is obvious that the
response of a structure and members are in elastic region, other reliable methods may be used forverification.
(2) The geometrical nonlinearity generally may be taken into account by the effect of additional
moment due to response displacement. When large plastic deformation occurs in structures andmembers, or high axial force is acted to slender columns, load carrying capacity of a member
decreases due to large additional moment and it is also strongly related to reach the mechanism ofload resistant. Therefore, this effect should be considered. If damage of a member due to shear
failure is avoided, collapse of the whole structure system is reached by the effect of geometricalnonlinearity. However, the effect needn’t to be considered in case that large deformation where theeffect of geometrical nonlinearity occurs is not allowed.
(3) Since the response of a structure during an earthquake is strongly affected by neighboring
ground and others, the whole structural system including foundation or neighboring ground should
be analyzed. To do so, a coupled analysis taking the interaction between structures and soil into
account directly should be used. Table C 7.3.1 shows a general analytical method. In modeling ofground, the influence of distant ground and others should be sufficiently examined. An example offinite element model of a structure is shown in Fig. C 7.3.1.
According to types or characteristics of structures and ground, there are some cases which
dynamic interaction between structures and ground can be neglected or modeled appropriately. In
108

Chapter 7 Calculation of Response Values

these cases, the responses of the structures and the ground may be analyzed independently
according to the provision in 7.3.4.2, because the response can be estimated with sufficientreliability without using coupled analysis.

Table C73.3.1 Method for a coupled analysis of structure and ground
Structure TypeGround structure, Underground Structure

Analytical Method

Time History Response Analysis

Analytical Model ofFinite Element Model or Beam Element Model

Analytical Model ofFinite Element Model

Input Value

Time History Acceleration Wave Form

Input PlaceBase Layer

Fig. C 7.3.1 Example of modeling for structure and ground in a coupled analysis(4) We have explicit and implicit integration methods of acceleration in time history response
analyses. Moreover, we have central difference calculus, Runge-Kutta and others in the explicit
method, and Newmark’s  method, Wilson’s  method and others in the implicit method. Amongthem, Newmark’s  (=0.25) method or Wilson’s  method are frequently used because of thestability of the solutions. Convergent calculation is necessary in these methods in order to satisfy
the equation of motion in each time step, and if the convergent calculation is skipped, it should be
noted that the analytical accuracy will be decreased. On the other hand, central difference calculus
is representative in the explicit method. In the central difference calculus, convergent calculation
used in the implicit method is not necessary and is quite accurate. However, the stability of thesolution is poor and definition of fine integration time interval for natural period of the highest
order in the vibration system is required.
(5) According to dynamic loading tests changing response velocity of member, it has been
confirmed for linear members and planar members that, in general, the characteristics of restoring
force including inelastic region are hardly affected by the displacement velocity. This means that theeffect of viscous damping in proportion to the response velocity is negligible in inelastic region, and109

Standard Specifications for Concrete Structures-2007, Design

it can explain that the effect of hysteresis damping is dominant. In order to consider the hysteresis
damping in time history response analysis, path-dependent mechanical models of material andmember are adopted in this specification. Consideration of excessive viscous damping leads todangerous evaluation due to estimating smaller structural response, and the physical significance ofviscous damping constant is ambiguous in nonlinear region. Therefore, it is specified in principle
not to consider viscous damping constant. However, viscous damping constant may be determined
for a structure in verification of the Seismic Performance 1 because nonlinear response is notconsidered. Since there may be cases where viscous damping is considered for numericalcalculation stability, in certain cases such as when the solution diverges, viscous damping may beconsidered after ascertaining that the influence on the structure under consideration is sufficiently
small.

7.3.4.2 Method for analyzing the structure and the ground independently(1) In calculating the dynamic response of the structure on the ground, the input wave
should be taken to act at the depth, which is obtained from the response analysis of only
the ground, and dynamic computations should be carried out in time domain.
(2) The response of the ground should, in principle, be carried out using dynamic
analysis by the model following 7.3.4.4.
(3) The response of the foundation and the underground structure may be calculatedusing the response displacement method. The value of the response displacement may betaken as the displacement at the time when the relative displacement of the ground in theposition of the structures reaches the peak.

[Commentary]
independently.

Table C7.3.2 lists the methods for analyzing the structure and the ground(1) When analyzing a structure on the ground independent of the ground, earthquake groundmotion at the base of the structure should be estimated by dynamic analysis of the subsurface
ground at the site, and then dynamic response analysis of the structure should be performed using
the estimated earthquake ground motion as shown in Fig. C 7.3.2.
(2) Analysis of seismic response of the ground, in general, is applied to the time history
response analysis method and to the response analysis method in frequency domain. In the time
history response analysis, the nonlinearity of the soil can be modeled as a stress-strain relationship.
On the other hand, in the response analysis in the frequency domain, it is pointed out that theconformity with the actual action of the ground reduces in the large strain area where the strainlevel of the soil exceeds 10-3, because the method approximates the nonlinearity of the soil by anequivalent linearized technique. Therefore, a proper analytical method corresponding to the strainlevel of the soil should be chosen.

110Chapter 7 Calculation of Response Values

Table C7.3.2

Methods to analyze the structure and the ground independently

Structural Type
Analytical method

Structure on the ground

Underground structureTime History Response Analysis

Response displacement method

Analytical model of Finite Element Model or Beam Element Model
structure
Analysis of Interaction model
Structure
Input value

Analysis of
GroundSpring modelTime History Acceleration Wave Displacement of ground
Form calculated from analysis of calculated from analysis of groundgroundInput place

Base part of structure

Side part of structure

Analytical method

Time history response analysis or response analysis in frequency
domainAnalytical model of One-dimensional continuous model or finite element model divided
groundin different layers
Input value

Time History Acceleration Wave Form

Input place

Engineering Base layer

Earthquake ground

Base part of

motionInput toEngineering base layer

Subsurface
grounds

Earthquake groundmotionFig. C7.3.2

Method to analyze a structure independent of the ground(5) Relative vibration against the ground is hard to occur on usual underground structure
constructed in the subsurface ground. The structural response follows the displacement anddeformation of the surrounding ground during an earthquake, and the influence of the inertia force
caused by the mass of the structure is small. When the oscillation mode of the ground coincides
with that of the structure, the forced displacement, which is obtained as the deformation of theground during the earthquake (response displacement), may be acted statically on the structure.

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Standard Specifications for Concrete Structures-2007, Design

Behavior of an underground structure during an earthquake is affected not by the scale of theabsolute displacement of the ground at the position of the structure, but by the rate of verticalchange of the horizontal displacement. Therefore, the displacement used for the response
displacement method is determined as the displacement of the ground at the time when the relative
displacement of the ground between the top and the bottom ends of the structure is the maximum.
As for long structures such as piles, the time when the relative displacement of the ground at each
depth is the maximum may be different due to the stratum condition. In such a case, some grounddisplacements that give a great influence in each section of the pile should be chosen from the time
history displacement.

7.3.4.3 Ground model for coupled analysis(1) In coupled analysis considering the superstructure, the foundation and the ground,
the ground should be modeled using finite element over a sufficiently large region. Whenground has any irregularity, its effects shall also be considered.
(2) If the influence of an earthquake is to be taken into consideration, a model thatcovers a sufficiently large region including the ground and allows the use of boundary
conditions so that the propagation of ground motion can be allowed for shall be used.
(3) When separation or sliding between the ground and the structure affect the
response of the structure, joint elements that can represent the effects of the separationand the sliding may be used between the structure and the ground.
(4) Constitutive models used to model the behavior of the ground shall be able to takethe characteristics of plastic behavior of the ground as well as its liquefaction into
account.

[Commentary] (1) When a coupled analysis is performed, the ground shall be modeled as large
region as possible so that the range in which the influence of the dynamic interaction of thestructure and the ground may become small enough. When the ground has remarkable irregularity
as in the case that the engineering base layer and the ground surface are inclined, wave propagation
becomes complicated. This sometimes leads to local amplification of earthquake ground motion or
elongation of the duration of the earthquake ground motion due to the occurrence of a secondary
wave such as surface wave. Therefore, if the ground has remarkable irregularity, the effect should
be taken into account. When the ground is modeled with finite elements, the layer thickness may be
about 1/4 –1/6 of the minimum wavelength (the period×the shear wave velocity of the consideredstratum) in the considered frequency band for the response analysis of the structure and the ground,because the wave motion beyond a certain frequency level is eliminated corresponding to the layer
thickness of the element.
(2) Since earthquake ground motion shown in 2.2 is defined on the engineering base layer andthe influence of the reflected wave of the subsurface ground is not included, the viscous boundary,which absorbs a reflected wave may be arranged on the bottom boundary of the ground model.
When the bottom boundary of the ground is modeled as a fixed boundary, input earthquake groundmotion should be applied considering the influence of the reflected wave. The side of the groundshould be modeled with enough distance and extension, and the boundary condition may bemodeled to absorb the reflected waves.
(3) When a strong earthquake ground motion such as Level 2 earthquake motion acts, aseparation and a slide phenomenon may occur between the structure and the ground due to the112Chapter 7 Calculation of Response Values

difference in relative movement between the structure and the ground. This may possibly affect thewhole response of the structure. Joint elements between the structure and the ground can be used tomodel such phenomenon in finite element model. In such a case, the behavior of the osculating
plane between the ground and the structure should be investigated and its results should be reflectedon the characteristics of the joint element. Since separation occurs when a normal stress at theosculating plane between the structure and the ground exceeds a tensile stress, relations between thenormal stress and the normal strain should be evaluated. Since a slide occurs when a shear stress atthe osculating plane exceeds the shear strength, relations between the shear stress and the shear
strain should be evaluated.
(4) Dynamic shear stress-strain relationship of soil should be evaluated properly corresponding
to the presumed scale of shear strain amplitude of the ground during an earthquake. Generally,
dynamic shear stress-strain relationship of soil is divided into hysteresis curves and their skeleton
curve as shown in Fig.C7.3.3. This skeleton curve shows a remarkable nonlinearity when the shear
strain amplitude becomes large. In order to obtain a hysteresis model representing suchcharacteristics, in many cases, the skeleton curve is expressed by a function such as a hyperbolic
one and Masing rule is applied to the hysteresis curve. While constructing a hysteresis model of thesoil, the strain dependency of elastic shear coefficient and damping factor of the soil may beevaluated by in-situ tests such as PS logging and laboratory tests such as deformation characteristics
test using a sample of the concerned ground.
When the ground liquefies, the stiffness of the soil is affected by the magnitude of excessive
pore water pressure. Therefore, the reduction in strength and stiffness of the soil caused by the riseof the excessive pore water pressure should be considered in addition to shear stress-strain
relationship. An effective stress analysis is conducted for taking such a phenomenon into
consideration. Not only a dynamic deformation characteristics test but also a liquefaction strength
test is necessary to perform an effective stress analysis.
G 0   a   a   a12 ryHysteresis curve
(l di

1

1

G0

G

 a,  a )

skeleton curve



1

y

  a ,  a 

Hysteresis curve(

Fig. C7.3.3

7.3.4.4l di)  a 

G 0


r

G 0   a   a1
2 r

Example of the dynamic shear stress-strain curve of the soil

Ground model to analyze a structure independent of the ground(1) The boundary between the structures and the ground may be modeled by nonlinear
springs to account for interaction between the foundation of structures and the ground.
Generally, these springs should be modeled in vertical, horizontal and rotating directions.
(2) The interface between the ground and the foundation or the underground structure
may be modeled using nonlinear springs, taking into consideration the characteristics ofthe surrounding ground.

113

Standard Specifications for Concrete Structures-2007, Design(3) The boundary between the ground including the foundation and the structure on
the ground may be modeled using nonlinear springs that support the structure on the
ground.
(4) An analysis model of the ground to be used to take earthquakes into consideration
should be a one-dimensional layered continuum model or a finite element model.

[Commentary] (1), (2) and (3) In general, the nonlinear support springs that support
superstructures are vertical, horizontal and rotation springs. They should be arranged appropriately
according to the ground condition, the form of the foundation and the bearing capacity
characteristics.

As to the nonlinear support springs that support underground structures, a normal directional
spring at the interface between the structure and the ground as well as a tangential one should beconsidered. In this case, the characteristics of the springs should be determined appropriately
corresponding to the ground condition, bearing capacity of the ground and the form of the structure.
For design of the support springs, the load-displacement relationship considering the nonlinearity of
the ground should be applied.
When determining the restoring force characteristics of a support spring, it is necessary to use
the load–displacement relationship reflecting the nonlinearity of the ground or of the ground and thestructure as a skeleton curve and take appropriate hysteresis characteristics into consideration.
In such cases, support springs may be defined to allow for the influence of dissipation damping
or internal damping appropriate for the foundation structure. The purpose of the modeling describedhere is to calculate the response values of a surface structure. When calculating the response valuesof a structural foundation, therefore, it is necessary to use a method that makes it possible to allow
for the influence of the vibration mode of the foundation such as modeling the ground and thestructural foundation with springs and masses.
(4) As dynamic analysis methods applicable to the ground, time history response analysis in thetime domain and response analysis in the frequency domain are generally used. Time history
response analysis, which keeps track of the nonlinear stress–strain relationship of soil according totime history, takes considerable time for response value calculation. Response analysis in thefrequency domain approximates the nonlinear stress–strain relationship of soil by the equivalentlinearization method. It has been pointed out, therefore, that the degree of agreement with groundbehavior falls in a large strain range. When conducting a dynamic analysis, therefore, it is necessary
to select an appropriate analysis method according to the soil strain level.
The equivalent linearization method is a method of response analysis in the frequency domain.
This method is often used in cases where the shear strain amplitude of the ground during anearthquake is relatively small (about 10−3 or smaller). An equivalent linear model is defined as a
viscoelastic body reflecting the stiffness and viscosity of soil. Equivalent shear moduli and viscousdamping ratios during ground motion are determined according to the amplitude of shear strain(effective strain) occurring during an earthquake. In the equivalent linearization method, linear
analysis using an equivalent linear model is repeated until the shear strain amplitude converges. The
method, therefore, is a practical approach because stable solutions can be obtained and computation
time is short.
When determining time history acceleration waveforms at a specified depth, it is common
practice to divide the ground around the structure of interest above the engineering bedrock surface
into layers or finite elements. If the ground around the structure consists of horizontal layers,
response analysis can be simplified by using a one-dimensional ground model.
114

Chapter 7 Calculation of Response Values

7.4 Calculation of Design Response Values
7.4.1 General(1) Design response values shall be calculated by converting the response values
obtained as described in Section 7.3 into verification indices by an appropriate method.
(2) Design response values of materials, design crack width and design response
values such as the displacement and deformation of structural members shall becalculated taking structural characteristics into account. In general, calculation shall bemade by the method described in this section by using the design sectional forces, etc.,
described in Section 7.3.

[Commentary] (1) There are two methods of structural modeling: the method of using
fiber-model-based sectional forces for calculation and the method of calculating stress, strain, etc.,
as response values by the finite element method. This section describes a method for calculating
design response values by converting sectional forces to verification indices such as material stress.
If stress or strain is used as verification indices or stress or strain response values are converted toverification indices in the finite element method, it is necessary to conduct a careful study because
at present there are various restrictions.

7.4.2 Calculation of sectional forces
7.4.2.1 Calculation of sectional forces in bar members by the finite element method(1) Computation of axial forces and flexural moments in the member shall be calculatedby the integration of the stress distribution obtained from the strain distribution in the
cross section, on the basis of following assumptions:i) Strain distribution across a cross section is linearii) Hysteresis is included in the stress-strain relationships of concrete and re-bar. In
general, the relationships used in the structural analysis may be used.
(2) Shear forces may be computed using the equilibrium condition for distribution of
flexural moment obtained in (1).

[Commentary] (1) and (2) The method of calculating sectional forces from the results ofstructural analysis that uses the constitutive equation for the stress–strain relationship is the same as
the assumption used to calculate the flexural strength of bar members. The validity of Navier's
hypothesis decreases in a large deformation range, but because calculated values are conservativewith respect to the response values of steel strain and the load-carrying mechanism along the axis of
the member, the application of Navier's hypothesis is allowed even in a large deformation range.

In general, compared with the flexural deformation component, the deformation component in
the out-of-plane shear direction of a bar member is small. This component, therefore, may beignored. If, however, the length of the member is small relative to the cross sectional dimension of
the member or if shear cracks are widely distributed in the member, it is recommended that either amodel capable of allowing for shear deformation be used or the shear deformation component be
added to the response displacement. In such cases, deformation may be determined according to
Section 7.4.5.
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Standard Specifications for Concrete Structures-2007, Design

7.4.2.2

Calculation of sectional forces in the case where a fiber-based model Is used

If a fiber-based model of a structural member is used, sectional forces obtained fromstructural analysis may be used as calculated sectional forces in the member.

[Commentary] If an analysis method that expresses nonlinearity with the relationship between
bending moment and the rotation angle, etc., is used, sectional forces obtained as a result ofstructural analysis may be used as are as calculated sectional forces in the member. If a fiber modelis used, sectional forces derived by replacement from element stresses may be used as in the casewhere the finite element method is used.

7.4.3 Calculation of material stress
Design stresses in materials under normal service conditions shall be calculated as
described in Items (1) to (3):(1) Design stresses in materials due to bending moment or due to bending moment
and axial force shall be calculated on the basis of the assumptions described in (i) to (iv):(i) Fiber strain is proportional to the distance from the neutral axis of the member
cross section.
(ii) In general, concrete and steel are assumed to be elastic.
(iii)Tensile stress in concrete is negligible.
(iv)Elastic moduli of concrete and reinforcement may be obtained in accordance with
5.2.5 and 5.3.4.
(2) Design stress in torsion reinforcement due to torsion shall be calculated from Eq.
7.4.3. Design response values in shear reinforcement due to shear force shall becalculated from Eq. 7.4.1 and Eq. 7.4.2.
σ wrd σ wpd where,( V pd  Vrd  k r  Vcd )sVrd
Aw  z  ( sinθ  cosθ ) V pd  Vrd V cd( V pd  Vr d  k r  Vcd )sV pd  Vcd

Aw  z  ( sinθ  cosθ ) V pd  Vrd  Vcd(7.4.1)(7.4.2)σwrd: design variable stress in shear reinforcement

σwpd: design stress in shear reinforcement due to permanent load

Vpd

: design shear force due to permanent load

Vrd

: design shear force due to variable load

Vcd

: design shear force acting on a bar member without shear
reinforcement; as per Section 9.2.2.2. Where, parameter b may betaken as 1.0 and 1.3 in the verifications for serviceability and fatigue
116

Chapter 7 Calculation of Response Values

failure, respectively.

kr: coefficient to take into account the effect of variable loads. It may,in general, be taken as 0.5. However, it may be taken as 1.0 for
members without significant effect of fatigue loadss: spacing of shear reinforcement

Aw: total cross-sectional area of shear reinforcement in section sθ: angle between shear reinforcement and member axisz

: distance between the resultant of compressive forces and thecentroid of tension reinforcement. It may be taken as d/1.15

d: effective depth(3) Design stress in torsion reinforcement due to torsion shall be calculated from Eq.
7.4.3.

w 

M tpd  0.7 M t1
M t 2  0.7 M t1

where, σwpd

 f wd

(7.4.3): design stress in lateral torsion reinforcement due to permanent load

M tpd

:

design torsional moment under permanent loads

M t1  M tcd 1  0.8V pd V yd 
M t 2  0.2M tcd V pd V yd  M tyd 1  V pd V yd M tcd : design pure torsion capacity in the case where there is no torsion
reinforcement; to be determined in accordance with Section 9.2.3.2,
where the material factor γc for concrete and the member factor γb areusually 1.0

M tyd : design torsion capacity determined by yielding of torsion reinforcement;
to be determined in accordance with Section 9.2.3.3, where the member
factor γb is usually 1.0

V pd

:

design shear force produced by permanent load

V yd

:

design shear capacity of a bar member; to be determined inaccordance with Section 9.2.2.2, where the material factor γc for
concrete and the member factor γb are usually 1.0

f wyd : design tensile yield strength of transverse torsion reinforcement[Commentary] (1) For the calculation of concrete and steel stresses in reinforced concrete
structures under normal service conditions, conventional assumptions are indicated. If the finite
element method or an analysis method that directly uses the material stress–strain relationship suchas a fiber model is used as a structural analysis method, material response values may be calculated
as described in this section by using sectional forces obtained in accordance with Section 7.4.2.

117

Standard Specifications for Concrete Structures-2007, Design(2) If both vertical stirrups and bent-up bars are used for shear reinforcement, stresses in them
may be calculated by using Eqs. (C7.4.1) - (C7.4.4).
vertical stirrups :  wrd  wpd bent bars :  brd  bpd V pd  Vrd  k rVcd3

Aw z Ab cos b  sin  b ssb
V pd  Vrd  k rVcd3

Aw z Ab cos  b  sin  b 

s
sb

V pd
V pd  Vrd  Vcd
V pd  Vcd
V pd  Vrd  Vcd

V pd  Vrd  k rVcd
V pd

Aw z
A cos b  sin  b  V pd  Vrd  Vcd bs cos b  sin  b sb
V pd  Vrd  k rVcd
V pd  Vcd
Aw z
A cos b  sin  b  V pd  Vrd  Vcd bs cos b  sin  b 
sb(C7.4.1)(C7.4.2)(C7.4.3)(C7.4.4)

where, σwrd : design variable stress in vertical stirrups
σwpd : design stress in vertical stirrups due to permanent load
σbrd : design variable stress in bent bars
σbpd: design stress in bent bars due to permanent loads

: spacing of vertical stirrupssb: spacing of bent bars

Aw

: total cross-sectional area of vertical stirrups in section sAb: total cross-sectional area of bent bars in section sb

b: angle between bent bar and member axis

(3) Eq. 7.4.3 was derived by assuming that stress in lateral torsion reinforcement increases ascracking occurs and reaches fwyd at failure. A previous study has shown that the torsion crack width
calculated by assuming that when torsional moment acts repeatedly after the occurrence of cracking,stress in lateral torsion reinforcement becomes zero at or below 70% of the cracking moment Mtc
and increases linearly as torsional moment increases thereafter shows close agreement withexperimental results.
In cases when flexural moments are applied to a beam having torsional cracks on both the upperand lower sides, or in cases when torsional moments are applied to a beam that has flexural cracks
on both its upper and lower sides, the direction of principal tensile stress due to torsional moment
and the direction of principal tensile stress due to flexural moment do not coincide. Therefore, theeffect of their interaction is less than the interaction between the torsional moment and shear force.
Further, in cases of vertically long rectangular section subjected to torsional moment, tensilestresses on upper and lower sides are smaller than those on the right and left sides. Thus, the effectof torsional moment on the stresses in longitudinal flexural reinforcement is considered small.
118

Chapter 7 Calculation of Response Values

Hence, the examination may be omitted in cases when a beam is subjected to combined loading due
to flexural and torsional moments.
Cracking associated with compatibility torsion does not need to be considered mainly because
torsion moment is released considerably owing to initial cracks, because such cracks, which occur
under normal service conditions, are relatively small and crack width does not tend to increase andbecause each member has at least a minimum amount of shear reinforcement so as to prevent
torsion cracking. The use of U-shaped stirrups in a beam, however, may cause excessively large
cracks on the upper surface of the beam. For this reason, if the height of a rectangular cross section
is not greater than three times the member width, closed stirrups should be used.

7.4.4

Examination for flexural cracks(1) The crack width, w, may be calculated using Eq.(7.4.4).

   pe    csd w  1.1k1 k 2 k 3 4c  0.7c s    se  orE p 
 E s where,(7.4.4)k1:

a constant to take into account the effect of surface geometry of
reinforcement on crack width. It may be taken to be 1.0 for deformed
bars, 1.3 for plain bars and prestressing steel.

k2:

a constant to take into account the effect of concrete quality on crack
width. It may be calculated using Eq.(7.4.5).

k2 

15
 0 .7f c  20(7.4.5)f c

:compressive strength of concrete (N/mm2). In general, it may be taken
to be equal to the design compressive strength, f cd .

k3:

a constant to take into account the effect of multiple layers of tensile
reinforcement on crack width. It may be calculated using Eq.(7.4.6).

5n  2 
7n  8k3 n(7.4.6):

number of the layers of tensile reinforcement.

c:concrete cover (mm).

cs:

center-to-center distance of tensile reinforcements (mm).

:

diameter of tensile reinforcement (mm).

 ' csd:

compressive strain for evaluation of increment of crack width due toshrinkage and creep of concrete.

 se

:

increment of stress of reinforcement from the state in which concrete
stress at the portion of reinforcement is zero (N/mm2).

119

Standard Specifications for Concrete Structures-2007, Design

 pe

:

increment of stress of prestressing steel from the state in whichconcrete stress at the portion of reinforcement is zero (N/mm2).

(2) In the examination for flexural cracks, in principle the reinforcement or prestressing
steel nearest to the surface of concrete, should be considered, and their stresses should
be calculated in accordance with Section 7.2.

[Commentary] (1) Flexural cracking in reinforced and prestressed concrete is affected by various
factors. According to the previous studies, the main factors are the types of reinforcement, increaseof stress in reinforcement, concrete cover, effective cross sectional area of concrete, diameter ofreinforcement, ratio of reinforcement, number of layers of reinforcement, surface geometry of
reinforcement, quality of concrete, magnitude of prestress, etc.

Equation (7.4.4) has been formulated on the basis of the existing equations for prediction of
crack width and results of recent studies. A more appropriate equation for crack width calculation
should be used in cases when reinforcement of different diameters are used together, high tensile
strength deformed bars with strength of 490 N/mm2 or more are used, and the effect of repeatedload is significant
Stresses increment in reinforcement,  se (or  pe ), should be computed considering the stateof stress of both concrete and reinforcement. When the concrete stress at the same position of thereinforcement induced by stress resultant is in compression,  se (or  pe ) should be zero even if
stress in the reinforcement increases due to stress resultant. When concrete stress changes fromcompression to tension under stress resultant  se (or  pe ) is defined as the stress difference
between the reinforcement stress when concrete stress changes from compression to zero and thereinforcement stress induced by stress resultant. In case that autogenous or drying shrinkage ofconcrete my not be neglected,  se (or  pe ) is defined as the stress difference between thereinforcement stress when concrete stress changes from tension to zero and the reinforcement stressinduced by stress resultant. The stress in the reinforcement when concrete stress changes fromtension to zero depends also on the ratio of reinforcement and may be more than reinforcement
stress corresponding to compressive strain of 300x10-6. However, it can be reduced to a value lessthan 200x10-6 if appropriate curing conditions for concrete are provided.
If shrinkage-compensating concrete is used, unlike in the case of shrinkage, the state ofcompression of concrete is regarded as the initial state. The amount of change, therefore, in the steel
stress caused by sectional forces from the steel stress at the time the concrete stress reaches zerofrom compression is taken as the amount of increase σse (or σpe). The steel stress occurring until theconcrete stress reaches zero from compression is calculated as the sum of the steel strain
corresponding to the chemical prestress introduced into the concrete and the chemical prestrain
multiplied by Young's modulus. Because those values are affected by such factors as concrete mix
proportions, the shape and dimension of the member, the state of reinforcement, curing method andenvironmental conditions, it is necessary to determine those values appropriately according to past
performance records, reliable literature and test results. If experimental results are not used, thosevalues may be determined by applying the concept of the amount of work. For
shrinkage-compensating concrete, the calculation of steel stress occurring until the concrete stressreaches zero from compression may be omitted. In such cases, ε'csd may be reduced according to thechemical prestress introduced by expansion and the elastic strain of concrete. If compressive
strength is higher than about 60 N/mm2, chemical prestress and chemical prestrain may be
calculated through linear creep analysis allowing for the time-dependent mechanical characteristics
of concrete.

120Chapter 7 Calculation of Response Values

Spacing of flexural cracks is affected by the bond between the reinforcement and the concrete.
Coefficient k1 in Eq.(7.4.4) is a constant to represent the effect of surface geometry of
reinforcement, which is one of the bond factors affecting crack width. Equation (7.4.5) should
basically be applied to members with deformed bars. In the case of plain bars and prestressing
steel, although changes in the crack width have not been clarified, k1 may tentatively be taken tobe 1.3. In the case of prestressing steel in pretensioned members, k1 may be set to a value notgreater than 1.3 (but not less than 1.0) provided its surface geometry provides good bonding
Coefficient k 2 in Eq.(7.4.4) is a constant to represent the effect of changes in bonding
characteristics between the reinforcement and the concrete due to changes of concrete quality on
crack width. It has been reported that concrete with little material segregation and having a dense
pore structure, possesses not only high resistance to cracking but also reduces crack width due togood bonding. Equation (7.4.5) expresses the effect of concrete quality on crack width in terms ofcompressive strength of concrete that represents properties of hardened concrete. Even for
concrete with a low strength, k 2 may be reduced to 0.9 if bleeding of concrete is kept small andhomogenous concrete cover is assured.
Coefficient k 3 in Eq.(7.4.4) is a constant to represent the effect of the reinforcement in thesecond and higher layers in members with multi layers of reinforcements on the surface crack width.
Equation (7.4.6) has been formulated by simplifying the term representing reinforcement layers in
the prediction equation for crack width in a previous study.

 ' csd in Eq.(7.4.4), which represents the effect of shrinkage and creep of concrete on crack
width, should be determined with the consideration of shape of cross section of the member,environmental condition, magnitude of stress, and others. Since the value of  ' csd differ in eachverification, it is necessary to calculated by using the value listed in 8.3.3, 10.3.2, 15.4.4, etc.
Loads used in calculation of  se (or  pe ) shall be determined considering time-dependentchanges in crack width due to sustained and repeated application of variable loads, duration ofsustained crack opening and other factors. For structures where the ratio of permanent to totalloads is small, and the frequency of application of variable loads is high, the effect of variable loads
should be set at a higher level, while for structures where the ratio of permanent to total loads ishigh and the frequency of application of variable loads is low, the effect of permanent loads may be
set to a smaller level.
The method for examination of crack width given here is not applicable to cases where
members have only prestressing steel as longitudinal reinforcement, because there have been only afew studies on crack widths in prestressed members without longitudinal reinforcing steel bars.
Further, deformed bars should be used as longitudinal reinforcement in prestressed concrete,because only limited experimental data with the use of plain bars is available, and deformed bars
are considered effective for the purpose of crack control.
(2) In cases when longitudinal reinforcement is provided in several layers, in general, the stressin the reinforcement nearest to the concrete surface should be used. In such cases, although thestress acting at the centroid of reinforcement may be taken, to simplify the computation, coefficient,k3, in Eq.(7.4.4) that accounts for the presence of several layers of reinforcement, shall be taken as
1.0, regardless of the number of layers. In the case of thin members with several layers of
reinforcement, the stress of reinforcement nearest to the surface is preferably used, as using themethod described above, may provide results, which may not be on the conservative side.

121

Standard Specifications for Concrete Structures-2007, Design

7.4.5 Examination for displacement and deformation of member(1) Short-term displacement and deformation of concrete members without cracks may
be computed based on the theory of elasticity assuming that the gross cross section iseffective.
(2) Short-term displacement and deformation of concrete members with flexural cracks
shall be computed considering reduction of stiffness due to the cracks.
(3) Long-term displacement and deformation of concrete members shall be computed
considering effects of creep due to permanent loads, shrinkage and crack of concrete.
(4) Short-term shear displacement and deformation of concrete members with shear
cracks shall be computed considering reduction of stiffness due to the cracks.

[Commentary] (1) In cases when precise computation of displacements and deformations are notrequired, displacements and deformations of cracked reinforced and cracked prestressed concrete
members, may be computed using the moment of inertia, I g , of a gross cross section assuming no

flexural crack.
(2) and (3) In computation of short-term or long-term displacements and deformations, for cases
when reduction of stiffness due to flexural cracking and the influence of creep and shrinkage aretaken into account, the effective flexural stiffness evaluated using Eq.(C7.4.5) or Eq.(C7.4.6) may
be used.
(i) In cases when the effective flexural stiffness is assumed as a function of flexural moment4M 
E e I e   crd  M d  1Ee I g
M csgM d  P d p  c g   M  4 
 1   crd    M d   1 

E e I cr
M csc r
M d  P d p  ccr (C7.4.5)(ii) In cases when the effective flexural stiffness is assumed constant in the longitudinal
direction3

 M crd E e I e  M
 d max  1 

where, Ee

Ee I g
M csgM d max  P d p  c g 3  Mcrd    1    M d max   1 

E e I cr
(C7.4.6)
M csc r
M d max  P d p  ccr : effective elastic modulus which can be computed using Eq.(C7.4.7)

Ee 

E ct
E ct

1   1  E ct E c  28

Ect: Young's modulus when dead loads are applied

Ec: Young's modulus at the age of 28 days

(C7.4.7)

  : creep coefficient since dead loads is applied, which is computed using Young's
modulus at the age when the dead loads start to act

122Chapter 7 Calculation of Response Values

 28

:

Ie

: effective moment of inertia of transformed cross section for either short-termor long-term

creep coefficient since dead loads are applied, which is computed using
Young's modulus at the age of 28 days

M crd : critical flexural moment when a flexural crack occurs in the cross section; orthe flexural moment when flexural tensile stress in concrete at the extreme
tension edge, in which axial force and prestressing force are considered, isequal to flexural cracking strength, fbck, where c and b are set equal to 1.0 ingeneralMd: design flexural moment to be used in the computation of either short-term or
long-term displacements and deformations

M d maxP:maximum value of design flexural moment to be used in the computation ofeither short-term or long-term displacements and deformations: axial force or prestressing force in either short-term or long-term

M csg: apparent flexural moment due to shrinkage in gross section and restraint byreinforcements, which can be computed by Eq.(C7.4.8)

 I ' sg
I sg
I pg 
M csg  E s  ' cs
 c g  d ' d  c g d p  c g 

(C7.4.8)

M csc r : apparent flexural moment due to shrinkage in the section excluding concrete
under tensile stress (hereafter "cracked section") and restraint byreinforcements, which can be computed using Eq.(C7.4.9)
 I '
I pcr I
M csc r  E s  scr  scr 
 ' cs
 c sr  d ' d  ccr d p  ccr Ig:

I ' sg: moment of inertia of compression reinforcement about the centroid of gross
cross section for either short-term or long-term

I sg: moment of inertia of tensile reinforcements about the centroid of the gross
cross section for either short-term or long-term

I pg

:

I cr

: moment of inertia of cracked cross-section around the centroid of cracked
cross-section for either short-or long-term

I ' scr :moment of inertia of gross cross section about
short-term or long-term(C7.4.9)
its centroid for either

moment of inertia of the prestressing steel about the centroid of gross crosssection for either short-term or long-term

moment of inertia of compression reinforcement around the centroid ofcracked cross-section for either short- or long-term

I scr: moment of inertia of tensile reinforcement around the centroid of cracked
cross-section for either short- or long-term

I pcr: moment of inertia of prestressing steel around the centroid of cracked crosssection for either short-term or long-term

cg:

distance from the compression edge to the centroid of gross cross section for
either short-term or long-term

ccr:

distance from the compression edge to the centroid of cracked cross section for123

Standard Specifications for Concrete Structures-2007, Design

either short-term or long-termd':distance of compression reinforcement from the extreme compression fiberedge tod:distance of tensile reinforcement from the extreme compression fiber

dp:

distance of prestressing steel from the extreme compression fiber

 'cs

:

shrinkage strain

Both Eq.(C7.4.5) and Eq.(C7.4.6) can be used for practical computation of short-term andlong-term displacements and deformations of both cracked and uncracked reinforced andprestressed concrete members. The effect of creep is considered in terms of the effective elastic
modulus. It is assumed that shrinkage of concrete is induced uniformly across the cross-section.
Prestressing force is taken as part of permanent loads. In computing deformations due topermanent loads, though bonded prestressing steel may be treated in a manner similar to ordinary
reinforcing steel, unbonded prestressing steel may be neglected. Time-dependent changes intension stiffness of concrete are neglected as approximate computation though, in reality, bonding
stress reduces slightly with time.
Flexural stiffness of a member without flexural cracks may be obtained using Eq.(C7.4.5) or
Eq.(C7.4.6), assuming that M crd  M d or M crd  M d max .
In the computation of short-term displacements and deformations, both the creep coefficient andshrinkage of concrete may be assumed to be zero. The effect of reinforcement may be neglectedin computing approximate values for moment of inertia of gross section.
In computation of long-term displacements and deformations, creep coefficient and shrinkage ofconcrete may be calculated using the concrete age since the time of application of dead loads. The
effect of reinforcement shall be taken into account in computing the moment of inertia of the grosssection. In cases when the age when prestressing is introduced and the age when loading starts are
considerably different, or in cases when total deformation under dead and live loads is required, it isadvisable to consider the effect of the difference in ages at application of such loads for a precise
computation of displacements and deformations.
In cases when Eq.(C7.4.6) is applied to continuous beams, M d max may be taken as the
maximum positive flexural moment.
Displacements and deformations in the case of (i) may be obtained using numerical integrationof curvature at each cross section, M d  Pd p  ce  E e I e , computed with Ee I e obtained using

Eq.(C7.4.5). The distance ce to be used in computation of displacements and deformations may beevaluated using either Eq.(C7.4.10) or Eq.(C7.4.11).
(i) In cases when the effective flexural stiffness is assumed to be a function of flexural moment,4  M  4 
 M crd  c g  1   crd  c cr
c e    M d  
 Md 

(C7.4.10)(ii) In cases when the effective flexural stiffness in the longitudinal direction is assumed to beconstant,33  M M crd 
crd   c cr c g  1  c e    M d max  
 M d max (C7.4.11)

124

Chapter 7 Calculation of Response Values

Approximate deflections in statically indeterminate structures, such as continuous beams, may
be computed using numerical integration for each member, using the flexural moment obtained
from elastic analysis
Equation (C7.4.6) in (ii) is originally for computing deflection in cases when the distribution of
flexural moment is parabolic. Though in a strict sense, the power term in the equation should
depend on the shape of distribution of flexural moment, third power has been adopted because it
had been found that using the third power does not introduce major errors.
In cases when an axial force is applied, the ratio of flexural moments in Eq.(C7.4.5) andEq.(C7.4.6) may be substituted by the ratio of the resulting tensile forces in the reinforcement.
In cases when there are no cracks in cross sections, approximate long-term displacements anddeformations may be computed as the sum of short-term displacements and deformations due topermanent loads and their creep components as given in Eq.(C7.4.12).

 l  1    ep
where,  l

 ep(C7.4.12): long-term displacements and deformations: short-term displacements and deformations due to permanent loads(4) Though shear stiffness of concrete members is reduced after onset of flexural or tensile
cracks, the effect of the reduction of shear stiffness on deformations of members is, in general,
small compared with the effect of flexural stiffness. The reduction of shear stiffness can becomputed using methods similar to those used to compute reduction in flexural stiffness. It has
been found from experimental work, however, that since shear stiffness of members is substantiallyreduced after shear cracking, deformations after shear cracking are underestimated when aconventional computational method in which only reduction of flexural stiffness is taken into
account, is used.
In the computation of shear deformation of members with shear reinforcements subjected to
flexural shear, the following method may be used after flexural and shear cracks occur.
(i) After flexural cracking and before shear cracking, shear deformation,  s , may be computed
using Eq.(C7.4.13), assuming a reduced shear stiffness, GAe , as given in Eq.(C7.4.14).
3
3
  M
  M
crd 
crd    Acr 1     GAg
GAe  G Ag   M d max   M d max  s  kVddx
GAewhere, G(C7.4.13)(C7.4.14): shear elastic modulus, which may be assumed to be the same as the shear
elastic modulus of concrete, Gc

Ag: gross cross-sectional area before flexural cracking

Acr: area of flexural compression zone in the cross section after flexural crackingk: coefficient depending on shape of cross section

125

Standard Specifications for Concrete Structures-2007, Design

Vd: design shear force(ii) After shear cracking, whether flexural cracks have occurred or not, the shear deformation
may be computed by Eq.(C7.5.14), where, as shown in Fig. C7.4.1, shear deformation of themember may be taken as the deformation of the truss mechanism, assuming concrete as thecompression diagonal member (BE in the figure) and shear reinforcements as the tensile diagonal
member (CE in the figure).





Vsd
Vsd s
1
 dx

 s   dx  

2 
4


sin
E
b


E
z cot   cot  
 c w
E w  Aw  c Ace  sin 3  
Ew





(C7.4.15)

where,   : shear strainz: distance from compression resultant to centroid of tension reinforcement. In
general it may be taken as d / 1.15

: angle between compression diagonal member and longitudinal axis of member.
It may be computed using Eq.(C7.4.16)

  45  k

Vd  Vcdbw d(C7.4.16)k  3.2  7800 pt p w a d (C7.4.17)

pt: ratio of tensile reinforcement, As /(bw d )pw: ratio of shear reinforcement, Aw /(bw s )a: shear span, which is the distance from loading point to the front of the supportd: effective depthbw: width of web: angle between shear reinforcement and the longitudinal axis of member

Vsd: design shear capacity of shear reinforcements, Vd  Vcd

Vcd: design shear capacity from sources other than shear reinforcements. It may
be computed using Eq.(6.3.3),where the material factor,  c , may be taken tobe equal to 1.0

Ec: elastic modulus of concreteEw: elastic modulus of shear reinforcement

Aw: area of shear reinforcements provided over the spacing, sAce:area of concrete around the reinforcements effective as tensile diagonal126

Chapter 7 Calculation of Response Values

member, which may be computed using Eq.(C7.4.18)
Ace  Aceo Vc V 

3Aceo :(C7.4.18)

Ace immediately after shear cracking

E

A

D
Z

θ
B

z cot   cot  

α
C

B’

C’

Fig. C7.4.1 Shear deformation of truss mechanism(iii) Tensile force in the tension reinforcement increases after formation of shear cracks as
explained by the truss mechanism. This phenomenon is known as the "moment shift". The
increase in deformation due to this increase in tensile force may be computed as flexural
deformation assuming that flexural moment, which induces the same magnitude of tensile force inthe reinforcement, is applied. The increment of tensile force may be computed using Eq.(C7.4.19).

sin     VsT  cot  
2 sin  sin  
(C7.4.19)

127

Standard Specifications for Concrete Structures-2007, Design

CHAPTER 8 VERIFICATION OF DURABILITY

8.1

General(1) Every structure shall maintain the required performance throughout the design
service life of the structure.
(2) Verification to ascertain that the required performance of a structure will not be lost
because of steel corrosion due to chloride attack or carbonation or concrete deterioration
due to freezing damage or chemical attack may be made by the methods described in thischapter. If two or more of these occur in combination, their influence should be taken into
consideration.

[Commentary] (2) In order to maintain the required performance of a structure throughout its
design service life, it is common practice to prevent the deterioration or changes in the state of thematerials in the structure due to environmental factors or to design the structure so that material
deterioration can be kept within the range in which the performance of the structure does notdecline. This chapter describes methods for checking whether a structure meets theserequirements with respect to representative types of deterioration of concrete structures, namely,
steel corrosion due to chloride attack and carbonation and concrete deterioration due to freezing
damage and chemical attack. Study methods associated with alkali–aggregate reaction andchloride attack caused by chloride ions existing in concrete mixes are described in the Construction
section of this Specification because they should be considered at the stage at which materials to be
used are selected.
A structure can be deemed to be capable of meeting the safety, serviceability and earthquake
resistance requirements throughout the design service life if (1) the structure meets the verification
criteria described in this chapter to ensure that problems due to the deterioration of materials in the
structure will not occur during the design service life and (2) the structure meets the safety,
serviceability and earthquake resistance criteria indicated in Chapters 9, 10 and 11.
Although factors affecting the durability of a concrete structure may act on the structure
independently, usually two or more of those factors act in combination. In many cases, evaluating
the influence of dominant factors independently suffices. There is as yet no establishedverification technique for evaluating the effect of a combination of two or more factors. Thissection, therefore, describes performance verification methods for individual factors. If a structure
is subjected to a combination of two or more factors, the deterioration of the structure may be
accelerated. If a high degree of influence is expected, therefore, it is desirable that control
measures such as using a large factor of safety be taken.
Even in cases where the performance of a structure has deteriorated over years of use, there is
no problem if the performance requirements are met. Research and development efforts in the
coming years make highly reliable prediction of structural deterioration possible, and performanceverification technology for structures that takes changes over time into consideration may beestablished. If such changes occur, it may become no longer necessary to assume no deterioration
over time, and it may make economical design with a high degree of freedom possible.

128Chapter 8

8.2

Verification of Durability

Environmental Factors(1) The degree of dryness should be taken into consideration when predicting the
progress of carbonation of concrete.
(2) The influence of adventitious chlorides on the penetration of chloride ions into theconcrete may be evaluated on the basis of the amount of adventitious chlorides arriving at
the structure.
(3) Environmental factors related to freezing damage shall be determined according to
the number of freeze–thaw cycles and the water content of concrete.
(4) Environmental factors related to chemical attack shall be determined according to
the type of chemically corrosive substances and the intensity of chemical attack.

[Commentary] (1) The carbonation of concrete is caused by carbon dioxide penetration from theatmosphere. Because civil engineering structures are in many cases constructed outdoors, thedegree of dryness of concrete, which affects carbon dioxide penetration, is taken into consideration.
This means that the rate of carbonation of concrete exposed to sunlight and located on the south
side of a structure tends to be higher than that of concrete in a rainfall-affected environment or a
relatively humid environment.
When predicting the rate of carbonation by the method described in Section 8.3.6, the influenceof environmental factors on the rate of carbonation may be evaluated in terms of a factor (βe)
indicating the degree of environmental influence shown in Table C8.2.1.

Table C8.2.1

Degree of environmental influence on prediction of the carbonation of
concrete
Environmental conditions

Factor indicating the degree ofenvironmental influence (e)Relatively dry environment

1.6

Relatively humid environment

1.0(2) When chloride ion penetration into concrete is predicted by the method described in
Section 8.3.7, the influence of adventitious chlorides on the rate of chloride ion penetration isexpressed with chloride ion concentration at the concrete surface. The amount of airborne
chlorides deposited on the concrete surface is affected by such factors as the climate of the regionin which the structure is constructed, the distance and height from the coast, topography and winddirection. In general, as the amount of airborne chlorides increases, the amount of chloride ionsthat penetrate into concrete increases. Even when the amount of airborne chlorides is large,
however, the amount of chlorides that penetrate into concrete may not become large if chlorides
are washed off by, for example, rain. Also, it is generally known from measurement results thatchloride ion concentration at the concrete surface of a structure is affected by not only theenvironmental conditions surrounding the structure but also the quality of concrete. When
conducting verification for individual structures, it is desirable that values of chloride ion
concentration at the concrete surface, based on performance data on similar structures andmeasurement data, that accurately express the environmental conditions surrounding the structure
129

Standard Specifications for Concrete Structures-2007, Design

be used.
If neither performance data on similar structures nor measurement data are used, chloride ion
concentration at the concrete surface may be determined from Table C8.2.2 according to the typeof the area in which the structure is located and the distance from the coast.

Table C8.2.2

Chloride ion concentration C0 at concrete surface (kg/m3)
Splashzone

Region withhigh airborne
chlorideconcentration
Region withlow airborne
chlorideconcentration

Hokkaido,
Tohoku,Hokuriku,
Okinawa
Kanto, Tokai,
Kinki,
Chugoku,
Shikoku,
KyushuDistance from coast (km)Nearshoreline

0.1

0.25

0.5

1.0

9.0

4.5

3.0

2.0

1.5

4.5

2.5

2.0

1.5

1.0

13.0

With respect to height in the coastal zone, C0 may be calculated assuming that a height of 1 m
corresponds to a distance of 25 m from the shoreline.
(3) Major factors affecting the occurrence and acceleration of freezing damage are freeze–thaw
cycles and the water content of concrete. When considering environmental factors affecting
freezing damage, it is therefore necessary to take into consideration such factors as the lowest
temperature, the number of freeze–thaw cycles and meteorological phenomena that supply water tothe concrete. Since, however, there is as yet no established verification method that incorporates
these factors, combinations of the meteorological phenomena and the states of exposure of thestructure listed in Table C8.2.3 may be regarded as environmental factors affecting freezing
damage.
Table C8.2.3

Environmental factors affecting freezing damage

Meteorological phenomena
State of exposure of structure• Environment with frequent freeze–thaw• Continuously or frequently saturated withcycleswater *• Environment in which below-zero• Normal state of exposure (other than the cases
temperature is rarementioned above)* Parts of a structure such as water channels, water tanks, abutments, piers, retaining walls andtunnel lining that are close to a water surface and are saturated with water, and parts of astructure such as girders and floor slabs besides those mentioned above that are distant from awater surface but are saturated with water because of snowmelt, flowing water, splashes ofwater, etc.
(4) Substances that chemically attack concrete can be largely classified, according to themechanisms of attack, into two categories. One category includes substances that react withcement hydrates in the concrete to alter them into soluble substances so as to cause the concrete todeteriorate. Many acids, some types of inorganic salts and corrosive gases such as hydrogen
130Chapter 8

Verification of Durability

sulfide belong to this category. The other category includes substances that react with cement
hydrates in the concrete to produce expansive compounds so as to cause the concrete to deteriorate
by expansion pressure. It can be said that not only certain types of structures such as sewer-related
facilities and chemical plants but also structures located in hot spring areas, acid rivers, acid orsulfate soil areas, etc., are in a chemically corrosive environment. In connection with thosestructures, it is necessary to determine the intensity of chemical activity as an environmental factor
affecting chemical attack, taking into consideration the type and concentration of chemical
substances that attack concrete, temperature, humidity, etc.

8.3
8.3.1

Verification Related to Steel Corrosion
GeneralDuring the design service life of a structure, the required performance of the structure
shall not be lost under given environmental conditions because of steel corrosion due tochloride ion penetration, carbonation, etc. In general, verification may be conducted bychecking on items (i), (ii) and (iii) listed below.
(i) Crack width at the concrete surface is not greater than the critical crack width forsteel corrosion.
(ii) Chloride ion concentration at the steel location does not reach the criticalconcentration for steel corrosion during the design service life.
(iii) Carbonation depth does not reach the critical depth for steel corrosion during thedesign service life.
In general, studies on steel corrosion do not need to be conducted for structures witha very short service period, temporary structures, etc.

[Commentary] Chloride ion penetration into concrete and the carbonation of concrete cause thecorrosion of the steel in the concrete. This chapter describes a method of study on steel corrosion
due to chloride ion penetration and a method of study on steel corrosion due to carbonation. Bothmethods assume one-dimensional migration of substances from the concrete surface to thereinforcing steel. These verification methods are valid only when local corrosion does not occur atthe crack locations. In order to make this assumption valid, crack width must be small. This is
why it is verified by check on Item (i) that crack width is not greater than the critical crack width forsteel corrosion, and then Item (ii), chloride ion concentration at the steel location, and Item (iii),
carbonation depth, are checked.
Checks on Items (ii) and (iii) are not necessary for a structure used in a normal outdoor
environment where airborne chloride ions do not exist or in an environment free from the risk ofcarbonation. Even in such cases, however, it is desirable that crack width be kept within theallowable crack width because excessively large crack widths are undesirable.

131

Standard Specifications for Concrete Structures-2007, Design

8.3.2

Limit value of crack width for corrosion of reinforcement(1) The limit value of crack width for corrosion of reinforcement may be determined
depending on the environmental conditions of structure. In general, environmental
conditions may be classified into "normal environment", "corrosive environment" and"severely corrosive environment" as given in Table 8.3.1.
Table 8.3.1

Classification of environmental conditions for reinforcement corrosion

Normalenvironment

Normal outdoor environment with ordinary conditions without any airborne salt,
underground, etc.
1. In comparison to the normal environment, environment with more frequent
cyclic drying and wetting, and underground environment below the level ofunderground water containing especially corrosive (or detrimental) substances,which may cause harmful corrosion of reinforcement.
2. Environment of marine structures submerged in seawater, or structures not
exposed to severe marine environment, etc.
1. Environment in which reinforcement is subjected to detrimental influences
considerably.
2. Environment of marine structures subjected to tides, splash, or exposed tosevere ocean winds, etc.

Corrosive
environment

Severely
corrosive
environment(2) The limit value of crack width for corrosion of reinforcement may be determined
depending on the environmental conditions, concrete cover and type of reinforcement, asgiven in Table 8.3.2. However, the concrete cover c used in Table 8.3.2 should not exceed
100mm.
Table 8.3.2
Type ofreinforcement
Deformed bars andplain bars
Prestressing steel

Limit value of crack width wa

Environmental conditions for reinforcement corrosion
NormalCorrosive
Severely corrosive
0.005c0.004c0.0035c0.004c--------[Commentary] In general, cracks occurring in concrete structures become a cause for reductionin durability due to reinforcement corrosion, deterioration in functions such as watertightness andairtightness, large deformations, impairment of appearance, etc. Therefore, it shall be examinedby an appropriate method that such functions of structures are not impaired due to cracking in
concrete. This clause deals with examination of crack from the viewpoint of prevention ofreinforcement corrosion in concrete. Examination of crack for watertightness and appearance isdealt in Chapter 10.
This clause deals with reinforced concrete members and prestressed concrete members in whichcracking is allowed. Examination for cracking in composite steel-concrete structures is given in
Chapter 16.
(1) Durability of concrete structures is greatly affected by corrosion of reinforcement. Cracks inconcrete cover with excessive width may cause local corrosion of reinforcement. Depending upon
the extent to which they affect the corrosion, environmental conditions have been classified into
three categories as shown in Table 8.3.1. For the different environmental conditions, the limit
value of crack width should be determined. The limit states of corrosion of reinforcement due tochloride ingress and carbonation shall be examined on the assumption that crack widths are smaller132

Chapter 8

Verification of Durability

than the permissible crack width.
"Severely corrosive environment" given in Table 8.3.1 corresponds to environments such as
tidal zones with cyclic wetting and drying or even air with occasional splashing of seawater.
Structures frequently exposed to deicing agents such as calcium chloride shall be regarded as beingin "severely corrosive environment." "Corrosive environment" corresponds to environments thatare more severe than the "normal environment" but are not as severe as "severely corrosive
environment". For instance, the condition in which concrete is permanently submerged inseawater or exposed to air containing salt. Structures located between 0.1 and 1 km from theshoreline may be regarded as being in "corrosive environment".
The term "marine" in Table 8.3.1 includes harbor, coast and ocean. In classification ofenvironmental conditions of a structure, not only the environment where the structure is located but
also the importance of the structure and other factors should be taken into account.
In the case of indoor or similar members, which are not exposed to wind and rain, examinationof crack widths for durability is not required. An environment with frequent freezing and thawing
may be classified as "corrosive" because an increase in crack width indirectly accelerates the
corrosion of reinforcement.
(2) Corrosion of reinforcement in concrete does not depend only on crack width. Hence, thepermissible crack widths indicated in this clause are minimum requirements to avoid risk ofcorrosion of reinforcement. It does not mean that reinforcement do not corrode once crack widths
are kept to levels smaller than the permissible width. For structures under "corrosive" or "severely
corrosive" environments not only should the crack widths be kept to levels smaller than the limit
value of crack width, but also an examination for the concentration of chloride ions at reinforcementlevel given in Section 8.2.7 should be carried out.
It is reasonable to consider that limit value of crack width at the surface of members, which has
a great influence on corrosion of reinforcement, depends on concrete cover. Thus, assuming thatthe permissible crack width may be increased with increasing concrete cover, the limit value ofcrack widths given in Table 8.3.2 have been determined depending on the environmental conditions
and the type of reinforcement. However, since the values given in this table are not definite values,
the permissible crack widths may be determined considering the environmental conditions of thestructure and the method used to estimate the width of cracks.
Permissible crack widths in the case of prestressing steel in "corrosive" and "severely corrosive"
environments are not given in Table 8.3.2 because flexural cracking can be avoided in prestressed
concrete and that special attention to corrosion needs to be paid for prestressing steel. In general,the members in such environments should be designed avoiding the occurrence of cracks.
However, in cases when cracking is allowed, an appropriate permissible crack width should bedetermined on the basis of investigations of environmental and loading conditions and the durabilityof the structure. In case that reinforcement nearest the surface is deformed bar in PRC structure, thelimit value of crack width in Table 8.3.2 may be adopted.

8.3.3

Examination for flexural cracks(1) Examination for flexural cracks should be made, by ensuring that the crack width
under service conditions is not greater than the limit value of crack width.
(2) Examination for flexural cracks need not be carried out in cases when the tensilestress in concrete due to flexural moment and axial forces is less than flexural cracking

133

Standard Specifications for Concrete Structures-2007, Design

strength of concrete, f bck .

[Commentary] (1) The basic approach to crack control from the viewpoint of resistance to steel
corrosion is to control the crack width at the concrete surface at or below the critical crack width forsteel corrosion determined by the environmental conditions and concrete cover. Flexural crack
width for reinforced concrete and prestressed concrete may be calculated by the method describedin Section 7.4.4 of Chapter 7.

 ' csd in Eq.(7.4.4), which represents the effect of shrinkage and creep of concrete on crack
width, should be determined with the consideration of shape of cross section of the member,environmental condition, magnitude of stress, and others. The value of  ' csd may be set 150x10-6
in general cases and 100x10-6 for high strength concrete, considering the coherence with the past
prediction equation, measured data in actual structures, the influences of cyclic drying and wetting
on crack width and corrosion of reinforcement and others. It has been reported that because thecrack width calculated by this method tends to be smaller than measured values obtained fromexisting structures, in order to make calculated crack width values closer to measured values, it isnecessary to make the value of ε'csd greater than 150 × 10−6. If, however, the value of ε'csd isincreased on the basis of measured values, it is necessary to reconsider the limit values of crack
width, too. This is why this section states that when evaluating the critical crack width for steel
corrosion in accordance with Section 8.3.2, the value of ε'csd in Eq. 7.4.4 may be assumed to beabout 150 × 10−6 or so (about 100 × 10−6 for high-strength concrete) for calculation purposes.
If the structure under consideration is located in a normal environment where harmful
substances such as chloride ions do not exist and the members of the structure are ones that arenormally deemed appropriate, a steel stress study may be conducted in place of a crack width study
described in this section. In such cases, verification may be made by ascertaining that the amount of
increase in reinforcing steel stress σse and the amount of increase in prestressing steel stress σpecaused by sectional forces under permanent loads are smaller than the values shown in Table
C8.3.1.
Table C8.3.1 Limiting values for stresses  se (N/mm2) due to permanent load, in ordinary
reinforcement and prestressing steel, when examination of crack width may be omitted
Type ofreinforcement
Deformed bars
Plain bars
Prestressing steel

Limiting values for the stressinduced in steel（N/mm2）
120
100
100

Values in Table C8.3.1 have been determined considering the presence or absence of prestressapplication, type of reinforcement, thickness of concrete cover, etc. using normally used design
values of stresses for railway and highway bridges, as references. If, however, the influence ofvariable loads is considered to be significantly greater than that of permanent loads, a study on
crack width needs to be conducted.
(2) If flexural cracking does not occur, the influence of flexural cracking on steel corrosion does
not need to be taken into consideration.

134

Chapter 8

8.3.4

Verification of Durability

Examination for shear cracks(1) For members subjected to shear forces, examination for shear cracks may not be
carried out in cases when the design shear force, Vd , is smaller than 70% of the design
shear capacity of concrete, Vcd , calculated using Eq.(9.2.5). In such cases,  b and  cshould, in general, be taken as 1.0.
(2) In cases when the examination for shear crack is required from the viewpoint ofreinforcement corrosion, it shall be carried out using an appropriate method.

[Commentary] (2) Because the mechanism of the occurrence and growth of shear cracks differsfrom that of flexural cracks, shear cracking needs to be studied separately by an appropriate method.
Not many studies have been done, however, on shear cracking. In the verification for shear
cracking, usually crack width is not directly checked. Instead, a common approach is to indirectly
make sure that adverse effects of cracking do not occur by keeping shear reinforcement stress at or
below the limit value. Since shear cracks may have a significant effect on the durability and thedeterioration of watertightness and airtightness of structures, a careful examination shall be carriedout, if necessary. It has been reported that shear cracks do not cause any problems in case of linear
members, in which strains of stirrups are not greater than 1000x10-6 and the service load is about
0.5 – 0.7 times as large as the ultimate load. In general, if it is confirmed that the stress in shear
reinforcement under the permanent loads is not greater than the values in Table C8.3.1, precise
examinations may not be required. The stress in stirrups under the permanent loads may be
estimated by the method shown in 7.4.3 in Chapter 7.

8.3.5

Examination for cracks due to torsion(1) Examination for cracks due to torsion may not be carried out in cases when thedesign torsional moment, M td , is smaller than 70% of design torsional moment capacityof a member without torsion reinforcement, M tud , obtained using 9.2.3.2. In such cases,
 b and  c should, in general, be taken as 1.0.
(2) When the examination for torsional cracks is required from the viewpoint ofreinforcement corrosion, it shall be carried out using an appropriate method.

[Commentary] (1) At serviceability limit states, torsional cracks do not easily occur if the design
torsional moment, M td , is smaller than the design torsional moment capacity of a member without
torsion reinforcements, M tud , which is the torsional moment when torsional crack occurs.
However, in order to take some safety margin, an examination of torsional crack may be omitted
only when the design torsional moment is smaller than 70% of the design torsional moment
capacity. In examinations of ultimate limit states, examinations for compatibility torsion are
omitted, considering reduction of torsional stiffness due to cracks.
In general, verification with respect to compatibility torsion crack width does not need to be
conducted mainly because (1) compatibility torsion moment is largely released because of initial
cracking, (2) these cracks that occur under normal service conditions are relatively small, and crack
width does not tend to increase and (3) at least a minimum amount of shear reinforcement isprovided in each member so that the growth of torsion cracks can be prevented.
However, when U-shaped stirrups are used in beams, excessive cracking in the upper side ofbeams may occur. When height of a member with rectangular cross section is not greater than
135

Standard Specifications for Concrete Structures-2007, Design

three times of its width, stirrups of closed-type is recommended.
When design torsional moment of a member subjected to equilibrium torsional moment issmaller than design torsional strength of a member without torsion reinforcements, examination
may be omitted because cracks due to torsion do not occur.
(2) In accordance with a rationale similar to that for shear cracking verification, in the casetorsion cracking, too, crack width is not directly checked. Instead, it is verified indirectly that noadverse effects of cracking can be prevented by keeping the stress in the reinforcement to control
torsion crack opening at or below a limit value. Precise examination may not be required, if it isconfirmed that the stress of torsion reinforcement due to permanent loads is smaller than the values
in Table C.8.3.1. The stress of torsion reinforcement may be obtained from Eq.7.4.3.

8.3.6

Examination for reinforcement corrosion due to carbonation(1) The required performance of concrete structures shall not be impaired by the
carbonation of concrete.
(2) Verification for carbonation should be carried out by ensuring thatiyd
 1 .0y lim(8.3.1)

where,  i:factor representing the importance of the structure. In general, it may
be taken as 1.0, but may be increased to 1.1 for important structures.

y lim

:

critical carbonation depth of steel corrosion initiation. In general, it
may be obtained from Eq.(8.3.2).

y lim  c d  c kwhere, c d:(8.3.2)

design value of concrete cover used for durability verification (mm);calculated, taking into account construction error, from Eq. (8.3.3).

c d  c  c e

(8.3.3)c:concrete cover (mm).

ce:construction error (mm).

ck:remaining non-carbonated cover thickness (mm). This may be taken
as 10mm for structures in a normal environment, and between 10 and
25 mm for structures located in chloride rich environments.

yd:

design value of carbonation depth, In general, it may be obtained from
Eq.(8.3.4).

y d   cb   d t
where,  d:(8.3.4)design carbonation rate ( mm  k  c   c
136

year ), which is given as

Chapter 8

Verification of Durability

k:characteristic value of carbonation rate ( mmt:designed service life of structure for carbonation (year). Equation(8.3.3) should be used to evaluate the carbonation depth only forservice lives less than 100 years.

e:factor indicating the degree of environmental influence; usually, thevalues shown in Section 8.2 may be used.

 cb

:

safety factor to account for the variation in the design value ofcarbonation depth. Normally, it may be taken as 1.15. In the case ofhigh fluidity concrete, it may be taken as 1.1.

c:factor to account for the material properties of concrete. In general, it
may be taken as 1.0, but should be taken as 1.3 for upper portions of
the structure. However, if there is no difference in the quality ofconcrete in structure and that of laboratory-cured specimens, thevalue of 1.0 may be adopted for the whole structure.

year ).

[Commentary] (1) The pH value in concrete reduces due to the carbonation of carbon dioxide
penetrating from atmosphere into concrete. If such a zone of reduced pH reaches the location ofreinforcing bars in concrete, these bars become vulnerable to corrosion. Once the corrosion is
initiated, the formation and deposition of expansive corrosion products on the bars may cause theformation of longitudinal cracks and the spalling of cover concrete, which accelerate Furthermore
corrosion and result in a significant reduction in the cross-section of reinforcing bars. It must be
ensured that the performance of structure shall not fall below the required level due to the corrosionof reinforcing bars. According to previous reports, factors affecting steel corrosion due tocarbonation include not only the quality of concrete and environmental conditions but also
construction-related factors such as inadequate concrete cover, honeycombing, cracking andinadequate curing. It is therefore important to perform careful construction control.
In non-reinforced concrete structures, when nominal steel bars are not installed, there is no riskof degradation of structural performance due to steel corrosion, so the carbonation verification is
not required. When nominal steel bars are installed, depending on the purpose of the installation,
this verification may be required. In such a case, the verification will be carried out in accordancewith the principles laid down in Clause (2).
(2) To ensure that reinforcing bars corrosion on account of carbonation in concrete does notoccur, is quite simple just by verifying that the carbonation depth does not exceed the depth ofreinforcing bars corrosion onset.
It has been learned from laboratory tests and investigations on actual structures that the corrosionof steel may begin before the carbonation depth actually exceed the cover thickness (i.e. before thecarbonation front reaches the location of the reinforcing bars). In many cases, a so-called“remaining carbonation depth”, i.e., the remaining part of cover thickness still not neutralized, isused to discuss the onset of corrosion. There have been very few cases where corrosion develops
to the extent that impairs the performance of a structure once the remaining carbonation depth
remains larger than 10mm.
The concrete cover value used in Eq. (8.3.2) is a value determined by allowing for construction
error. The concrete cover value used for verification is a value obtained by subtracting
construction error as in Eq. (8.3.3) in view of the fact that steel corrosion due to carbonation may becaused by inadequate concrete cover, and it may be difficult to accurately control concrete cover137

Standard Specifications for Concrete Structures-2007, Design

during construction. The amount of shortage in concrete cover caused by carbonation varies
depending on the level of construction control. According to study results obtained by comparing
design values of concrete cover with concrete cover measurement results, the maximum amount ofshortage from the design value of concrete cover is about 10% of the design value. The amount ofconstruction error in concrete cover may be set by referring to the Design: Standards, Part 5, of thisSpecification.
However, when salt permeated into concrete, chloride ions entrapped in hydration products of
cement could become free during the carbonation process. These ions migrate towards
un-neutralized regions and possibly accelerate the initiation of corrosion. Therefore, in such cases,
a remaining carbonation depth higher than that of normal environment is recommended, taking into
account the existence of salt. However, since the ingress of chloride ions into concrete occurs
under wet condition and carbonation proceeds relatively fast in dry condition, it is unlikely that bothphenomena proceed with high speed at the same time. From these reasons, remaining carbonation
depths should be taken to be from 10 to 25mm. Since the practical value of the remaining
carbonation depth depends on environmental conditions (such as temperature, humidity or salt
supply etc.), or quality of concrete, it is not clarified at this time. The upper limit of the remaining
carbonation depth of 25mm is used when chloride ions are present in concrete under salty
environment. The value 25mm is also recommended for safety reason when reliable data is notavailable to estimate the remaining carbonation depth of corrosion initiation. The remaining
carbonation depth can be reduced to less than 25mm if the safety of concrete structures is fully
confirmed by inspections or experiments in the same condition.
The “square-root” law (i.e. the depth of carbonation varies linearly with the square-root of time)is selected for the estimation of the carbonation depth because it is the most general approximation
based on the data of the past studies.
In Eq. (8.3.4), the safety factor for considering the variation of the designed carbonation depth,
is determined by taking into consideration the accuracy of the equation itself, the assumptions thatcarbonation proceeds uniformly throughout the cross-section and that the effect of cracks can beneglected if the crack width is smaller than that stipulated in Section 8.3.2. In the case of highfluidity concrete, because its segregation resistance is high and the homogeneity is ensured, thesafety factor for considering the variation of designed carbonation depth can be eliminated.

138

Chapter 8

8.3.7

Verification of Durability

Examination for chloride attack(1) Performance of a structure shall not be impaired by corrosion of reinforcement due
to ingress of chloride ions.
(2) Examination for corrosion of reinforcement due to ingress of chloride ions may be
carried out by ensuring that the criteria in Eq. (7.4.4) is satisfied:

i

Cd
 1.0
C lim

where,

i(8.3.5):structure factor. It may be taken as 1.0 for ordinary structures and 1.1
for important structures.

Clim : threshold value of chloride concentration for onset of reinforcement
corrosion. This may be determined by referring to measurement
results or test results for similar structures. If those results are notrelied upon, 1.2 kg/m3 may be used. It may be preferably set at a valueless than 1.2 kg/m3 for structures subjected to freezing and thawing
action.

Cd:

design value of chloride concentration at location of reinforcement. It
may, in general, be estimated using Eq.(8.3.6).

 0.1  c  C d   cl  C o 1  erf  2 Dd  t  

(8.3.6)

where, C o:concentration of chloride ions at the concrete surface (kg/m3). In
general, it may be determined according to Section 8.2.

 cl

:

safety factor to take into account the scatter in Cd , the design valueof chloride concentration at location of reinforcement. In general, it
may be taken to be 1.3.

cd:

design value of concrete cover used for durability verification (mm);calculated, taking into account construction error, from Eq. (8.3.7).

c d  c  c e

(8.3.7)c:concrete cover (mm).

ce:construction error (mm)t:

design lifetime for chloride attack (year). In estimating theconcentration of chloride ions at location of reinforcement using
Eq.(8.3.6), an upper limit of 100 years for the design lifetime should be
used.

Dd

:

design value of diffusion coefficient of chloride ions (cm2/year) in
concrete. In general, it may be estimated using Eq.(8.3.8).

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Standard Specifications for Concrete Structures-2007, Design2 w  w 
Dd   c Dk   Do l  wa (8.3.8)c:material factor for concrete. In general, it may taken to be 1.0.
However, it should be taken to be 1.3 for the top face of a structure. In
cases when the quality of concrete in a structure is the same as that ofspecimens cured under standard conditions, the material factor for allparts of the structure may be taken to be 1.0.

Dk:characteristic value of diffusion coefficient of chloride ions in
concrete (cm2/year).

Do:a constant to represent the effect of cracks on transport of chloride
ions in concrete (cm2/year). It should be considered only in cases
when flexural cracks are allowed. In general, it may taken to be 200
cm2/year.

w:

crack width (mm), calculated in accordance with 8.3.3.

wa:limit value of crack width (mm), determined in accordance with 8.3.2.

wl:ratio between crack width and crack spacing.
evaluated using Eq.(8.3.9).

where,   σ pe w   csd  3 se  orlEs  Es 
In general, it may be(8.3.9) are the same as in Eq.(8.2.1) and their
where, the definitions of σ se , σ pe and  csd
values may be taken as those used in the computation of crack width.
erf(s) is an error function defined as: erf ( s ) 

2
1/ 2

π

s

e
0

 2

d

(3) In cases it is difficult to satisfy the requirement prescribed in (2), reinforcement
protected against rusting is preferably used or the surface of the concrete should becoated, etc. to protect the reinforcement from corrosion. In such cases, the effectivenessof these techniques should be evaluated using appropriate methods, keeping in mind themaintenance planning for the structure.
(4) In environments free from the effect of external chlorides, it may be assumed thatprovided the total chloride ion content at the stage of mixing is less than 0.30 kg/m3, theperformance of structures is not impaired due to presence of chloride ions. In the caseof PC strands, which are more vulnerable to stress corrosion, this value is preferably
reduced.
(5) For a concrete structure where the use of antifreeze agents is expected, particularattention shall be paid to the durability of concrete, and reliable waterproofing anddrainage works should be carried out during construction in order to prevent chloride ion
penetration into the concrete.
140Chapter 8

Verification of Durability[Commentary] (1) Even when the corrosion develops in reinforcing bars, the structure isconsidered serviceable if all the required performances are not impaired by the corrosion. In otherwords, the performance of structure is considered to be satisfactory even when the corrosion has
started so long as the corrosion-induced longitudinal cracks are not formed along the reinforcingbars.
In the case of plain concrete, there is no potential degradation of structural performance due tochloride-induced corrosion if nominal reinforcing bars are not installed, so the verification forchloride-induced corrosion is not necessary in this case. When nominal reinforcing bars are used,the verification for chloride-induced corrosion as stipulated in Clause (2) may be required in somecases depending upon the purpose of using nominal reinforcing bars.
(2) Regarding the verification of the performance of structure under chloride attack, the settingof the condition that chloride-induced corrosion of reinforcing bars does not occur during theservice life of structure is relatively easy to understand from safety viewpoint. Therefore, it isimportant to verify that the concentration of chloride ion at the location of the reinforcing bars is
below the critical concentration that could initiate the corrosion of reinforcing bars. However, if
possible, the verification could also be carried out by checking the onset of corrosion-induced crack
in concrete as a limit state, taking into account the required performances and the importance of thestructure. It should be mentioned that the ‘chloride concentration’ mentioned in this specificationrefers to the total chloride content present per unit volume of concrete and not to the concentrationof actual chloride ions of the liquid phase (or pore solution) in concrete.
The critical chloride concentration in the vicinity of reinforcing bars that could initiate thecorrosion in reinforcing bars has been reported to be about 0.3~1.2 kg/m3 of concrete. For
example, values of about 0.3~0.6 kg/m3 have been reported from accelerated tests carried out withchlorides added into fresh concrete, and from exposure tests carried out at the field, values of
1.2~2.4 kg/m3 have been reported. Differences in the critical chloride concentrations reported inthose accelerated and exposure tests, etc. can be attributed to factors such as differences in thewater-cement ratio of the concrete, thickness of cover concrete, etc. High temperatures used inaccelerated tests can also be an influential factor. Thus, since the critical chloride ion
concentration for steel corrosion varies depending on various conditions, it is desirable, whenchecking on individual structures, that the critical concentration be determined by referring tomeasurement results or test results obtained under conditions, such as materials used andenvironmental conditions, similar to those for the structure under consideration. If those results
are not relied upon, verification may be done by using a conservative limit value of 1.2 kg/m3.
Mathematical formulations based on the diffusion theory are most commonly used to simulate
the penetration of chloride ions into concrete. Since the diffusion is a process involving the
movement of ions with the driving force due to the difference in the ion concentration of theliquid, it is desirable that the formulation used is based on the difference in the chloride ion
concentration in the pore solution. The chloride ions in concrete are either entrapped orabsorbed on the surface of hydration products of cement or constituent components of cement.
Since these states of chloride within concrete also depend on chemical factors such as changes in
the pH on account of carbonation, etc., it is desirable that a formulation that takes all these factors
into account in a comprehensive manner.
The use of Eq. (8.3.6) in which the Fick’s law of diffusion is used to simulate the diffusion ofchloride ions at the position of reinforcing bar corresponding to the number of years in service
has been considered satisfactory. This equation is based on the concept that chloride ions diffuse
equally toward steel. When bending crack is generated on concrete cover, the distribution ofchloride ion concentration depends on the distance between crack and steel. However, whencrack width is very narrow, the variation of concentration of chloride ion may trend to be small.
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Standard Specifications for Concrete Structures-2007, Design

In the case of well-compacted concrete, the inconsistent distribution of chloride ion may occur
due to the influence of crack, but steel is well protected in uncracked parts against the corrosion.
From these reasons, the limit for the onset of steel corrosion can be estimated by averaging theinfluence of crack based on the concept that chloride ions diffuse equally toward steel.
Therefore, when the bending crack width is narrower than the allowable one defined in Section
8.3.2, the diffusion coefficient can be estimated using Eq. (8.3.8), taking into consideration theinfluences of concrete quality and crack. In this estimation, the concentration of chloride ions at
the position of reinforcing bars is evaluated using Eq. (8.3.6).
The Eq. (8.3.8) is to estimate the average diffusion coefficient of chloride ions in coverconcrete considering the quality of non-cracked portions of concrete and the influence of crack
opening. The term “ratio of crack width to crack interval”, w/l, is introduced in order to express
the influence of crack averagely. This averaging method is effective when crack width issmaller than the allowable crack. The resistance to the ingress of chloride ions is greatly
affected if the crack width is large, so the term (w/wa)2 of the ratio between the crack width andthe limit value of crack width is introduced to consider that influence.
In the case of early-time cracks such as thermal crack or shrinkage crack, the verification ofsteel corrosion due to the ingress of chloride ions must be carried out properly by measuring thecrack width and interval. However, it may be difficult to measure accurately the crack width andinterval. In these cases, the following formula can be used when the crack width is smaller thanthe limit value of crack width stipulated in Section 8.3.2.

Dd  D   c   cl

(C2.3.1)

Where,  cl is a factor representing the influence of early-time crack. It may be taken to be
1.5.
The safety factor to account for the variation in the design value of chloride concentration in
the vicinity of reinforcing bars in Eq. (8.3.6) should take into account the accuracy of theprediction methodology adopted as well as localized effects of chloride ions on the corrosion ofreinforcing bars. In the case of high fluidity concrete, the safety factor, which considers
variations in the Design value, can be eliminated because high fluidity concrete has highsegregation resistance and the assumed condition of homogeneity is highly satisfied. As far as
the determination of the surface chloride concentration is concerned, it is important that theamount of airborne salt and the environmental condition are appropriately taken into account.
(3) If the environment of the structure is harsh or if corrosion cannot be allowed, it may bedifficult to meet verification criteria even if concrete with a small diffusion coefficient is used andconcrete cover is increased. In such cases, it may be economical to use corrosion resistantmaterials and methods, such as epoxy coated steel as reinforcing bars, durable coating materials forconcrete surface, which could reduce the ingress of air-borne chloride ions, electro-chemicaltreatment (cathodic protection), to protect reinforcing bars against corrosion. When these methods
are used, it is recommended that the following guidelines be followed: Recommendations for
Design and Construction Using Electrochemical Corrosion Control Method (Concrete Library 107),
Recommendations for Design and Construction of Reinforced Concrete Structures Using
Epoxy-Coated Reinforcing Steel Bars (Concrete Library 112) and the Recommendations forConcrete Repair and Surface Protection of Concrete Structures (Concrete Library 119). The
abovementioned recommendations describe a recommended verification method for steel corrosion
due to chloride ion penetration occurring in cases where epoxy-coated reinforcing bars are used.
Concrete calculation methods, however, for performance verification that can be used to evaluate
the durability-improving effects of different construction methods have not yet been specified.

142

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Verification of Durability

It is important that the corrosion prevention method is determined by considering the structuralcharacteristics, environmental condition and the life cycle cost of concrete structure.
(4) Basically speaking, so long as the chloride ion concentration in the vicinity the reinforcing
bars remains below a critical level for the onset of steel corrosion, during the designed service lifeof structure, it can be considered that the corrosion of reinforcing bars does not impair the
performance of concrete structure. Therefore, even in cases where concrete is likely to containchloride ions at the time of mixing, no problem is likely to arise provided the chloride level does notexceed the above mentioned critical level during the designed service life of the structure.
However, it should be borne in mind that chloride ions present in concrete at the time of mixing
may not be mixed uniformly within the matrix on the account of causes such as bleeding, etc.
Furthermore, even after concrete has hardened, chloride ions could migrate and concentrate at someplaces due to several reasons. Taking the above into consideration, it is not advisable to use thesame critical level of chloride ions (that cause the onset of reinforcing bars corrosion) for thepermissible one at the time of mixing.
For this reason, to ensure that any degradation of the structure due to the steel corrosion is kept
below an allowable level, the permissible level of chloride ions in concrete at the time of mixing
has been set to be lower than 0.30 kg/m3, the same as prescribed in the previous version of thisdocument, and is considered to be realistically achievable. However, in cases that there is no
likelihood of the ingress of chloride ions during the service-life of the structure, the water content
and the water-cement ratio is set as low as possible, proper construction practices are adopted,
segregation is avoided and the placed concrete is dense enough to prohibit the free movement ofchloride ions in hardened concrete, the permissible level of chloride ions in concrete at the time of
mixing can be raised to 0.6 kg/m3.
(5) The use of deicing agent for concrete structures has become a popular practice in order toensure the safety of road traffic in winter. However, the use of deicing agent facilitates thechloride-induced corrosion of steel. Structural damages have been observed in North-America. In
recent years, damages due to the excess of critical chloride concentration for steel corrosion becauseof the widespread use of deicing agent have also been reported in Japan and this problem may
spread in the future. Basically, the influence of antifreeze agents can also be verified by themethod described in Item (2). Since, however, it is difficult to determine chloride ion
concentration at the concrete surface, it is more realistic to take measures to prevent the watercontaining chloride ions from reaching the concrete such as adopting a type of structure without
expansion devices as well as carrying out appropriate waterproofing and drainage works or to use
antifreeze agents that do not contain chloride ions. Appropriate treatments are also expected for
concrete structures currently in service if deicing agent is used.

8.4
8.4.1

Verification Related to Concrete Deterioration
Verification for freezing-thawing action(1) The required performance of concrete structure shall not be impaired byfreezing-thawing action.
(2) Verification related to freezing damage may be done by ascertaining that in the casewhere the concrete in a structure undergoes deterioration, the value obtained bymultiplying the ratio between the minimum limit value Emin of the relative dynamic modulus
of elasticity in a freeze–thaw test and its design value Ed by the structure factor γi is 1.0 or
smaller.
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Standard Specifications for Concrete Structures-2007, Design

i

Emin
 1.0
Ed

(8.4.1)where i : a factor representing the importance of the structure. In general, it may be taken as
1.0, but may be increased to 1.1 for important structures.

Ed : design value of relative dynamic modulus of elasticity in freeze–thaw test (= Ek/γc)
Ek : characteristic value of relative dynamic modulus of elasticity in freeze–thaw test.

 c : material factor. In general, it may be set at 1.0, but should be taken as 1.3 for upper
positions of the structure. However, if there is no difference in the quality ofconcrete in the structure (in situ) and that of laboratory-cured specimens, thisvalue may be set at 1.0 for all positions.

Emin : critical minimum value of relative dynamic modulus of elasticity to ensuresatisfactory performance of the structure under freezing-thawing action. In general,
it may be obtained from Table 8.4.1.
Table 8.4.1 Minimum limit value Emin (%) of relative dynamic modulus of elasticity infreeze–thaw test to meet freeze–thaw resistance performance requirements for a concrete
structure
ClimateExposureof structure

SectionSevere weather conditions or
frequent freezing-thawing action

Not so severe weather
conditions, atmospherictemperature rarely drop to below
0C

Thin 2)

GeneralThin 2)

General(1) Immersed in water oroften saturated with water 1)

85

70

85

60

(2) Not covered in item (1)above and subjected tonormal exposure conditions

70

60

70

60

1) Structures close to the water surface or in contact with water such as waterways, water-tanks, abutmentsof bridge, bridge piers, retaining walls, tunnel linings, etc. Besides, structures such as slabs, beams etc not
close to the water surface but may be exposed to snow, water flow, spray, etc., also belong to this category.
2) Members with thickness less than 20cm may be considered ‘thin’.

[Commentary] (1) There has been almost no quantitative information available to relate anychange in the performance of structure to the manifestations of damage on account of cyclic
exposure to freezing and thawing action, such as pop-outs, scaling, and formation of micro cracks
in concrete. Therefore, at present it is difficult to establish criteria for the required performance ofa structure subjected to cyclic freezing and thawing, and fix a limiting or maximum permissiblelevel of ‘allowable’ deterioration, based on such criteria. The recommended method at present is toregard the level of deterioration at which a certain degree of concrete deterioration occurs because of
freeze–thaw cycles but the structure does not lose its functionality as the critical state of performance of thestructure under freeze–thaw cycles and use the verification of the performance of the concrete under144

Chapter 8

Verification of Durability

freeze–thaw cycles in place of the verification of the performance of the structure under freeze–thaw cycles.

Furthermore, for concrete not likely to be exposed to cyclic freezing and thawing actions, theverification for freezing-thawing action is not necessary.
(2) The freeze–thaw resistance of concrete is difficult to evaluate accurately because it isaffected by many factors such as the quality of concrete, lowest temperature, the number offreeze–thaw cycles and the degree of saturation. In many cases, freeze–thaw resistancerequirements can be met by giving an appropriate level of freeze–thaw resistance to the concrete.
On the other hand, the relationship between the results of accelerated tests and the extent of frost
damage of actual structures, is somewhat better understood, thanks to past research works and fielddata. For this reason, it is recommended that parameters such as the relative dynamic modulus ofelasticity and the weight loss in accelerated tests are used as indices for the verification of concrete
resistance against frost damage. Accelerated freezing and thawing test must be carried out inaccordance with the method specified in JIS A 1148 (A method): “The Freeze-thaw Test Method ofConcrete (Freeze-thaw test method of concrete underwater)”. However, when the conditions of thefreezing-thawing action are especially severe and the designed service life of the structure isrelatively long, appropriate changes of testing conditions prescribed in JIS A 1148 (A method)should be made to bring the test closer to the actual conditions that the structure is likely to be
subjected to. When a new structure is built in the same conditions with those of previously built
structures, if the latter is proved to be strong against frost damage, the verification of frost
resistance of the newly built structure can be omitted.
In the case of an ordinary structure that is not required to have a very high level of durability,
freeze–thaw resistance verification may be omitted if the characteristic value of the relative
dynamic modulus of elasticity in the freeze–thaw test of concrete is set at or above 90%. In thecaser of a structure that is required to have a very high degree of durability such as the ability tomaintain the initial structural soundness throughout the service life of the structure without affecting
its appearance, it is necessary to prevent a decrease in the relative dynamic modulus of elasticity oftest specimens or in the mass of specimens in freeze–thaw tests. In such cases, the relative
dynamic modulus of elasticity may be kept at a level higher than 95%.

8.4.2

Verification related to chemical attack(1) The required performance of a structure shall not be lost because of chemical
attack.
(2) Verification related to chemical attack may be done by ascertaining that the value
obtained by multiplying the ratio of the design value of chemical penetration depth (yced) to
concrete cover cd by the structure factor γi is 1.0 or smaller. If the concrete meets thechemical corrosion resistance requirements, it may be assumed that the required
performance of the structure is not lost because of chemical attack, and this verification
does not need to be done.

i

y ced
 1.0
cd

(8.4.2)where
yced: design value of chemical penetration depth (= γcyce)

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Standard Specifications for Concrete Structures-2007, Design

yce : characteristic value of chemical penetration depth c : material factor for concrete, which may be assumed to be 1.0 but should beassumed to be 1.3 for the upper surface sections of a structure and may be
assumed to be 1.0 for all parts of a structure if there is no difference in quality
between the concrete in the structure and standard-cured specimens

cd: design value of concrete cover used for durability verification (mm); to be
calculated from Eq. (8.4.3).

c d  c  c e
c(8.4.3):concrete cover (mm).

ce :construction error (mm).
(3) If chemical attack is severe, it is generally recommended that measures to control
chemical attack such as covering concrete surfaces and using corrosion-proofed
reinforcing materials be taken. In such cases, verification may be omitted if the control
measures are evaluated by an appropriate method in accordance with the Maintenancesection of this Specification.

[Commentary] (1) Chemically induced deterioration includes the dissolution and deterioration of
concrete caused by contact with a corrosive substance, and cracking of concrete and spalling of
cover concrete due to expansion that occur when a corrosive substance that penetrates concrete
reacts with cement ingredients or steel. Current knowledge, however, is not necessarily goodenough for quantitative evaluation the influence of concrete deterioration due to contact with or
penetration of corrosive substances on the functional decline of structures. A realistic approach atpresent, therefore, is to define a limit state of a structure in terms of whether there is any visible
deterioration of concrete due to contact with or penetration of corrosive substances or whether the
influence of such deterioration reaches the steel location, taking into consideration such factors as
the required performance, type of structure, degree of importance and maintainability of thestructure and the severity of environmental conditions.

There is also deterioration due to biochemical activity besides deterioration due to chemical
attack, but the durability of a structure against such deterioration may be verified in accordance withthe method described in this section.
(2) It is difficult to evaluate the resistance of concrete to environmental deterioration factors ofdifferent types and degrees by a standard test method. When conducting tests for environmental
deterioration factors of different types and intensities, therefore, it is necessary to determine
different limit values associated with chemical corrosion resistance for different tests.
In cases where a structure is subjected to the deterioration activity of sulfates, verification may
be done by ascertaining that the specified penetration depth will not be reached during the service
life of the structure by using an appropriately determined characteristic value of sulfur penetration
depth.
In a highly corrosive environment such as a hot spring or acid river where the deterioration of
concrete cannot be controlled completely, a more reliable method of verification is to verify theperformance of concrete specimens actually exposed to the environment. In such evaluation, therate of corrosion of concrete is determined from the exposure period, and verification is done byascertaining that concrete deterioration does not reach the critical depth for the structure during its
146

Chapter 8

Verification of Durability

service life.
Deterioration in an environment where corrosive activity is severe andmicroorganisms such as sulfur-oxidizing bacteria are involved in corrosion such as a sewer
environment occurs as the hydrogen sulfide gas generated by sewage sludge is oxidized bysulfur-oxidizing bacteria, and the sulfuric acid thus generated corrodes concrete. Consequently,
the rate of corrosion of concrete varies depending on the type of sulfur-oxidizing bacteria involved
and their habitat conditions. An appropriate method of verification, therefore, is to ascertain that
deterioration will not reach the locations of steel in the structure during its service life by
conducting exposure tests designed specifically for the deterioration situation for each facility anddetermining the rate of deterioration from the exposure period.
(3) If chemical corrosion is very severe as in a sewer or hot spring environment, it is generally
difficult to meet chemical resistance requirements by means of cover concrete and the resistance ofconcrete alone. It can be said that sewerage facilities and structures in hot spring areas are in suchenvironments. In such cases, it is often realistic and rational to take control measures such as
coasting the concrete surface for protection from chemical attack and using corrosion-proofed
reinforcing materials. If such control measures are taken, verification may be omitted byconducting exposure tests after actually taking control measures to verify the resistance to chemical
attack.

147

Standard Specifications for Concrete Structures-2007, Design

CHAPTER 9 VERIFICATION OF STRUCTURAL SAFETY

9.1

General(1) It shall be verified that the concrete structure meets the required safety
performance during its design life.
(2) Safety of a structure shall be verified by confirming that (a) the ultimate limit state
for failure of cross section for any of the members, and, (b) the ultimate limit state for rigid
body stability for the structure, is not reached.
(3) Examination of the ultimate limit state for failure of cross section shall be carriedout by confirming that Equation 9.1.1 is satisfied, i.e. the value obtained by multiplying theratio of design member force ( S d ) to design capacity of member cross section ( Rd ) by the
structure factor (  i ) is not greater than 1.0.

 i S d / Rd  1.0(9.1.1)(i) The design capacity of cross section Rd shall be obtained from Eq. 9.1.2, bydividing computed member capacity (considering its cross section, design strength ofmaterials, f d , etc.), R ( f d ), by the member factor,  b .

Rd  R  f d  /  b(9.1.2)

Generally,  b defined in Section 9.2 and below may be used.
(ii) The design member force S d shall be obtained from Eq. 9.1.3 as the sum ofmember forces S , computed using the design loads, Fd , multiplied by a structural
analysis factor  a .

S d    a S Fd (9.1.3)(4) Examination of the ultimate limit state for fatigue failure shall be carried out inaccordance with the followings:(i) It shall be confirmed, that Eq. 9.1.4 is satisfied, i.e. the ratio of design variable
stress,  rd , to design fatigue strength, f rd , divided by the member factor,  b , multipliedby the structure factor,  i , is not greater than 1.0.

 i rd /( f rd /  b )  1.0(9.1.4)

where f rd is the characteristic value of fatigue strength for materials, f rk , divided by
the material factor,  m .
(ii) As an alternative to the above, examination for safety in fatigue can also be carriedout by ensuring that Eq. 9.1.5 is satisfied.

 i S rd / Rrd  1.0(9.1.5)where S rd , is the fatigue variable member force, S r ( Frd ) , obtained by multiplying the148

Chapter 9

Verification of Structural Safety

design variable load, Frd , by the structural analysis factor,  a ; the design fatigue
capacity of the member, Rrd , is the fatigue capacity of the member, Rr ( f rd ) , obtained by
dividing the design fatigue strength of material, f rd , by the member factor,  b .
(iii) The member factor,  b , may be taken to be between 1.0 and 1.1.
(5) Examination of ultimate limit states for displacement, deformation, formation ofcollapse mechanism and others, and, examination of the ultimate limit state of a member
or structure using non-linear analysis without considering member forces, shall be carriedout using methods whose applicability to the structure and accuracy have beenpreviously established.

[Commentary] (1) and (2) This chapter describes standard methods for verifying the safety ofstructures under static loads without consideration of material deteriorations through design life, incases where the provisions of Chapter 8, “Verification of Durability,” Chapter 12, “Verification
Related to Initial Cracking”, and the constructability requirements described in the Standard
Specifications for Concrete Structures “Materials and Construction”, are satisfied. Further, safety
against the effect of earthquakes should be verified in accordance with provisions of Chapter 11,“Verification of Earthquake Resistance.”
A structure may be considered to be safe, i.e., its safety is maintained, as long as it or its
members do not fail. In the case of a statically highly indeterminate structure, its safety may not be
immediately lost even when some of the members reach the ultimate limit state and become
incapable of carrying load. In cases where partial failure of members is permitted but the overall
safety of the structure still needs to be maintained even after partial failure of some of the members,
the nonlinear and the post-failure behavior of members should be appropriately taken into
consideration at the time of safety verification as in seismic performance verification. In general,
however, even if structures are ascertained to meet safety performance requirements under static
loading beyond the limit state for failure of cross sections of members, the actual economic benefits
are small. Also, verification of safety after failure of cross sections requires the use of larger
factors of safety. The present specification, therefore, uses a standard approach: for the purposesof safety verification, it is simply required to verify that none of the members reaches the ultimate
limit state. All units including the strength of materials used in verification methods described inthis chapter are as described in Chapter 5, “Design Values for Materials.”(3) When a member is subjected to a combination of loads such as flexural moment and axialload, verification of safety against failure of member cross section shall be carried out by comparing
the appropriate design member forces with design capacity of the member cross section, taking into
account of the action of combined loads.
(i) The member factor (  b ) is described in Section 9.2 and subsequent sections. When an
empirical formula is used, calculated values of the load carrying capacity of the member are averagevalues (see Section 4.4). For example, design equations for shear capacity of concrete members
without shear reinforcement are in many cases based on experimental results obtained from testingsmall specimens. In view of considerable scale effects, the member factor may be taken as 1.3
even when precise empirical equations are used. If it is verified that an empirical equation isapplicable to structures in realistic dimensions, the member factor may be taken as 1.15.
Computation for torsional capacity of members without shear reinforcement is made using anelastic theory. According to experimental results of small-scale specimens, this formulation gives
a conservative estimate of the torsional capacity of the member. However, the torsional failure ofmembers without shear reinforcement occurs in tension, and in this case the ultimate strength iseasily affected by non-structural cracks. Considering factors including the scale-effect, etc. the149Standard Specifications for Concrete Structures-2007, Design

member factor may be taken as 1.3 as in the case of calculating the shear capacity as given above.
Computation for flexural and shear capacity of members with shear reinforcement, which yields
according to the truss type mechanism is made using well-documented theoretical approaches.
The present specification recommends use of a member factor of 1.1 to take into account variationsin the geometry of members.
(4) Fatigue capacity of a member depends on the fatigue strength of the concrete and thereinforcement, which make up the member. If capacity of cross section of a member is
proportional to the fatigue strength of the materials, same results will be obtained in theexamination of safety for fatigue by either equation. However, since there are some cases thatthey are not proportional with each other, safety for fatigue shall be examined by using fatigue
strength of materials in principle.
(5) In the examination of the ultimate limit state for deformation, it is examined whether plastic
deformations, cracking, creep and others cause large deformations in the structure or its members to
the extent that they lose their shapes or dimensions. Any loss of structural stability caused bylarge deformations should also be examined at this stage.
Examination of the ultimate limit state for mechanism formation is carried out by examining
whether or not moment redistribution through plastic hinges causes formation of a collapse
mechanism in statically indeterminate structures, on the basis of the rotational capacity for plastic
hinges.
In cases where examination of the limit state for structural failure is carried out by non-linear
analysis, the performance verification may be carried out using indices other than member force.
Such indices include the average in-plane principal strain in the case of a shell structure subjected toshear, and, the average curvature and the rotation angle at the plastic hinge in the case of a member
subjected to flexure.

9.2

Examination of safety for failure of cross section

9.2.1
9.2.1.1

Flexural moment and axial forces
Design capacity of member cross section

 in compression for members subjected to(1) The upper limit for axial capacity N oud
axial compressive force shall be calculated by Eq. (9.2.1) if ties are used, and by Eq.
(9.2.1) or Eq. (9.2.2), whichever is greater, if spiral reinforcement is used.
N oud k 1 f cd A c  f yd A st   b

N oud(9.2.1) k 1 f cd A e  f yd A st  2 . 5 f pyd A spe   bwhere,(9.2.2)

Ac : area of concrete section
A e : area of concrete section surrounded by spiral reinforcement
A st : total area of axial reinforcement

Aspe : converted area of spiral reinforcement (=πdsp Asp/s)
d sp : diameter of cross section surrounded by spiral reinforcement
150Chapter 9

Verification of Structural Safetys : pitch of spiral reinforcement

Asp : area of spiral reinforcement
f cd : design compressive strength of concretef yd : design compressive yield strength of axial reinforcementf pyd : design tensile yield strength of spiral reinforcement
k1 : strength reduction factor (  1  0.003 f ck  0.85 ,where, f ck : characteristic value for strength of concrete (N/mm²))

 b : member factor, which may generally be taken as 1.3(2) When the member is subjected to a flexure or combined flexure and axial loads, themember factor  b may be taken as 1.10, and the design capacity may be computed indirections corresponding with member forces, keeping in mind the following
assumptions:(i) Strain is proportional to the distance from neutral axis.
(ii) Tensile stress of concrete is neglected.
(iii) Stress-strain relationship of concrete follows that given in Fig. 5.2.1.
(iv) Stress-strain relationship of steel follows that given in Fig. 5.3.1.
(3) Except when the compressive strain is distributed over entire cross-section, thecompressive stress distribution of concrete may be assumed as an equivalent stressblock as shown in Fig. 9.2.1.

cu

k1 f cdk1  1  0.003 f ʹ ck  0.85

d

x

βx

 1 0f ʹ.003 f ck  0.85
k1155
ck
 0.0035
 f ck155
30000
0.0025   cu 
 0.0035
30000
2
where f ʹ0ck.52 8080N/mm
cu ʹ cu   0.52  80 ʹ cu

Fig. 9.2.1

Equivalent stress block(4) The design capacity of members subjected to biaxial flexural moments and axial
loads simultaneously may be determined by the assumptions in (2) above.
(5) The effect of an axial force may be considered ‘small’ in cases when e / h  10 ,where h is the height of the cross section, and eccentricity e is the ratio of design
flexural moment M d to design axial compressive force N d . In such cases the design
capacity of a member may be calculated as for a member subjected to flexure alone.

151

Standard Specifications for Concrete Structures-2007, Design[Commentary] (1) The coefficient k1 has been conventionally taken as 0.85. In the case ofhigh-strength concrete members, the design axial capacity of members may be smaller than that
calculate on the basis of the strength of conventional cylindrical test specimens, with the difference
growing larger as the strength of concrete increases. To take this effect into k1 , should be treatedas a function of the compressive strength, in the case of high strength concrete.
A small increase in the flexural moment caused by some misalignment of members at theconstruction stage, for example, can significantly reduce the ultimate resistance of members
subjected to axial compression with a small M d / N d . To account for such cases, the present
specification places an upper limit on the design load carrying capacity and suggests use of a higher
member factor (=1.3).
(2) A general relationship between the design axial capacity and design flexural capacity ofmembers subjected to combined axial load and flexural moment is described in Fig. C9.2.1.
Therefore, safety under combined axial load and flexural moment should be examined by ) curve, that is, at the side ofconfirming that the point (  i M d ,  i N d ) is located inside of ( M ud , N ud
the origin as shown in Fig. C9.2.1.

Fig. C9.2.1

Relationship between axial capacity and flexural capacity

Flexural moment from structural analysis is generally obtained using the centroid of member
cross section. The flexural capacity should also be calculated using the same centroidal axis.
Assumption (i) addresses the strain distribution across a member cross-section, and, (ii) and (iii),
deal with stress distribution in concrete.
Assumption (iv) is related to the stress-strain relationship of steel. Considering that, (a) the
capacity of a member is hardly affected by the ultimate strain of reinforcing steel, and, (b) byspecifying this value computation becomes more complicated, the Specification does not
specifically define the value of the ultimate strain of steel.
Lateral confinement of concrete in beams and columns by spiral or tie reinforcement
significantly improves the deformability of the member, and can be used to an advantage formoment redistribution and in seismic design. The effectiveness of the lateral reinforcement is,however, related to several factors, including properties of the materials used, shapes, interval andvolume ratio of steel and the gradient and rate of strains of confined concrete, and thus, generalized
design equations are yet not available. The load-deformation relationship may be determinedusing appropriate experimental results, if possible.
152

Chapter 9

Verification of Structural Safety(3) The equivalent stress block shown in Fig. 9.2.1 has been determined on the basis of thestress-strain curve shown in Fig. 5.2.1. An exact correspondence between the magnitude andlocation of resultant in the equivalent stress block and those determined from the actual stress-strain
relationship can be obtained only by varying the stresses in the stress block using the ultimate strainof concrete and the stress-strain relationship. For the sake of convenience, however, it has been
assumed in the present specification that stress in the stress block is the same as the maximum stress,
as given in the stress-strain relationship. Also, the height of the stress block is determined in amanner that the resultant lever arm is such that the axial force and flexural moment are roughly inagreement.
(4) The capacity of members subjected to biaxial flexure and axial loads simultaneously should
be calculated in a manner similar to the members subjected to uniaxial flexure and axial loads. In
such cases, all reinforcement used in the member may be taken into account. In the analysis,
careful attention should be paid to the arrangement of reinforcement in the member, and it should beensured that the direction of the neutral axis does not coincide with the direction of the principal
axes of stresses, except in the case of uniaxial flexure.
Figure C9.2.2 shows an example of a rectangular cross section of a member under the action ofa concentrated load acting at a location other than the centroid and causing biaxial flexure. The
load-carrying capacity of such a member may be calculated through an iterative procedure to berepeated till the eccentricity in the vertical and horizontal directions, e x and e y , calculated byassuming the location of the neutral axis, y o , and the angle of the neutral axis,  , to the specified
value.
In general, exact calculations of changes in concrete and steel stresses due to changes in y oand  is very tedious. Stresses, therefore, may be calculated from strains at the location of thecentroid by dividing the cross section into small elements and assuming that stress in each element
is constant.
(5) The present specification permits ignoring the effect of axial force when e / h  10 tosimplify the calculations and on account of the fact the results thus obtained are conservative atbecause the value of  i N d is considerably smaller than axial compressive capacity N ud
equilibrium. Tensile axial forces, however, should not be ignored.

Eccentric loading point
N'
y

n'

ey

yo

ex
Mx

θ

x

ex = My / N 'ey = Mx / N 'nFig. C9.2.2

My

Rectangular cross section subjected to biaxial flexure

153

Standard Specifications for Concrete Structures-2007, Design

9.2.2
9.2.2.1

Shear
General(1) Design for shear shall take into consideration such factors as the type of member,e.g., linear, planar, and the direction of shear.
(2) For a linear member, the safety under the action of shear loads shall be examinedon the basis design shear capacities V yd and V wcd as discussed in Section 9.2.2.2. If theshear span ratio is small, safety shall be checked with respect to the design shear
compression capacity Vdd instead of these design shear capacities.
(3) For a planar member subjected to transverse shear, examination for transverse
shear shall be made in a manner similar to that for a linear member. Examination forpunching shear shall be carried out in accordance with the provisions of Section 9.2.2.3,
when a concentrated load Vd is applied on the member.
(4) For a planar member subjected to in-plane shear, examination for in-plane shear
shall be made in accordance with provisions of Section 9.2.2.4.
(5) If the shear force Vd must be transferred across construction joints or planes
where the probability of crack occurrence is large, examination for direct shear transfer
on shear planes shall be carried out in accordance with provisions of Section 9.2.2.5.
(6) For linear members subjected to reversed cyclic loads the member factor shall beappropriately increased to enhance the level of safety against shear failure.
(7) Strength verification tests or high-accuracy analyses should be conducted withrespect to those parts of the structure where the flow of force changes considerably or the
cross section changes abruptly, corners, opening zones, steel anchorage zones, or otherregions to which the beam or plate theory cannot be applied, that is, so-called
discontinuity regions. If such special verification is not used, verification may be done byusing the strut-and-tie model.

[Commentary] (1) Behavior and failure mechanism of members subjected to shear forces
depends on factors such as type of the member, e.g., linear or planar. In the case of planar membersthese are also affected by the direction of shear forces, e.g., transverse or in-plane. Design in shear
shall be carried out taking account of these factors through appropriate methods.
This section explains the methods for examination of safety of commonly used structuralmembers, such as linear members, e.g., beams and columns, and planar members, e.g., slabs,
subjected to transverse shear forces, and, walls of cylindrical structures subjected to in-plane shear,in (2), (3) and (4) below. The method for examination of safety in direct shear transfer on planes
such as those created by construction joints, and precast concrete joints, where the possibility ofcrack occurrence is large, is given in (5).
(2) For a linear member provided with shear reinforcement, the shear force is carried by shear
reinforcement after the initiation of diagonal cracks and the load-carrying mechanism istransformed to a truss-type mechanism. Members lose their ability to resist further shear either by
the yielding of the shear reinforcement, which act as tension chords of the truss, or, by thecompressive failure of web concrete, which acts as the compression chords of the truss.
Examination for safety in the cases of yielding of shear reinforcement and diagonal compressive
154

Chapter 9

Verification of Structural Safety

failure of web concrete is carried out using Eq. (9.2.3), and Eq. (9.2.8), respectively.
If, however, the shear span ratio (shear span/effective depth) is small (about 2.0 or smaller), theshear capacity may become greater than the shear capacity calculated from Eq. (9.2.3) because adeep-beam-like mechanism comes into play. Verification for the design shear compression strength,
therefore, may be done by using Eq. (9.2.9).
(3) It is presented here that examination for shear of a planar member such as a one-way slab,
which behaves like a beam, may be conducted in accordance with that of a linear member. The
method to examine safety for punching shear failure caused by concentrated loads acting on aplanar member is also described.
(4) On the basis of the several available methods for examination of safety of planar members
subjected to in-plane shear, the present specification recommends use of a practical method todesign an orthogonally reinforced planar member–design forces Txd and T yd in the reinforcementin the x and y directions and design diagonal compressive force of concrete ( C d ) is determined inaccordance with provisions of Section 9.2.2.4(1) are compared with capacities Txyd , T yyd and Cudrespectively computed using the provisions of Section 9.2.2.4(2).
(5) For a T-beam with a wide flange and a thin web, a larger shear force acts at the base of theflange which may sometimes cause shear failure. It is desirable to examine this phenomenon as
the direct shear transfer.
(6) For a linear member whose safety is governed by reversed cyclic loading, it is necessary toenhance the level of safety against shear failure in order to prevent brittle failure. The member
factor in such cases should, therefore, be increased by about 1.2.
(7) The design approach described here makes rational safety design possible for members, suchas columns and beams, for which there is accumulated design and construction experience and thereis extensive empirical knowledge about member cross sections and reinforcement methods needed
to meet performance requirements. The load-carrying capacity, however, of abrupt-cross-sectionalchange regions, corners, opening zones, etc., is difficult to verify by the standard method describedin Chapter 9, and past construction data on reinforcement methods in regions where the flow offorce changes considerably are not necessarily available. One way to verify safety in such cases is
to identify the load-carrying mechanism by conducting experiments or high-accuracy nonlinear
analyses with respect to the assumed member configuration or material arrangements. Anothermethod is to determine a load-carrying mechanism for design loads in advance and determine
reinforcement patterns and material strength requirements so that the load-carrying mechanism canbe achieved. As a method that is useful when employing the latter method of verification, the use of
the strut-and-tie model is permitted. The strut-and-tie model is a structural model that clearly
defines the load-carrying mechanism for design loads and the flow of force. In the strut-and-tie
model method, a concrete structure or its members are discretized into one-dimensional struts andties and nodes that connect together these elements, and the load-carrying capacity for the assumed
flow of force is calculated from the equilibrium of forces and the strength of the struts and ties.
Verification by the strut-and-tie model method is to be done in accordance with the Standard
Specifications for Concrete Structures “Design: Design Methods, Part 6, Strut and Tie Model.”155

Standard Specifications for Concrete Structures-2007, Design

9.2.2.2

Design shear capacity of linear members(1) The design shear capacity of a member V yd may be obtained using Eq. (9.2.3).
When both bent longitudinal bars and stirrups are arranged as shear reinforcement, it
should be ensured that the stirrups provided carry at least 50% of the shear force
provided by shear reinforcement.

V yd  Vcd  Vsd  V ped
where(9.2.3)

Vcd : design shear capacity of linear members without shear reinforcing
steel, obtained using Eq. (6.2.4).

Vcd   d   p   n  f vcd  bw  d /  b(9.2.4)f vcd  0.203 f ' cd (N/mm2) where f vcd  0.72 (N/mm2)(9.2.5) d  4 1000 / d ( d : mm)

when  d > 1.5,  d is taken as 1.5.

 p  3 100 p v

when  p > 1.5,  p is taken as 1.5.

 n  1  2M o / M ud

N d  0

 1  4M o / M ud  N d  0
N d:

when  n > 2,  n is taken as 2.
when  n < 0,  n is taken as 0.

design axial compressive force

M ud : pure flexural capacity without consideration of axial force

Mo :flexural moment necessary to cancel stress due to axial force at
extreme tension fiber corresponding to design flexural moment M dbw:

web widthd:effective depthp v  As /(bw  d )As:area of tension reinforcement (mm2)

f cd

:

design compressive strength of concrete (N/mm2)

b:

1.3 may be used in generalVsd:

design shear capacity of shear reinforcement, obtained using Eq.
(6.3.5)Vsd  Aw f wyd sin  s  cos  s  / S s  A pw pw sin  p  cos  p  / s p z /  b
Aw
A pw

:

(9.2.6)

total area of shear reinforcement placed in S s: total area of prestressing steel expected to act as shear reinforcement
placed in S p
156

Chapter 9 pw

Verification of Structural Safety: tensile stress in prestressing steel acting as shear reinforcement
when shear reinforcing steel yields

 pw   wpe  f wyd  f pyd wpe: effective tensile stress in prestressing steel acting as shear
reinforcement

f wyd

:

design yield strength of shear reinforcement, and should not exceed
400 N/mm². However, if the characteristic compressive strength of
concrete ( f ck ) is 60 N/mm2 or more, a value of up to 800 N/mm2 may
be used.

f pyd:design yield strength of prestressing steel expected to act as shear
reinforcement

s:angle between shear reinforcement and member axis

p:angle between prestressing steel acting as shear reinforcement andmember axis

Ss:

spacing of shear reinforcementSp:spacing of prestressing steel expected to act as shear reinforcementz:distance from location of compressive stress resultant to centroid oftension steel; may generally be taken as d /1.15.

b:member factor. May generally be taken as 1.10

V ped

:

component of effective tensile force in longitudinal tendon parallel tothe shear force, obtained using Eq. (9.2.7).

V ped  Ped  sin  p /  b(9.2.7)

Ped:

effective tensile force in longitudinal prestressing steel

p:angle between extreme compression fiber and member axis

t:angle between longitudinal prestressing steel and member axis

b:1.10 in general(2) When linear members are supported directly, no further examination for V yd may
be required over a distance of one-half the total depth of members ( h ) from the face of the
support. In this region, shear reinforcement not less than that required at the crosssection located h /2 from the face of the support shall be provided. The depth at the faceof the support may be used for members with varying depth, assuming that the haunch(whose slope does not exceed 1:3) is also effective in resisting shear forces.
Appropriate methods of design shall be used to estimate the design shear capacity inthe neighborhood of supports, when planar members subjected to transverse shear are
treated as linear members, and the provisions of Section 9.2.2.1(3) are used.
157

Standard Specifications for Concrete Structures-2007, Design(3) The design diagonal compressive capacity Vwcd of web concrete in resisting
applied shear forces may be calculated by Eq. (9.2.8).

Vwcd  f wcd  bw  d /  b
where

f wcd  1.25 f ' cd

(9.2.8)(N/mm2), when f wcd  7.8 (N/mm2)

 b : member factor. May generally be taken as 1.3(4)

Web width of members(i) In cases when the diameter of a duct in prestressed concrete members is equal to or
greater than 1/8 of the width of the web, the width used in Eq. (9.2.4) shall be appropriately
reduced (from the actual width, bw ). It is recommended that the web width may be
reduced to ( bw  1 / 2   ), i.e. by an amount equal to one-half the sum of all the diametersof the ducts ‘  ’ spaced in the cross section.
(ii) For members with variable web width in the direction of member depth except forcircular cross sections, the web width bw shall be taken as the minimum width within theeffective depth d . For members with several webs, the total width of webs shall be taken
as bw . For members with solid or hollow circular cross sections, the web width shall bedefined as the side length of the square with the same area as solid circular cross sectionor the total width of webs of the square box having the same area as hollow circular crosssection. In these cases, the area of longitudinal tensile steel As may be defined as thearea of steel being arranged in 1/4 (90°) portion of the cross tensile section. The effective
depth d may be taken as the distance from the edges of the squares or the square boxes
at the compression side to the centroid of the steel section accounted as As , as shown in
Fig.9.2.2.
These definitions of area for longitudinal tensile steel shall not be applied for thecomputation of flexural capacity.

Fig. 9.2.2

Definitions of bw and d concerning various shapes of cross sections(5) The design shear compression capacity may be calculated from Eq. (9.2.9).

Vdd  d  n  p  a  f dd  bw  d / b

(9.2.9)158

Chapter 9

where

Verification of Structural Safety

Vdd : design shear compression capacity (N)f dd  0.19 f cd (N/mm2) d  4 1000 / d ( d : mm)

 n  1  2M o / M ud

N d  0

 1  4M o / M ud  N d  0p 

1  100 p v
2(9.2.10)when  d > 1.5,  d is taken as 1.5.
when  n > 2,  n is taken as 2.
when  n < 0,  n is taken as 0.
when  p > 1.5,  p is taken as 1.5.

a 

5
1  (a / d ) 2bw:

web widthd: effective depth at the loading point in case of a simple beam or at the
support front end in case of a cantilever beam (mm)a:distance from the support front end to the loading point (mm)p v  As /(bw  d )As:area of tension reinforcement (mm2)

M ud : pure flexural capacity without consideration of axial force

Mo :flexural moment necessary to cancel stress due to axial force at
extreme tension fiber corresponding to design flexural moment M d

N d

:

design axial compressive force

f cd

:

design compressive strength of concrete (N/mm2)

b:

1.3 may be used in general[Commentary](1) The design shear capacity V yd is basically the sum of the components carriedby concrete Vcd and by shear reinforcement Vsd . The value of Vsd is calculated in accordancewith the truss theory that assumes yielding of shear reinforcement and considers 45 compression
diagonals.
Consequently, V yd gives the capacity corresponding to yielding of shear
reinforcement. In reality, shear capacity may be considerably greater than V yd if the amount ofshear reinforcement is relatively small. However, no precise method to estimate the actual shear
capacity is yet available, and therefore the present specification recommends use of Eq. (9.2.3) as apractical and conservative formula.
Eq. (9.2.4) is derived taking in to account the effect of concrete strength, member depth,
reinforcement ratio and axial force on Vcd . Relationship between the shear strength by thisequation and the characteristic compressive strength of concrete is shown in Fig. C9.2.3. f cd in

159

Standard Specifications for Concrete Structures-2007, Design

Eq. (9.2.5) is the design compressive strength of concrete, obtained by dividing the characteristic
compressive strength of concrete, f ck , by the material factor  c . The effects of the effective depth,
ratio of axial reinforcement and axial forces are shown in Fig. C9.2.4 (a), (b) and (c). When thecharacteristic compressive strength of concrete exceeds 80 N/mm2, there may not be a significant
increase in Vcd even when the concrete compressive strength increases.
The Standard Specifications for Concrete Structures “Design” adopted in 1996, therefore, had . In preparation for the change in the value of theplaced an upper limit of 0.72 N/mm2 for f vcd
material factor  c for concrete having a characteristic compressive strength of 60 N/mm2 or morefrom 1.5 to 1.3, this upper limit was reviewed taking into consideration recent research results
including the latest experiment data. As a result, although Vcd for concrete having a compressive
strength of 60 N/mm2 or more tended to level off, the review confirmed that safety can be ensured
for all types of test specimens considered, even in the formula proposed by Niwa et al. that takes
into account the effect of a d , from which Eq. (9.2.4) was derived, by setting an upper limit of and using a material factor of 1.3. In view of the fact that Eq. (9.2.4) gives more
0.72 for f vcd
conservative values than the Niwa formula because the former neglects the effect of a d , use of
 of 0.72 and a member factor  b of 1.3 was permitted.
Eq. (9.2.4) with an upper limit of f vcd
f'vcd (N/mm2)

1.0
0.8

γc=1.3

0.6
0.4
0.2
0.0
0 10 20 30 40 50 60 70 80 90

f'ck (N/mm2)

Fig.C9.2.3 Relationship between characteristic
compressive strength of concrete f ck and f vcd

Fig. C9.2.4

Influencing factors on the shear capacity

Taking  n as ( 1  2M o / M u ) may bring better applicability for the case of failure of members
subjected to axial compression also, but for a conservative and safe estimate it may be assumed that
2M o / M u ≈ M o / M d , where M d is the design flexural moment obtained based on the load for theultimate limit state, and M u is the design flexural capacity of members.
Only a few papers address the estimation of shear strength of members subjected to axial
tension, and further research on the subject is required. Based on the experimental verification
with previously reported test data, the value of  n is found to be 1  4 M o / M d , where the160Chapter 9

Verification of Structural Safety

definition of M o is as shown in Fig. C9.2.5. For simplicity, the gross cross section of concrete
may be considered to be effective when obtaining M o .

Fig. C9.2.5

Meaning of M o ( M d >0)

Eq. (9.2.5) is applicable to normal concrete and the value in the case of lightweight aggregate
concrete may be taken to be 70% of value calculated by this equation. The first term in the bracket
in Eq. (9.2.6) represents the shear capacity of shear reinforcement including stirrups, hoops and bent
bars, and the second one is the contribution to the capacity by diagonal or vertical prestressing steel.
When extremely high strength bars are used for shear reinforcement, the design yield strength ofshear reinforcement f wyd shall be limited to 400 N/mm², because an excessive width of diagonal
crack at shear failure reduces the shear force resisted through aggregate interlock across crack
planes, or dowel actions of the tensile reinforcement. However it has been confirmed
experimentally that Eq. (9.2.3) may be used even when high strength reinforcement having yieldstrength of 800 N/mm2 is used as shear reinforcement, if the concrete used has a characteristic
compressive strength f ck of 60 N/mm2 or more. Therefore, the upper limit of f wyd whenf ck >60 N/mm2 is set at 800 N/mm2.
It has been reported that in cases for self-compacting concrete Eq. (9.2.3) holds true for shear
reinforcement having yield strength of around 800 N/mm2 even when f ck is 50 N/mm2. It has
also been reported that bond characteristics, crack distribution and crack width of concrete varywith self-compactability even when compressive strength is the same. Since it has been pointed
out that distribution of diagonal cracks is related to shear capacity, the upper limit of f wyd of 800
N/mm2 may be used for self-compacting concrete if the characteristic compressive strength of theconcrete is not lower than 50 N/mm2.
Stirrups resist shear force as tension web chord in the assumed truss system and furthermore,prevent diagonal cracks from propagating along tension reinforcement by their enclosure. The
minimum amount of stirrup reinforcement required for this effect to take place has not yet beenclearly established. Therefore, the present specification requires that at least 1/2 of the shear force
to be carried by shear reinforcement is carried by stirrup.
When designing rectangular cross sections subjected to biaxial shear forces, it may be ensured
that Eq. (C9.2.1) is satisfied.

 V / V    V / V   1.0
2

i

dx

yx

2

i

dy

(C9.2.1)yy

161

Standard Specifications for Concrete Structures-2007, Design

where, V yx

: design shear capacity along x -axis

V yy: design shear capacity along y -axis

Vdx: design shear force along x -axis under biaxial shear forces

Vdy: design shear force along y -axis under biaxial shear forces

For circular cross sections, hoop reinforcement and spiral reinforcement may be regarded as
shear reinforcement.
(2) The truss mechanism may develop in regions separated from the supports by some distance,
but the so-called arch mechanism operates in the neighborhood of the supports, where compression
is transferred directly to the supports. It is generally considered that failure is not initiated inregions close to the supports because of the enhanced shear capacity due to the arch action. It has
also been confirmed that the effect of shear reinforcement arranged close to supports differs fromthat placed in the middle of beams, but the actual behavior at the edges of beams is not very wellunderstood yet. Considering the need for simplicity of design procedures, the shear capacity ( V yd )based on the truss mechanism need not be examined within a distance of one half the member total
depth from the faces of supports.
However, in special situations if large concentrated loads are applied at sections close tosupports, appropriate examination for shear compression capacity, Vdd . As the shear capacity oflinear members subjected to distributed loads in regions near supports and in corners is also larger
than in other regions, use of a more appropriate review for design is recommended.
In a member supported directly compressive stresses are developed in the member web due toapplied loads and support reactions as shown in Fig. C9.2.6 (a). This rule shall not be applied tothe case shown in Figure C9.2.6 (b) where the support reaction is transferred to the main beamthrough the lateral beams and others, or, in the case shown in Figure C9.2.6 (c) where the applied
loads do not produce any compressive stress in the member web.

(a) Direct loading,
direct support(b) Indirect support

Fig. C9.2.6(b) Indirect loading

Direct and indirect supports

In many cases no shear reinforcement is arranged for planar members such as box culverts andretaining walls. Therefore, the design method regarding sections close to supports of linear
members assuming that shear reinforcement is necessary is not always applicable. Planar
members subjected to distributed loads and the corner regions of members may be designed using amore accurate and well-founded method.
For simply supported slabs subjected to uniform loads, for example, it is enough to check thesafety of the section at distance d of the effective depth from the support. Further examination
at other sections may not be required on the premise that the main tension reinforcement at this162

Chapter 9

Verification of Structural Safetysection is embedded beyond the support. Design for planar members with comparatively large
thickness subjected to loads other than those that are uniformly distributed may be carried out inaccordance with Section 12.7 “Footing”.
(3) When excessive amounts of shear reinforcement is provided, there is a possibility that
failure of member is caused by the compressive failure of web concrete and the shear reinforcement
does not yield. This section is given to avoid the occurrence of this type of failure. Given thelack of experimental data, the present specification recommends use of Eq. (9.2.8) for a safe
estimate. Relationship between f wcd and the characteristic compressive strength of concrete f ck
is shown in Fig. C9.2.7.
Since the indicated formula was derived for application to ordinary concrete, appropriate
experiments should be carried out to verify its applicability to high-strength concrete, etc. In casethe applicability is not verified through tests the equation may be adopted only for concretes notexceeding f ck =50 N/mm2.

Fig. C9.2.7 Relationship between characteristic
compressive strength of concrete f ck and f wcd(5) If the shear span ratio a/d is small, a directly supported bar member, even after theoccurrence of diagonal cracking, continues to behave like a tied arch with the tension reinforcement
acting as a tie. Failure results, therefore, from the yielding (flexural yielding) of the reinforcement
acting like a tie or crushing failure (shear failure) of concrete. In this case, the tension reinforcement
must not be anchored midspan because the tension reinforcement acts as a tie in a tied arch, and it isnecessary to anchor all reinforcing bars needed to resist the maximum bending moment
continuously beyond the support points.
Failure of the concrete in an arch rib is likely to occur as a shear failure. In this section, theshear compression strength equation has been formulated by conservatively simplifying a recently
derived equation (C9.2.2) so that it asymptotically approaches the shear strength formula forordinary bar members at a shear span ratio a / d of 2.5 or so. An arch rib considered here is formed
by a cantilever beam or simple beam. If, therefore, a different type of arch rib formation is expected,
detailed verification should be done separately on an as-needed basis.
Vc 

2/3
0.24  k  f c  (1  100 p v )  (1  3.33r / d )1  (a / d ) 2163

bw  d

(C9.2.2)

Standard Specifications for Concrete Structures-2007, Designk  1  7.43 100 p w  (a / d  0.75) / f c

2/3

where, r : length of bearing plate along the longitudinal axis
It has been confirmed experimentally that a beam with a small a / d value has a shear
reinforcement effect if horizontal reinforcement is provided in the main section of the member. In
this case, the tensile steel ratio p v is a value obtained from Eq. C9.2.3, and the design shear
compression strength Vdd can be calculated by substituting that value in Eq. 9.2.9.
p v  p v1  pv 2  d 2 / d1

(C9.2.3)

where, p v : tension steel ratio
p v1 : tension steel ratio of tension steel
p v 2 : tension steel ratio of horizontal reinforcement provided in the main section of thebeam
d 2 : distance from the extreme compression fiber of tension reinforcementd 1 : distance from the extreme compression fiber in horizontal reinforcement provided
in the main section of the beam

It has been shown that shear reinforcement contributes to shear reinforcement by controlling
local failure of arch rib concrete. If the effect of shear reinforcement is also taken into consideration,
Eq. C9.2.4 may be used for calculation. There are cases, however, where there is little reinforcing
effect if the amount of shear reinforcement is too small. When considering the effect of shear
reinforcement, therefore, it is necessary to arrange shear reinforcing bars so that the shear
reinforcement ratio becomes 0.2% or higher.
Vdd  (  d   n   w )  p   a  f dd  bw  d /  b(C9.2.4)

where, Vdd : design shear compression capacity (N) d  4 1000 / d ( d : mm)

when  d > 1.5,  d is taken as 1.5.

 w  4.23 100 p w  (a / d  0.75) / f cd

when  w < 0,  d is taken as 0.

 n  1  2M o / M ud

N d  0

when  n > 2,  n is taken as 2.

 1  4M o / M ud  N d  0p 

when  n < 0,  n is taken as 0.

1  100 p v

when  p > 1.5,  p is taken as 1.5.

2

a 

5
1  (a / d ) 2bw:

web widthd:effective depth at the loading point in case of a simple beam or at the support front
164

Chapter 9

Verification of Structural Safety

end in case of a cantilever beam (mm)a:distance from the support front end to the loading point (mm)p v  As /(bw  d )As:area of tension reinforcement (mm2)pw:

shear reinforcement ratio:total cross-sectional area of shear reinforcement perpendicular to the memberAwaxis in section s s (mm2)ss:spacing of shear reinforcement perpendicular to the member axis (mm)M ud : pure flexural capacity without consideration of axial force

M o : flexural moment necessary to cancel stress due to axial force at extreme tension fiber
corresponding to design flexural moment M d

N d

:

design axial compressive force

f cd

:

design compressive strength of concrete (N/mm2)

b:

1.3 may be used in general

If Eq. 9.2.9 and Eq. C9.2.4 are used to calculate the shear strength of a member with a large
amount of longitudinal reinforcement its cross section such as a bridge pier with a small shear span
ratio, shear strength tends to be underestimated. The design shear strength of such a member,therefore, should be calculated appropriately, taking into account the influence of the longitudinal
reinforcement in the main section of the member. Eq. 9.2.9 can also be used in cases where concretewith a compressive strength of about 60 to 80 N/mm2.
The scope of application of Eq. 9.2.9 has been determined conservatively by referring toprevious research results. If multiple loads or distributed loads act in the span, the distance from thecenter of gravity to the support front end may be taken as a. If a member is not supported directly orif the structural detail requirements are not met, Item (5) must not be applied because theload-carrying mechanism as described here may not be formed.
Eq. 9.2.9 is applicable to normal concrete. If the equation is to be applied to lightweightaggregate concrete, the value needs to be reduced. Generally, 70% of the value calculated from Eq.
9.2.9 may be used.

165

Standard Specifications for Concrete Structures-2007, Design

9.2.2.3

Design punching shear capacity of planar members(1) When the loaded area is positioned far from free edges or openings and theeccentricity of the load is small, the design punching shear capacity V pcd shall be
determined using Eq. (9.2.11).

V pcd   d   p   r  f pcd  u p  d /  b(9.2.11)where  0.20 f cd (N/mm2), where f pcd  1.2 (N/mm2)
f pcd

 d  4 1000 / d ( d : mm) p  3 100 p(9.2.12)

when  d > 1.5,  d is taken as 1.5.

when  p > 1.5,  p is taken as 1.5.

 r  1  1 / 1  0.25u / d 
f cd : design compressive strength of concrete(N/mm2)u: peripheral length of loaded areau p : peripheral length of the design cross section located at a distance d /2 fromthe loaded aread and p : effective depth and reinforcement ratio defined as the average values forthe reinforcement in two directions

b:Member factor. May generally be taken as 1.3(2) When the loaded area is located in the vicinity of free edges or openings inmembers, the reduction of the punching shear capacity shall be appropriately taken into
account.
(3) When the loads are applied eccentrically to the loaded area, the effects of flexure
and torsion shall also be considered.

[Commentary] (1) When a local load is applied to a planar member such as a slab, the punching
shear failure may occur in a manner that the concrete under the loaded area dents from thesurrounding portion. For members subjected to the local loads such as column-slab connections
and footings, the possibility of punching shear failure shall be examined.

The Specification assumes that the punching shear capacity of slabs can be estimated using theequation used for the estimation of the shear capacity of beams in view of the difficulty inestablishing exact formulations to derive the punching shear capacity of slabs. The parameters
used in Eq. (9.2.11) are determined by previously reported experimental results concerning
punching shear for slabs and footings.
Relationship between the calculated value by Eq. (9.2.12) and the characteristic compressive
strength of concrete is shown in Fig. C9.2.8. The factor  r in Eq. (9.2.11) represents the effectof the loaded area and its value should be taken as shown in Fig. C9.2.9.
Since the formula was derived for application to ordinary concrete, appropriate experiments
166

Chapter 9

Verification of Structural Safety

fpcd (N/mm2)

should be carried out to verify its applicability to high-strength concrete, etc. In case theapplicability is not verified through tests, the equation may be adopted only for concretes notexceeding f ck =50 N/mm2.

1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0

γc=1.3

0

10

20

30

40

50

60

70

80

2

f' ck (N/mm )Fig. C9.2.8 Relationship between characteristic
compressive strength of concrete f ck and f pcd

Fig. C9.2.9

Influence of loaded area on punching shear capacity

d/2

d/2

The failure mode of punching shear shall be such that the conical or pyramidal shape offractured slope is created. Equation (9.2.11) for the shear capacity is derived on the assumptionthat the design cross-section is located d /2 from the loaded area as shown in Fig. C9.2.10.
d/2

up

d/2

up

Fig. C9.2.10

Design cross section

The failure mode of members subjected to pull-out loads, such as steel tower footings, is similar
to the failure mode of punching shear. The design capacity shall be calculated by the followings:i) When the design for pull-out shear is conducted in accordance with the case for punching
shear, the peripheral length u of loading face shall be computed by Eq. (C9.2.5) (See Fig.
C9.2.11).
u  4  2  r : with attachment 2    r : without attachment(C9.2.5)
167

Standard Specifications for Concrete Structures-2007, Design

where, r : distance between center of pier and the edge of attachment for the case with
attachment and distance between center of pier and the connection of anchor for the case without
attachment.

with

Fig. C9.2.11 Critical cross section forshear of footing with pull-out force

Fig. C9.2.12 Critical cross section forthe case with closely spaced pilesii) When the distance l between the edge of loading face and the center of the piles is less thanthe effective depth d , the critical cross section shall be, in general, at 1/2 of distance between theedge of loading face and the center of the piles (See Fig. C9.2.12).
iii) When pull - out force is applied to footing, the mechanism of failure is clearly similar to thecase of punching shear. Some experimental results with shear reinforcements show them to be
similar to the cases of directly transmitted shear. However, there are not many experimental datafor cases with shear reinforcement and formula has not yet been established to-date. Therefore,
when the effect of shear reinforcement is confirmed by an experiment or other method, pull-out
shear strength may include this effect.
It has been confirmed that the shear failure of simply supported circular slabs (See Fig. C9.2.13),
such as bottom slabs of tanks, on their peripheral sides subjected to uniformly distributed or line
loads is not similar to the punching shear failure specified in this section but to the shear failure oflinear members. Hence, it is appropriate that this type of shear capacity is determined according to
Eq. (C9.2.6).

168Chapter 9

Verification of Structural Safety

Fig. C9.2.13 Circular slabs subjected to uniformly
distributed load or line load

As provided above, when designing a slab section, examination should be carried out for
moments and shear forces assuming the slab to act as a beam. Further, in slabs subjected to aconcentrated load, the examination for punching shear should be carried out.
However, available researches have shown that slabs such as an underground LNG tank, whose
width is larger than their thickness, have greater shear resistance than that of ordinary slender beams.
For example, experiments have shown that shear resistance of circular slabs is larger than that ofordinary beams because of the restraint to radial expansion provided by the reinforcing bars
arranged in the circumferential direction. Experiments have also shown that the shear strength ofsimply supported and uniformly loaded circular slabs, whose diameter is larger than ten times theeffective depth, may be computed by Eq.(C9.2.6), which has been derived from Eq.(9.2.4) andmodified to account for the resistant due to circumferential reinforcements, which results in radial
compressive forces.
Vcdp   d   p      a d  f vcd  bw  d  b(C9.2.6)

where,    1  2M 0 / M u
f A
pr f y  , P n  y s n
M 0  Pn (d  h / 3) , M u  p r f y d 2 1 r
 1 .7 f ' c d:effective depthh: overall heightpr :reinforcement ratio in radial directionAs :cross sectional area of one circumferential reinforcementr :radius of slab at critical sectionn: number of tensile reinforcements in circumferential direction installed outside of thecritical section

 a / d  0.75 
a/d :

1.4
a/d

shear span to depth ratio 0   a / d  1.5
169

Standard Specifications for Concrete Structures-2007, Design

Other notations have same definitions with those in Eqs.(6.3.4) and (6.3.5).
(2) If a free edge is located near the loaded area of a one-way slab, the punching shear capacity
decreases. In such cases, it is advisable to regard the slab as a linear member having a width equal
to the effective width of the slab and calculate the design shear capacity of a linear member as
described in Section 9.2.2.2.
(3) Eq. (9.2.11) cannot be used when combined flexural and torsional moments are applied in amanner that corner columns support the slabs or when the applied loads are eccentric to the loaded
area. Though sufficient experimental data is not available concerning the combined flexural andtorsional moments in the presence of axial loads, it is proposed to reduce the punching shear
capacity by multiplying the obtained capacity under axial loads by 1/α (See Fig. C9.2.14).

(1) For circular loaded area
Fig. C9.2.14(2) For rectangular loaded area

Strength reduction rate 1/α for eccentric loading

170

Chapter 99.2.2.4

Verification of Structural Safety

Design member forces in planar members subjected to in-plane forces(1) For reinforced concrete planar members reinforced in two perpendicular directions,subjected to in-plane member forces, tensile forces Txd and T yd in each of thereinforcing directions and diagonal compressive force C d may be calculated as design
in-plane forces using Eqs. (9.2.13), (9.2.14) and (9.2.15), respectively.

Txd  N 1 cos 2   N 2 sin 2    N 1  N 2 sin  cos (9.2.13)

T yd  N 1 sin 2   N 2 cos 2    N 1  N 2 sin  cos (9.2.14)

C d  2 N 1  N 2 sin  cos (9.2.15)

where, Txd , T yd :design tensile force per unit width in the reinforcement along thex -axis and y -axis directions, respectively: angle between the in-plane force N1 and the reinforcement along thex -axis (≤ 45°)Cd: design diagonal compressive force per unit width

N1 , N 2: design value of principal in-plane forces; N 1  N 2 ; N1 being tensile(2) For the examination of in-plane member forces for design member forces inaccordance with (1), the design yield capacity of the reinforcement, Txyd , T yyd and the , may be obtained using Eqs. (9.2.16),
design capacity of concrete in compression, C ud
(9.2.17) and (9.2.18), respectively.
(i) Design yield capacity of reinforcement

Txyd  p x  f yd  b  t /  b(9.2.16)

T yyd  p y  f yd  b  t /  b(9.2.17)

where, p x and p y : ratio of reinforcement in x–axis and y–axis directions ( As / bt )b:member width: unit width in generalt:member thicknessb:

may be generally taken as 1.15

(ii) Design capacity of concrete in compression  f ucd
 bt /b
C ud(9.2.18)

where,

  2.8 f cd
f ucd

b

(N/mm2), where  17 N/mm2
f ucd: may be generally taken as 1.3

171(9.2.19)

Standard Specifications for Concrete Structures-2007, Design[Commentary] (1) When in-plane normal forces in the two perpendicular directions ofreinforcement, and in-plane shear forces act together in reinforced concrete plate members
reinforced in two perpendicular directions, the resultant state of stress can be represented byprincipal in-plane forces N1 and N2 having the angle α with reinforcement direction.

Equations (9.2.13) − (9.2.15) have been derived assuming that compressive forces develop in a
direction diagonal to the orthogonal reinforcement and cracks form at an angle of 45°to thedirection of reinforcement. These equations further assume that the shear force in the plane of thecrack can be separated into two components – that parallel to the reinforcement and that parallel tothe direction of the diagonal of reinforcement in the two directions, and, that the shear force iscarried by the axial tension component of the reinforcement and the compressive stress component
in the concrete.
Ny
N2
Nxy

N1

Nx

Nx

α

α
N1

N2
Ny

Fig. C9.2.15

Orthogonally reinforced concrete plate subjected to biaxial tension(2) After cracking, the combined in-plane normal and shear forces are carried as axial tensile
forces in reinforcement and compressive forces in concrete. Equations (9.2.16) and (9.2.17) for
estimating the yield capacity of reinforcement are based on the assumption that the distribution of
in-plane normal and shear forces over the depth of members is uniform.
In the estimation of the capacity of cracked concrete in compression, there are many unknown
factors and Eq. (9.2.18) has been suggested for its simplicity to give a conservative estimate of the in this equation anddegree of reduction in compressive strength. The relationship between f ucd
the characteristic compressive strength of concrete is shown in Fig. (C9.2.16).

Fig. C9.2.16 Relationship between characteristic
compressive strength of concrete f ck and f ucd

Recent research has shown that the reduction factor can be determined so that the reduction rate
does not become extremely low even in cases where concrete strength is relatively high. On the172Chapter 9

Verification of Structural Safetybasis of the results of recent studies on the reduction factor for compressive strength of cracked
concrete, the reduction factor for the compressive capacity for in-plane forces of heavily cracked
reinforced concrete members can be calculated from the expected maximum average tensile lateral may be calculated using Eq. (C9.2.7).
strain (See Table C9.2.1). Therefore, f ucd
    f cd
f ucd(C9.2.7)

where,  is a compressive strength reduction factor, whose value is given in Table C9.2.1
depending on the lateral strain.
Table C9.2.1

Lateral strain  t * (x10-6)

Reduction factor  for lateral strain  t

2400 or less

3600

4800 or more


0.8
0.7
0.6
* Average tensile strain in the direction perpendicular to crack
For conditions other than those shown in Table C9.2.1, linear interpolation may be used forintermediate lateral strains.
The values of the reduction factor given above, however, are based on the experimental results
using test specimens comprising of ordinary concrete having a compressive strength of not greaterthan 50 N/mm2) ordinary deformed steel bars, and, having a reinforcement ratio of up to about 2%.
In the experiments, the specimens were subjected to compression and tension in orthogonal
directions or pure shear. The values for the reduction factor given above are, therefore, valid only
under these conditions, with an upper limit of lateral tensile strain as 5000x10−6. When the
reduction factor is used for cases where reversed cyclic loading could be repeated until a larger
lateral tensile strain occurs, or, in cases where the effect of cyclic loading is large, 0.2 should be
subtracted from the value given above to obtain the new reduction factor.

9.2.2.5

The design capacity for shear transfer(1) When reinforcement is placed in a shear plane, the design capacity for shear
transfer Vcwd under axial force may be computed using Eq. (9.2.20).







Vcwd   c  p   s  sin 2     p  f yd  sin   cos  Ac  Vk /  bwhere,(9.2.20) c    f cd b   pf yd   nd 1b
 s  0.08 f yd /   0.751  10 p  1.7 nd / f yd 

where,

0.08 3    0.75 (for deformed bars)

 nd : average normal stress acting on the shear plane; / 2 In all cases,
for compression,  nd may be taken as equal to   nd(   p  f yd   nd ) must be positive.
 : average normal compressive stress acting on the shear plane
 nd

173

Standard Specifications for Concrete Structures-2007, Designt:angle between tensile reinforcement and member axisp:reinforcement ratio along the shear plane, where reinforcing steel with
sufficient development length in both directions from the shear plane
is taken into accountAc:

area of shear plane:angle between shear plane and reinforcementb:coefficient representing configuration of planes and ranging between
0 and 1; in general the values may be taken as follows:
2/3 for a cracked surface (in the case of normal strength concrete),
and, 1/2 in the case of a treated construction joint, cracked surface inthe case of high-strength concrete, or, in the case of anadhesive-bonded joint between precast concrete membersu:average coefficient of friction for solid-to-solid contact and may betaken as 0.45

Vk:shear capacity of the shear key

Vk  0.1Ak  f cd , where Ak is the cross-sectional area of the shear key
at the shear planeb:

may be generally taken as 1.3(2) Design shear transfer capacity Vcwd in cases when flexural moment and axial force
act on the shear plane may be determined by finding the neutral axis under the action of
the flexural moment and axial force to define tension and compression zones divided by
the neutral axis, following the steps i) through iii) described below and then substituting
the values of Vcwd ,t and Vcwd ,c calculated using Eq. (9.2.20) in Eq. (9.2.21).

Vcwd   M  Vcwd ,t  Vcwd ,cwhere,(9.2.21)

Vcwd ,t : shear transfer capacity of the tension side of the shear plane
Vcwd ,c : shear transfer capacity of the compression side of the shear plane M : reduction factor to allow for the effect of flexural moment. In general,
it’s values may be taken as follows: M  41  M d / M y  where  M  1 : for construction joints and cracks= 0 : for joints of precast concrete members

M d : design flexural moment acting on the shear plane
M y : moment at yielding of the outermost reinforcement on the tension sidei) Calculation of axial forces carried by reinforcement and concrete under flexural
moment and axial force
174Chapter 9

Verification of Structural Safety

In cases when flexural moment, M d , and axial compressive force, N d , act on theshear plane, Pst , Psc and Pc are calculated on the basis that assumptions (i) through(iv) of Section 9.2.1.1 (2) hold. Eq. (9.2.22) and Eq. (9.2.23) may be assumed for the
stress-strain relationship for concrete and reinforcing steel, respectively.

 c  E s  c (where  c  0 )(9.2.22)

  Es  (9.2.23)

where, N d:

design axial compressive force acting on the shear plane

Pst:

Total axial tensile force carried by the reinforcement on the tension
side

Psc

:

Total axial compressive force carried by the reinforcement on thecompression sidePc

: Total axial compressive force carried by the concrete on thecompression sideii) Calculation of yield moment M y
The moment M y at which the stress in the outermost reinforcing steel on the tension
side reaches its design tensile yield strength, f yd , should be calculated by a method
similar to the one described in i) above.
iii) Calculation of shear transfer capacities Vcwd ,t and Vcwd ,ca) Assuming  nd  Pst / Act , Vcwd ,t is calculated using Eq. (9.2.20). In such cases, shear
capacity Vk due to shear keys on the tension side should be ignored.
b) Assuming  nd  1 / 2 Psc  Pc  / Acc , Vcwd ,c is calculated using Eq. (9.2.20), where
Act and Acc are the shear area on the tension and the compression side, respectively.
(3) When the entire shear plane is in compression, design shear transfer capacity Vcwd
  N d / Ac and ignoring the effect of
may be calculated using Eq. (9.2.20), assuming  nd
flexural moment.

[Commentary] (1) Shear transfer capacity is the sum of the transferred force on the concrete
shear plane and the shear plane components of axial force and shear force acting on the intersecting
reinforcing steel. Transferred force to be carried by the concrete depends on the compressive force
acting on the concrete shear plane, surface roughness of the concrete, and the compressive strengthof the concrete. The shear reinforcement also assumes the role of exerting vertical confining force
on the concrete shear plane. Shear transfer capacity, therefore, is the sum of the forces transferredby the concrete and the reinforcement when the reinforcement loses confining force as it yields.

With respect to confining force exerted by reinforcement, yielding of the entire cross section canbe assumed in the longitudinal direction if the reinforcement ratio is not greater than 1%. It is
generally known, however, that in cases where shear displacement becomes large because of anincrease in reinforcement ratio or loads acting perpendicularly on the shear plane, flexural momentand shear force as well as axial force act on the reinforcement cross section so that confining force
is lost before the entire cross section of the reinforcement yields in the longitudinal direction. The
reduction factor  in Eq. (9.2.20) expresses decreases in axial capacity of shear reinforcement and175

Standard Specifications for Concrete Structures-2007, Design

increases in shear capacity. The transfer capacity formula was derived by adding up the components
in the direction of shear in the reinforcement and the concrete.
The shear transfer capacity of concrete is dependent on two factors: the interlocking effect due
to the roughness of shear surfaces, and friction at the points of contact. In the case of shear alongsmooth construction joint surfaces, the interlocking effect decreases while friction becomesdominant. As a result, the influence of confining force becomes stronger as the concrete strength
becomes lower. The coefficient b in Eq. (9.2.20) represents the effect of surface roughness.
For cracks in high-strength concrete, the value of the coefficient b need to be made smaller
because surface roughness decreases as the coarse aggregate particles fracture. If construction
joint surface is not properly treated, 2/5 may be used for coefficient b. For safe and conservativeevaluation,  nd   nd / 2 is to be used if  nd is compressive. When  nd is tensile, theequation is to be used as it is.
Since Eq. (9.2.20) is applicable to a shear plane with reinforcement, p  0 may be used when
it is applied to a plane without reinforcement. “Reinforcement with sufficient development length”
refers to reinforcement having a development length equal to at least 10 times the reinforcing bar
diameter in both directions from the shear plane.
Precast concrete member joints are usually bonded with adhesives or mortar. The formula
shown in this specification is applicable to adhesive-bonded joints for which sufficient experimental
data is available as well as implementation examples. If mortar or other materials are to be used, aseparate study needs to be conducted. The reason why shear capacity is given as the sum offriction due to axial force and the capacity of shear keys is that shear keys are often used withprecast concrete.
(2) When flexural moment acts on a shear plane, the amount of shear stress that can betransferred varies within the shear plane depending on such factors as crack width. It is notpossible, therefore, to apply Eq. (9.2.20), which assumes uniform shear stresses, as is in this case.
For example, crack width is smaller where compression is greater in the cross-section, so greater
shear stresses are transferred in areas where compression is greater. An exact calculation requires
dividing the shear plane into small elements, calculating the shear transfer capacity of each element
and summing the shear transfer capacities thus calculated, but performing such computations is an
onerous task. Comparison was made of the method of defining the shear plane into a compression
zone and a tension zone divided by the neutral axis and evaluating the shear capacity of each zone,
and the method of rigorous analysis that divides the shear plane into smaller areas. The
comparison showed that the former method is sufficiently accurate for practical purposes. For thisreason, Eq. (9.2.21) is adopted as the formula for calculating shear transfer capacity under flexural
moment and axial force.
If the shear surfaces are rough like crack surfaces, shear force is transferred to some degree
because of the interlocking effect of the rough shear surfaces even if they are open. If, however,the shear surfaces cannot be reliably expected to become sufficiently rough, the shear transfer
capacity of the tension zone should not be counted on. This is why a coefficient,  M , by which toallow for the influence of flexural moment was introduced so that shear transfer capacity of thetension zone can be evaluated according to the acting flexural moment and the degree of roughnessof the shear surfaces. If an adhesive is used at precast concrete member joints, a certain degree of
surface roughness is likely. Therefore, if the value of  M can be set so as to allow for the
influence of such surface roughness, the shear transfer capacity of the tension zone may be taken
into consideration.
Linear relationship is used when axial forces to be carried by the reinforcement and the concrete
under flexural moment and axial force were calculated. The reason for this is that in cases where176

Chapter 9

Verification of Structural Safety

flexural moment is so large as to cause the outermost reinforcement in the tension zone to yield, theshear transfer capacity of the tension zone is ignored in evaluating  M in order to be on the safe
side. In general, in the design of cross sections before the yielding of steel reinforcement, thestress-strain relationship for reinforcement and concrete can be assumed to be elastic withoutcausing significant errors.
In cases where the entire cross section is in tension, the shear transfer capacity of the tension
zone alone needs to be evaluated because the neutral axis is out of the shear plane.
(3) The results of the rigorous analysis mentioned in (2) indicate that when the entire crosssection is in compression, the influence of flexural moment on shear transfer capacity is relatively
small. This is the reason that Eq. (9.2.20) is specified when the entire cross section is incompression.

9.2.3
9.2.3.1

TorsionGeneral(1) For structural members not significantly affected by torsional moment and thosesubject to only compatibility torsional moment, the entire examination specified in Section
9.2.3 regarding safety against torsion may not be carried out. Here, ‘structural members
not significantly affected by torsional moment’ refers to those structures where the value
obtained by multiplying the ratio of the design torsional moment, M td , to the design puretorsional capacity, M tcd , as specified in Section 9.2.3.2 for no torsion reinforcement by astructure factor,  i , is less than 0.2 for all cross-sections(2) When the design torsional moment, M td , and the design pure torsional capacity,
M tcd , calculated using Eq. (9.2.26) satisfy Eq. (9.2.24) for all cross sections, examination
specified in Section 9.2.3.2 may be omitted provided that the minimum torsional
reinforcement is provided in accordance with Section 13.4.3.

 i M td / M tcd  0.5(9.2.24)(3) When the design torsional moment, M td , does not satisfy Eq. (9.2.24), torsion
reinforcement shall be provided in accordance with Section 9.2.3.3.
(4) When torsional moment and flexural moment, or torsional moment and shear force
act simultaneously, the examination for safety shall be carried out in a manner to taketheir interactions into consideration.

[Commentary] (1) From a design point of view, torsional moments are classified into equilibrium
torsional moments and compatibility torsional moments (See Fig. C9.2.17).

177

Standard Specifications for Concrete Structures-2007, Design(a) Equilibrium torsional moment (b) Equilibrium torsional moment(c) Compatibility torsional moment(Statically determinate structure) (Statically indeterminate structure)(Statically indeterminate structure)

Fig. C9.2.17

Equilibrium torsion and compatibility torsion

An equilibrium torsional moment is a torsional moment against which a structure must resist inorder to keep the force equilibrium in the overall structure system. If this torsional moment isneglected in the calculation of the force equilibrium of the structure, the stability of the overall
structure is destroyed. Namely, the capacity of the overall structure is completely dependent on
the capacity of the members subject to torsion.
Meanwhile, a compatibility torsional moment is a torsional moment caused by the compatibility
between the members composing a statically indeterminate structure, and provides an influence
mainly on the elastic deformation of the structure. In general, the torsional rigidity of a concrete
member is greatly reduced after diagonal cracking or plastic deformation by torsion. Hence, thetorsional moment acting on the member becomes very small when a concrete member of a staticallyindeterminate structure reaches such a state.
Therefore, in the ultimate limit state, compatibility torsion may be neglected in the force
equilibrium calculation, and it is clearly stated that the safety against a failure of a cross section
under torsional moments is examined only for equilibrium torsion. Also, when a member issubject to compatibility torsion, it is necessary to assume that the torsional rigidity of the member
cross-section is zero.
In an actual design, the examination for torsional moments may be deleted if a condition,
 i M td / M tcd  0.2 , is satisfied. This condition is defined for the case where the influence of
torsional moments is not significant. This is because examination for safety against torsion inaccordance with Section 9.2.3 is cumbersome even when only small equilibrium torsional moments
are acting.
(2) In the safety examination for torsion, torsion reinforcement is not required in general, when
the design torsional moment is not greater than the design torsional capacity with the resistance ofconcrete only. However, even in such a case, the suitable minimum reinforcement is required to
avoid a sudden failure, because cracking may occur due to the constraint at the member ends, stressconcentration, drying shrinkage, temperature differences in concrete, and others.
The minimum torsional reinforcement is determined so that the torsional capacity is at least
one-half of that of the member without torsion reinforcement.

178

Chapter 99.2.3.2

Verification of Structural Safety

Design torsional capacity for members without torsion reinforcement(1) The design torsional capacity, M tud , of a linear member without torsion
reinforcement, subject to torsional moments only, shall be obtained using Eq. (9.2.25).

M tud  M tcd
where,(9.2.25)

M tcd : design pure torsional capacity
M tcd   nt  K t  f td /  b(9.2.26)

K t : See Table 9.2.1

 nt : coefficient for axial compressive force such as prestress nt  1   ' nd /(1.5 ftd )f td : design tensile strength of concrete : average working compressive stress due to axial forces
 nd  7 f td
 nd

 b = 1.3 (in general)(2) When flexural moment, M d , and torsional moment, M td , act simultaneously,
examination for safety may be carried out by verifying that Eq. (9.2.27) is satisfied.

 i M td / M tcd  0.2  / 0.72  M d / M ud  1.0
where,(9.2.27)

M ud : design flexural capacity calculated in Section 9.2.1.1(3) When shear force, Vd , and torsional moment, M td , act simultaneously,
examination for safety may be carried out by verifying that Eq. (9.2.28) is satisfied i M td / M tcd  0.8Vd / V yd   1.0
where,(9.2.28)

V yd : design shear capacity calculated from Eq. (9.2.3)

179

Standard Specifications for Concrete Structures-2007, Design

Table 9.2.1

Factors for torsion[Commentary] (1) The mechanical behaviors of a concrete member before torsional cracking canbe estimated by a formula based on the elasticity theory, assuming that the entire concrete crosssection is effective. Since the strain is small at this stage, the torsional resistance provided byreinforcement is, in general, neglected when compared with that of concrete. Therefore, before thecracking, the formula based on the elasticity theory is applied to a concrete cross section neglecting
the effect of reinforcement, and the factors shown in Table 9.2.1 are used. Incidentally, K t for abox section is obtained the same as for a hollow section. The specifications for a box section in
Table 9.2.1 are determined by calculating with the ratio between member thickness and the overall
width of the box section in the direction of the thickness as the parameter.

The factor,  nt , in Eq. (9.2.26) for the axial compressive force such as prestressing forces
corresponds to  n in the equation to calculate the design shear capacity. This factor is derived
from the maximum principal tensile stress theory that a failure occurs when the principal tensilestress due to the combination of the axial stress and the torsional shear stress reaches the tensile
strength of concrete.
The term, 1.5 f td , in the equation for  nt is an approximate value of the average tensile
180

Chapter 9

Verification of Structural Safety

 , is the average value in the crossstrength of concrete. Also, the axial compressive stress,  ndsection.

When a member cross section is subjected to axial compressive stress with a triangular
distribution such as prestress, but not to uniform axial compressive stress, the theoretical torsional
capacity based on the elasticity, generally, does not coincide with the value calculated by using  nt
obtained from the average stress. However, it was decided that the average stress may be used in
the calculation of  nt , considering the fact that the theoretical values based on the elasticity are
considerably on the safety side according to experimental results, and that, in actual cases, theultimate axial stress distribution is different from that due to axial forces only, because of theflexural effect, and others.
 exceeds 7 f td , due to the combination of the compressive stress by torsional
When  ndmoments and the axial compressive stress, a member is in the domain of compressive failure andnot in the domain of failure by the maximum principal tensile stress. In this case, even a small
torsional moment may cause a sudden failure, which should be avoided. Therefore, the foregoing
limit is specified.
For a member subject to axial tensile forces,  nt given by Eq. (C9.2.8) may be used when theaxial tensile force is small and does not cause cracking  td  f td  . Also, it is assumed that nt  0 when cracking occurs only due to axial tensile forces  td  f td  .

 nt  1   td / f td 0   nt  1(C9.2.8)

where,  td : average working tensile stress due to axial tensile force
However, designing in such a manner that the overall member is subject to axial tensile forces,
and considering the combined load of torsional moments and axial tensile forces may result in the
reduction of the torsional capacity of the member, so that considerable torsion reinforcement may
be required. Therefore, it is desirable in such a case to consider means to avoid a design where amember is subject to combined load of torsional moments, and axial tensile forces by, for example,
applying prestress.
(2) The load capacity of a member subject to combined load of torsional moments and flexural
moments is calculated by using the interaction relationship obtained from the maximum principal
stress theory.
For a member without torsion reinforcement, and in the range where torsional moments are
dominant, it is the principle of design that a member develops no cracking. However, in the range
where flexural moments are dominant, the above design will present a large difference from thedesign method for flexural moment, unless cracking due to flexure is allowed. Therefore, herein,
Eq. (9.2.27) that assumes occurrence of cracking is specified for the tensile region due to flexure.
Eq. (9.2.27) integrates structure factors according to the interaction relationship indicated in theStandard Specification for Concrete Structures-1991 “Design”. When the structure factor is 1.15,
there is little difference from the conventional equation. When  i is smaller than 1.15,
Eq.(9.2.27) gives conservative values.
(3) For the load capacity of a member subject to combined torsional moments and shear forces
as well as that of a member subject to combined torsional and flexural moments, no cracking isallowed, in principle, in design for a member without torsion reinforcement when torsional
moments are dominant. When shearing forces are dominant, Eq. (9.2.28) which assumes occurrence
181Standard Specifications for Concrete Structures-2007, Designof cracking due to shear forces is specified.

γi Mtd / Mtcd

When torsional moment and flexural moment, or torsional moment and shear force are applied
simultaneously, the interaction relationships can be expressed, using the design member force, thedesign capacity of member cross section and the structure factor, as shown in Fig. C9.2.18 (a) and(b). Safety verification can be made, therefore, by confirming that the values obtained from agiven set of member forces are located inside the curve, that is, on the origin side. The reason for
the fact that these interaction relationships are shifted to  i M td / M tcd  0.2 is that the examination
for torsion may be completely omitted for  i M td / M tcd  0.2 .

Eq. (6.4.4)
Eq.(9.2.27)

0.9

0.2
0

1.0

Eq.(9.2.28)
Eq. (6.4.5)

0.2
0γi Md / Mud 1.0(a) Flexural moment and torsional
momentγi Vd / Vyd 1.0(b) Shear and torsional
momentFig. C9.2.18 Interaction relationship9.2.3.3

Design torsional capacity for members with torsion reinforcement(1) The design capacity for diagonal compression failure of web concrete against
torsion, M tcud , may be obtained using Eq. (9.2.29).

M tcud  K t  f wcd /  bwhere,(9.2.29)

fwcd  1.25 f 'cd (N/mm²), where f wcd  7.8 N/mm²

Kt:

See Table9.2.1

b:

1.3 (in general)(9.2.30)(2) The design torsional capacity of rectangular, circular, and annular cross sections,

M tyd , may be obtained using Eq. (9.2.31).
M tyd  2 Am qw  ql / bwhere,(9.2.31)

Am : effective area for torsion (b0d0: rectangular, d 02 / 4 : circular, annular)bo:length of the shorter side of transverse reinforcement

do:length of the longer side of transverse reinforcement for a rectangularcross section and the diameter of concrete cross section enclosed bytransverse reinforcement for circular and annular cross sectionsq w  Atw  f wd / s
q l   Atl  f ld / u182

Chapter 9

Verification of Structural Safety

 Atl : area of the longitudinal reinforcement that works effectively as torsion
reinforcement

Atw : area of a single reinforcing bar that works effectively as torsion
reinforcement

f ld , f wd : design yield stresses of longitudinal and transverse reinforcement,
respectivelys:longitudinal spacing of transverse
effectively as torsion reinforcement

reinforcement

that

works

u

:

length of the centerline of transverse reinforcement (2(b0+d0):
rectangular, πd0: circular, annular)b:

1.3 (in general)

When q w  1.25q l , q w  1.25q l , and when q l  1.25q w , ql  1.25qw(3) The design torsional capacity for T-, L-, and I-shaped sections may be obtained byconsidering the cross-section to be made up of rectangular sections and adding thetorsional capacities of individual rectangular components , M tydi , given by Eq. (9.2.31) inaccordance with the following (i)−(iv). However, each M tydi shall not exceed  · Ami .
where,

Ami : effective area for torsion of each component rectangle:

Mtydi/Ami of the component rectangle with maximum torsional effective
cross section(i) Ami may be taken as the area enclosed by the transverse reinforcement, as shownin Fig.6.4.1.
(ii) In cases when a longitudinal reinforcing bar for torsion belongs to more than one
component rectangles, it shall not be taken into consideration more than once in thiscalculation.
(iii) For a T-shaped section with a continuous flange, the transverse reinforcement in
the flange may be considered effective, although it does not enclose the longitudinal
reinforcement. However, when the amount of the upper and lower reinforcement in theflange is different, the smaller value shall be taken as the limit.
(iv) The one-side effective flange width for torsion, t , may be computed using Eq.
(9.2.32).

t  3t i
where,(9.2.32)t  l c(for the cantilever part)t  lb / 2 (for the middle part)ti:

average thickness of flange

lc , lb : lengths of cantilever slab and net spacing of beam, respectively

183

Standard Specifications for Concrete Structures-2007, DesignFig,9.2.3

Calculation scheme of Ami for T and L sections(4) A box section for which the ratio of the wall thickness to the overall width of the box
section in the direction of thickness is not less than 1/4 shall be designed as a solid
section. However, when the minimum ratio of the wall thickness to the overall width of
the box section in the direction of thickness is less than 1/4 the provisions of (7) below
shall apply.
(5) When a member is subject to flexural moment M d and torsional moment M td
simultaneously, examination for safety of rectangular, circular and annular sections may
be carried out by verifying that Eqs. (9.2.33) through (9.2.35) are satisfied.

 i M td / M tu min  1.0
 ) and  i M d   M ud  M ud
(for M ud  M ud

(9.2.33)2
  1 .3 ( MM d  M ud  M ' ud 
0
.
2
M
)

td
tcd
 
 ≤1.0γ i  M ' ud  M tu min  0 . 2 M tcd  and M ud  M ud
   i M d   M ud
(for M ud  M ud

(9.2.34)2
  1 . 15 ( MM d 
td  0 . 2 M tcd ) 
γ i 
 ≤1.0
  M

M
0
.
2
M
tu
tcd
ud
 

min


 and  i M d   M ud )(for M ud  M ud
where, M tu min :(9.2.35)

smaller value of M tucd and M tyd

Md:design flexural moment

M ud

:

absolute value of the design flexural capacity when the longitudinal
reinforcement located on the tension side under M d is considered as
tension reinforcement


M ud

:

absolute value of the design flexural capacity when the longitudinal
reinforcement located on the compression side under M d isconsidered as tension reinforcement
184Chapter 9

Verification of Structural Safety(6) When a member is subject to shear force Vd and torsional moment M td
simultaneously, examination for safety of rectangular, circular and annular sections may
be carried out by verifying that Eq. (9.2.36) is satisfied.

 i M td / M tu min  1  0.2 M tcd / M tu min Vd / V yd   1.0
where, M tu min :

V yd

:

(9.2.36)

smaller value of M tucd and M tyddesign shear capacity calculated from Eq. (9.2.3)(7) For a box section for which the ratio of the wall thickness to the overall width of thebox section in the direction of thickness is less than 1/4, the design torsional capacity,
M tyd , may be obtained using Eq. (9.2.37).

M tyd  2 Am Vodi min(9.2.37)

where, Vodi min : minimum value of the in-plane shear capacity per unit length of eachwall
In this case, the provisions of Section 13.4.3 shall be adopted for the joint part of eachwall and the anchoring of the reinforcement in concrete.
When a member is subject to flexural moments or shear forces together with torsional
moments, examination for safety may be carried out in a manner similar to that used for arectangular cross section[Commentary] (1) When a large amount of torsion reinforcement is arranged in such a mannerthat they do not yield in both longitudinal and transverse directions, concrete will crush due to the
diagonal compression in concrete before the torsion reinforcement yields. Since such a brittle
failure should be avoided, the failure capacity for this case is taken by Eq. (9.2.29). This equation
is an approximate one proposed as a substitution for limiting the quantity of torsion reinforcement
to be not greater than that of balanced strain reinforcement.

(2) The resistance of a concrete member against torsional moment after the occurrence of
torsional cracking may be considered as mainly due to the tensile force of reinforcement and thecompressive force of concrete. However, according to experimental data, it is deduced that a partof the resistance is apportioned by the tensile force in concrete, the dowel action of reinforcement,
the aggregate interlock, and others.
As the modeling methods for the analysis of the load bearing mechanism in this case, there are
two methods of which one is the space truss theory and the other the diagonal flexure theory.
Between them, the method based on the space truss theory is easier to calculate the torsional
capacity due to yielding of torsion reinforcement. Therefore, the design method based on thespace truss analogy is specified herein.
Equation (9.2.31) is an equation for the design torsional capacity derived from the force
equilibrium when reinforcement is composed by reinforcing bars in the longitudinal direction andtransverse reinforcing bars perpendicular to those, and when they both yield. However, when oneof the reinforcement is dominant, the reinforcement up to 1.25 times the lesser is considered as
torsion reinforcement.
Equation (9.2.31) may be considered as an equation for torsional capacity, replacing the solid
cross section by a hypothetical thin-wall box section and assuming that q  q w  q l is the ultimate
shear flow. In this case, the area enclosed by the centerline of the thin-wall section (the centerline
185

Standard Specifications for Concrete Structures-2007, Designof the shear flow) is the torsional effective cross-sectional area. Here, this area is assumed to be
the area enclosed by the centerline of the transverse reinforcement. There are various methods todefine the effective cross-sectional area, and one of them is to take the area enclosed by the line
connecting the center of each longitudinal reinforcing bar. At the present, as the conclusion towhich of the methods are the best has not been obtained, the torsional capacity computed by Eq.
(9.2.31) may be overestimated. Therefore, 1.3 is selected for the value of  b . The difference inthe effective cross-sectional area by each method becomes larger for a smaller section and smaller
for a larger section. Therefore,  b may be reduced up to about 1.15 when the precision of Eq.
(9.2.31) is confirmed.
(3) For T, L, or I section, information for the torsional capacity, M tyd is not sufficient at thepresent. Herein, the torsional capacity is basically considered as the sum of the torsional capacityof each component rectangle, based on a similar idea for the case of a member without torsion
reinforcement. The method to obtain Ami used in Eq. (9.2.31) is determined by considering theactual configuration of transverse reinforcement. According to this method, a part of concrete isdouble counted. However, it seems that there is no problem because the safety for concrete
crushing is examined by Eq. (9.2.29) for the entire cross section.
(4) For a box section, it has been confirmed from experimental data that it may be treated inapproximation as a solid cross section when the wall thickness is more than a certain value.
Therefore, this rule is proposed as a simple method for a box section.
(5) The interaction relationship of the capacity of a cross section of a member subject to flexuraland torsional moments simultaneously is influenced by the arrangement of longitudinal
reinforcement. For symmetric reinforcement arrangement with respect to the horizontal axis
(torsion type), the interaction curve becomes parabolic. A torsional capacity, however, increases
by flexural effects when the tensile flexural reinforcement is provided more than the compressive
reinforcement.
Various interaction relationships of the member capacity have been proposed. Herein, thefollowing two equations which can express the effect of reinforcement allocation by a simple form
are modified and shown below.
2

Fty  Mtd 
Md
1

 
Fby  Mtyd 
Mud(C9.2.9)2

 Mtd Fby  Md 

 

1
Fty  Mud  Mtyd (C9.2.10)

where, Fty, Fby : tensile forces at yielding of upper and lower longitudinal reinforcement,
respectively
 instead of Fby and Fty , respectively, and neglecting the increase of
Using M ud and M ud
torsional capacity due to the flexural effect from the safety point of view, and further considering
the consistency with the negligible torsion limit under which the effect of torsion is negligible(  i M ty  0.2M tcd ), Eqs. (9.2.33), (9.2.34) and (9.2.35) were derived. Eq. (9.2.34) integrates
structure factors according to the interaction relationship indicated in the Standard Specification forConcrete Structures-1991 “Design”. When the structure factor  i is 1.15, if M d / M ud is small
and the torsional effect is dominant, the equation is more conservative than the conventional
formula. If M d / M ud is large and the flexural effect is dominant, the equation becomes less
186

Chapter 9

Verification of Structural Safety

conservative than the conventional formula. Considering the fact, however, that the conventional
interaction relationship equation gives highly conservative approximations, and that design
torsional moment are relatively small, it was decided to make modifications mentioned above anduse a single structure factor. When  i becomes smaller than 1.15, the degree of safety graduallyrises even in the range where the flexural effect is dominant.
Like Eq. (9.2.34), Eq. (9.2.35) integrates structure factors according to the interaction
relationship indicated in the Standard Specification for Concrete Structures-1991 “Design”. In thiscase, differences from the conventional formula are small even when  i is 1.15. As  i becomes
smaller than 1.15, the new formula becomes even more conservative than the conventional formula.
Although these equations are for the case where reinforcement yields, they can be applied to thecase where concrete crushes before the reinforcement yields.
(6) Eq. (9.2.36) expresses the linear interaction relationship between torsion and shear, and also
is consistent with the concept of the negligible torsion limit.
(7) If the wall thickness of a box section becomes smaller, the torsional deformation andcapacity becomes different from those of a thick wall. If the wall thickness is thin, the shear flow
theory which assumes uniform torsional shear stresses in the direction of wall thickness can beapplied. In this case, in-plane shear forces due to torsional shear flow act in each wall composing
the box section. Therefore, calculating the in-plane shear capacity of each wall, the torsional
capacity of a box section is obtained. When the in-plane shear capacity is obtained in accordancewith Section 9.2.2.4, the in-plane shear capacity, Vod , is the smaller value of Txyd and T yyd . The
value of  b in the calculation of Txyd and T yyd may be chosen as 1.30. If the precision of Eq.
(9.2.37) is sufficiently confirmed from the torsional loading tests of large-scale box sections, andothers, the value of  b may be reduced to about 1.15.
The condition of applying the shear flow theory is that there is no out-of-plane deformation ineach wall surface. Therefore, when the wall is thin, such measures as installing more than one
inner partition wall may be necessary so that out-of-plane deformation is constrained.
When a box section is subject to shear forces and torsional moments at the same time, or issubject to flexure and torsional moments at the same time, safety examination may be made in asimilar manner as with a rectangular section.

187

Standard Specifications for Concrete Structures-2007, Design

9.3
9.3.1

Examination of Safety for Fatigue
General(1) Examination for performance of a structure in fatigue shall be carried out when theratio of variable loads to total loads is large, or the structure is subjected to a large
number of loading cycles.
(2) Safety of a beam under fatigue load shall be examined for flexural moment andshear force.
(3) Safety of a slab under fatigue load shall be examined for flexural moment andpunching shear.
(4) For a column, examination of safety under fatigue loading is not required in general.
However, when the applied flexural moment or axial tensile force is large, examination for
fatigue shall be carried out in a manner similar to that for beams.

[Commentary] (1) Fatigue failure of a material in a structure will directly affect the safety of thestructure. In Section 9.3, standards of verification of safety of a structure relating to fatigue failureof the material in the structure are provided, among the performance requirements of a structure forfatigue. Since, in most cases, serviceability of a structure is assured until the fatigue failure, safetyof the structure for fatigue load and environmental attack during the design life has only to be
examined in general. When the examination of serviceability for fatigue is required, anappropriate method based on experimental results, etc. should be employed.

(2) and (3) Examination of the limit state of failure of section in fatigue is required, in general,
primarily for fatigue failure of main and shear reinforcement subjected to repeated tensile force.
However, in special cases examination of concrete under fatigue may be necessary. Such cases
include those where lightweight aggregate concrete is used or the concrete is wet, as described in
the Commentary of Section 5.2.2. Such concretes may be relatively weak in fatigue comparedwith normal concrete and dry concrete, and shall, therefore, be examined for fatigue. Further,
shear capacity of a member in water may be lower. Therefore, for a member submerged in water,in addition to stress in shear reinforcement, examination of its fatigue capacity as a member without
shear reinforcement shall also be carried, even though shear reinforcement may actually beprovided in the member.

9.3.2

Design variable force and equivalent number of cycles

Irregular variable member forces may be divided into sets of individual variable
member forces and substituted for actions having an equivalent number of cycles, N , on
the basis of Minor’s hypothesis, to determine the design variable member force, S rd .

[Commentary] The variable force acting on the cross-section of a member on account of theapplication of different variable loads varies in a complex manner. This force could be considered
as a sequence of individual variable member forces ( S r1 , S r 2 ,  , S rm ) acting for different number ofcycles (n1 , n2 ,  , nm ) , respectively. Various methods have been proposed for this purpose, such as
the range-pair counting method. Depending on the characteristics of the variable loads applied, anappropriate method should be chosen.

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The equivalent number of cycles, N , for the design variable member force, S rd , can beobtained using Minor’s hypothesis for the sets of the individual variable member force. Thishypothesis, also denoted as a direct damage rule, is based on cumulative damage and assumes thatfatigue failure occurs on the basis of the sum of the damage caused by individual loads as describedin Eq. (C.9.3.1).
m

 N  1.0
ni

(C9.3.1)ii 1

For a member whose capacity of cross section is governed by fatigue strength of the steel
reinforcement, the equivalent number of cycles, N , for the design variable member force, S rd ,can be evaluated using Minor's hypothesis if the gradient of the S  N line is given by such as Eq.
(5.3.2). The equivalent number of cycles, N , for flexural moment ( M rd , M ri ) can be calculated
by Eq. (C.9.3.2). The equivalent number of cycles, N , for shear force (Vrd ,Vri ) can be calculated
by Eq. (C.9.3.3).
mN n (M / M )
i

ri

rd

1/ k

(C9.3.2)i 1

VVri  V pd  k 2Vcd Nni  ri 
Vrd Vrd  V pd  k 2Vcd 


i 1
m



1/ k

(C9.3.3)

where, k :a constant representing gradient of S  N line of steel reinforcement, may
be estimated in accordance with such as Section 5.3.2 (2),V pd

: design shear force due to permanent load,

Vcd: design shear capacity without shear reinforcementk2: a coefficient representing the influences of variable loads, which may be set to 0.5
in general.

For a member whose capacity of cross section is governed by the fatigue strength of concrete,the equivalent number of cycles, N , for the design variable member force, S rd , can be evaluatedby Eq.(C9.3.4) using Minor's hypothesis if the design fatigue strength of concrete is given by
Eq.(5.2.7).
m

N   ni  10

K
( S ri  S rd )k1 f S d(C9.3.4)t 1

where S d :member force when stress reaches f d

 p : stress due to permanent load,
k1 f , f d , K : defined in Section 5.2.2 (3).

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Standard Specifications for Concrete Structures-2007, Design

9.3.3

Fatigue strength of concrete members without shear reinforcement(1) Design shear fatigue capacity Vrcd , of reinforced concrete beam members without
shear reinforcement, may be computed using Eq. (9.3.1).
 log N 
Vrcd  Vcd (1  V pd / Vcd )1 

11 


(9.3.1)

where N : fatigue life,

Vcd is given by Eq. (9.2.4).
(2) Design punching shear fatigue capacity, Vrpd , of reinforced concrete slabs as plane
member may be computed using Eq. (9.3.2).
 log N 
Vrpd  V pcd (1  V pd / V pcd )1 

14 


(9.3.2)where, V pcd is derived using Eq. (9.2.11).

[Commentary] Although shear reinforcement is not usually provided for a footing and aretaining wall, these structures rarely fail in shear fatigue. However, in cases when fatigue does
become an issue, examination shall be performed using Eq. (9.3.1) or Eq. (9.3.2). When applying
these equations, it is recommended that the number of cycles is less than approximately 2  106 .

Fatigue capacity may be computed using Eq. (9.3.1) or Eq. (9.3.2) even in cases when amember is subjected to fatigue load underwater. In this case, however, the design compressive
strength of concrete, f cd , necessary to calculate Vcd or V pcd , shall be determined from results ofexperiments carried out in water.
The mechanism of contribution of shear reinforcement to shear capacity of a member subjected
to fatigue load underwater is not sufficiently clear. Thus, in such cases, it is recommended that to
be on the safe side, the fatigue shear capacity without shear reinforcement be adopted as the design
value.
Recent research has revealed that punching shear fatigue capacity is considerably reduced under
the action of repeated moving loads, such as a slab of highway bridges. In such cases, fatigue
capacity shall be estimated by appropriate methods, including laboratory tests. It has also beenfound that the fatigue capacity of the plane member is reduced to a greater extent if its surface iswet. Equation (9.3.2) in the Specification shall not be applied in cases of moving loads, since it
was derived from experimental results in which loading point was fixed.

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Verification of Serviceability

CHAPTER 10 VERIFICATION OF SERVICEABILITY

10.1

General(1) It shall be verified that concrete structures satisfy the required serviceability during
the design life.
(2) As a general rule, in the verification of the serviceability of a structure, it shall beverified that neither the structure nor any of its members reaches the serviceability limit
state under design loads.
(3) In general the serviceability limit states should be represented by indices such as
stress, crack, displacement, deformation and vibration, and the examination for the limit
states shall be carried out using an appropriate method.
(4) In limit state verification, compressive stress in the concrete and tensile stress in
the reinforcement due to bending moment and axial force shall be limited appropriately,
and the comfortability and other serviceability-related functions shall be verified by anappropriate method.

[Commentary] Structures or members are required to preserve sufficient functions suitable forthe purpose of their usage during their design life. Serviceability limit states are required to be
determined to suite the purpose of use of structures and shall be checked by appropriate methods ofwhich accuracy and applicable range are clarified. In Chapter 10, standard methods to verify
serviceability of structures are presented based on the assumption that they satisfy required the
durability verification specified in Chapter 8, the verification of early-age cracking specified in
Chapter 12, and constructability specified in the Standard Specifications for Concrete Structures,“Materials and Construction”, and therefore material deterioration during the design life isnegligible.
As far as the serviceability, its limit states, and verification index are concerned, various limit
states may be considered. In general, however, only the serviceability limit states listed in Table
C4.1.1 may be examined. In this chapter, verification for appearance, vibration, displacement, anddeformation associated serviceability, water resistance, and damage due to fire is explained. Other
functions, which are not mentioned in this chapter, may be verified by appropriate method, if
necessary.
Although the relationship of specific serviceability-related performance items with compressive
stress in the concrete and tensile stress in the reinforcement due to bending moment and axial force
is not indicated clearly, this chapter examines them as a basis for serviceability verification, taking
past design examples, etc., into consideration.

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Standard Specifications for Concrete Structures-2007, Design

10.2

Limit Value of Stresses

Compressive stress in concrete and tensile stress in reinforcement due to flexural
moment(s) and axial force(s) shall not exceed the limiting values given in (1) and (2),respectively.
(1) Limiting value of flexural compressive stress and axial compressive stress inconcrete under permanent load shall be 0.4 f ck , where f ck is the characteristic
compressive strength of concrete. In cases when concrete is permanently subjected tomulti-dimensional restraint, the limiting value of stress may be increased in accordancewith the state of stress in multi-dimensional compression. However, such increment
shall not exceed 10% and 20% in the case of two-dimensional and three-dimensional
restraint, respectively.
(2) Limiting value of tensile stress in reinforcement shall be f yk , wherecharacteristic yield strength of reinforcement.

f yk is[Commentary] (1) Maximum limit on the compressive stress of concrete is introduced in order
to avoid excessive creep strains and cracks in the longitudinal direction due to compressive forces.
These limiting values have been determined considering the modulus of elasticity of concrete given
in Table 5.2.1 in Section 5.2.5 and the conditions in which the provisions for the creep coefficient of
concrete described in Section 5.2.9 can be adopted. However, in cases when the modulus ofelasticity and creep coefficient of concrete are determined differently, the limiting value ofcompressive stress of concrete may be determined in a manner independent of the provisions of thissection. The standard methods to examine safety, serviceability and seismic performance ofstructures that are shown in the Specification are based on the provisions in this clause. In casethat these limit values are not adopted, safety and seismic performance shall be examined taking theeffect of nonlinear creep strain into account.
The limiting value of compressive stress in concrete may be increased for concrete confined
three-dimensionally, such as concrete in steel-concrete composite columns, and concrete subjected
to permanent earth pressure or water pressure, such as concrete in underground structures. This isbecause compressive strength of the concrete increases and creep decreases depending upon the
degree of confinement. It has been reported so far that static strength of concrete increases by
20-30% under two-dimensional confinement and 30-40% under three-dimensional confinement bysteel. However, from safety considerations, the permitted increment in strength should be limited
as shown in this section.
(2) No limits may be imposed on the tensile stress in the reinforcement when carrying out theexamination for the cracking in concrete and the fatigue of reinforcement. However, in cases
when the tensile stress exceeds the elastic limit, some difficulties, such as the assumptions madeduring structural or stress analysis no longer holding, may be encountered. Therefore, the tensilestress in the reinforcement shall be smaller than the yield stress. This is why the maximum values ofpermanent loads and variable loads under service conditions must be used as design loads.

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Chapter 10

10.3
10.3.1

Verification of Serviceability

Verification Related to Appearance
General(1) In the verification of the appearance-related serviceability of a structure, design
response values shall be calculated in accordance with Chapter 7, and design limit values
shall be determined according to the environment of the structure or its members.
(2) The appearance-related serviceability of a reinforced concrete structure orprestressed and reinforced concrete structure is verified by using crack width as averification index may be done in accordance with Sections 10.3.2 and 10.3.3. The
verification of the appearance-related serviceability of prestressed concrete structuresusing crack width as a verification index may be omitted.
(3) When appearance-related serviceability is verified by using displacement or
deformation as an index, Section 10.5 shall be followed.

[Commentary] (1) Concrete structures must not make people uneasy or uncomfortable or obstruct
the use of the structures with cracks, dirt, etc., on their surfaces.
This specification describes a verification method to make sure cracks do not mar theappearance of concrete structures. Verification with respect to other factors contributing toappearance degradation such as dirt, etc., must be done separately by an appropriate method.
(2) In the verification related to cracks from the viewpoint of appearance, crack width or stress
may be used as a verification index.
There are many kinds of cracks in concrete structures. This clause deals with cracks due tostructural loads, namely flexural moment, shear force, torsional moment and axial load.
The verification related to cracks due to loading needs to be performed under service condition.
If the structural system changes during construction, member forces need be calculated taking into
account the effect of these changes.
Since cracks may be also induced on account of the materials used, methods of construction, etc.
the effect of these on cracking should be accounted for during design. For example, it is noted that
thermal cracks due to heat generated during hydration of cement in concrete, or, cracks formed due
to shrinkage of concrete during construction, may greatly affect the structure. Concerning this,
Chapter 12 must be followed. Crack control measures to be taken at the design stage include crack
width control reinforcement, crack inducing joints and crack control prestressing. When designingcrack control measures, it is good practice to refer to previous studies and past examples. For aprestressed concrete structure in which cracking is not permissible under normal service conditions,verification concerning flexural crack width may be omitted if the extreme fiber tensile stress in theconcrete under permanent loads does not become a tensile stress and if the extreme fiber stress inthe concrete under a combination of permanent loads and variable loads is not greater than thedesign flexural crack strength and the required tension reinforcement is in place.

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Standard Specifications for Concrete Structures-2007, Design

10.3.2

Flexural cracks

In flexural crack verification, the flexural crack width at the concrete surface shall betaken as a design response value, and the limit value of the maximum crack width at theconcrete surface from the viewpoint of appearance shall be taken as a design limit value.

[Commentary] (1) In crack width verification for reinforced concrete structures and prestressed
and reinforced concrete structures that permit the occurrence of cracking under normal service
conditions, the basic rule is to use crack width as a verification index. In this case, in view of thefact that appearance evaluation is affected by psychological factors, the limit value of crack width
needs to be a value that does not pose any appearance-related problem. According to past examples
and experience, usually the limit value may be set at about 0.3 mm. In this case, the maximum
value of flexural crack width at the concrete surface may be calculated from Eq. 7.4.4. The earlier
the age at which concrete cracking occurs, the greater the crack width at the concrete surface
becomes. The recommended method when verifying the appearance-related performance of astructure located in a dry environment by calculating crack width from Eq. 7.4.4 is to determine thevalue of ε'csd in accordance with Section 5.2.8, assuming construction steps such as placing theconcrete for the structure and removing the formwork and false work and taking into accountmeasured values of shrinkage strain and the ages at which cracking occurs. In general, in the case of
concrete with a shrinkage strain as determined by the JIS test method of 1000 × 10−6 or smaller, if
cracking occurs at ages of 30 to 200 days, ε'csd may be assumed to be about 450 to 300 × 10−6. Ifshrinkage-compensating concrete is used, ε'csd may be reduced in view of the steel stress reduction
due to the crack control effect and expansion of the shrinkage-compensating concrete.
In the case of a reinforced concrete structure, if the extreme fiber tensile stress in the concretewith a fully effective cross section is not greater than flexural crack strength, verification
concerning flexural crack width may be omitted by making the stress in the tension reinforcement
under permanent loads not greater than the limit value of steel stress, sl1, in accordance with
Chapter 8. In this case, to apply the limit value of steel stress under permanent loads, the values fornormal environmental conditions may be used.

10.3.3

Shear cracks and torsion cracks(1) As a general rule, verification for shear cracking and torsion cracking shall be doneby using shear or torsion crack width at the concrete surface as a design response value
and the limit value of the maximum crack width at the concrete surface determined fromthe viewpoint of appearance as a design limit value.
(2) Verification for shear cracking and torsion cracking may be omitted if therequirements described in Chapter 8 are met.

[Commentary] The mechanism of initiation and propagation of shear cracks and torsion cracks isdifferent from that of flexural cracks, and is not clear enough. Therefore, it is difficult to calculatecrack width in the present technical level. By limiting the stress in shear reinforcement and torsion
reinforcement, precise examinations may not be required.

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Chapter 10

10.4

Verification of Serviceability

Verification for Vibration

When vibration is considered in the verification of serviceability, examination forvibration caused by variable loads shall be carried out using appropriate methods toensure that functions and serviceability of the structure are not impaired.

[Commentary] Vibration are rarely cause of problems in concrete structures. However, in cases
when the time period of variable loading is close to the natural period of members, resonance may
result. This may bring lead to an uncomfortable environment during use and cause cracks in the
structure. In such cases, it is advisable to take some countermeasure, such as altering the natural
period of the member by changing the dimension of members, etc.

10.5

Examination for Displacement and Deformation(1) When displacement and deformation are considered in the verification ofserviceability, it is required to follow the method in this section.
(2) Short-term displacement and deformation, and long-term displacement anddeformation shall be considered separately. Short-term displacement and deformationrefer to instantaneous displacement and deformation of the structure or member upon
application of load(s). Long-term displacement and deformation include short-term
displacement and deformation and additional displacement and deformation undersustaining loads.
(3) Short-term displacement and deformation, and long-term displacement anddeformation of the structure or member shall be smaller than the permissible
displacement and deformation.
(4) Permissible displacement and deformation of the structure or member shall be
determined considering the type and the purpose of use of the structure, the type ofload(s), etc.

[Commentary] (1) Displacements and deformations, in general, are related to maintaining
functions and serviceability for safety and comfort with moving traffic, preventing damages due toexcessive displacements and deformations, and maintaining esthetics of structures. Considering
the purpose of use of a structure, enough stiffness and appropriate camber should be provided, andsupport need to be selected adequately. It is advisable to examine the influences of gasp kinks
between members and expansions/shortenings of members if necessary. For structures resting
directly on the ground, it is advisable to examine the serviceability limit state of vertical support
using an appropriate method, in cases when such an examination is specially required.
(2) There are two types of displacements and deformations. One is short-term displacements
and deformations caused instantaneously at the time of application of load. The other is additional
displacements and deformations caused by shrinkage and creep of concrete due to permanent loads.
Long-term displacements and deformations are defined as the sum of the short-term and the
additional displacements and deformations.
(3) When the span length of a member is much shorter than the height of its cross section,
examination of displacements and deformations may be omitted. However, if long-term
displacements and deformations due to shrinkage or creep of concrete cannot be neglected, there isa need to examine the long-term displacements and deformations.
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Standard Specifications for Concrete Structures-2007, Design(4) Excessive displacements and deformations of structures or members cause an uncomfortablefeeling when using structures and reduce its functionality and good appearance. In order that sucha situation is avoided and the structures are used in a good condition, it is necessary to determine
the permissible displacements and deformations, considering the type and planned use of thestructure, and the type of loads.
Permissible displacements and deformations, in general, are determined for the ordinary
serviceability limit states. However, if necessary, they may be determined for limit states inextraordinary cases such as earthquakes.

10.6

Verification for Water-Tightness(1) In the verification for water tightness, the performance of concrete structure shallnot be impaired by water or moisture permeation.
(2) The verification of water-tightness must be carried out on the each part of structurewith the verification index to be the transmissibility. The performance of the concrete
structure in terms of water tightness may be secured using appropriate surface treatment.
In such cases, the effectiveness of the treatment shall be evaluated using appropriate
methods.
(3) In the case of the verification for water tightness by water flow, the verification
should be carried out by ensuring that:

i

Qd
 1.0
Qmax

(10.6.1)

where,

 i : a constant, representing the importance of the structure. In general, it may be taken
as 1.0, but may be increased to 1.1 for important structures.

Qmax : allowable flow rate per unit time (m3/s).
Qd : designed flow rate per unit time (m3/s).
h
Qd  γpn  K d  A   Qcjd L(10.6.2)

where,

K d : design value of permeability coefficient of concrete in structure (m/s).
 Kk  c

K k : characteristic value of the permeability coefficient of concrete (m/s).
A : total surface area of concrete through which water may penetrate (m2)h : difference in the water levels between the interior and exterior surfaces of thestructure (m).

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Chapter 10

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L : expected length of water permeation. In general, L may be taken as the designed
thickness of member.

Q jcd : design value of the flow rate from crack or joint (m3/s)

 pn : safety factor to account for the variation in the designed transmissibility, Qd .
Normally, it should be taken as 1.15.

 c : concrete material factor. In general it may be taken as 1.0.
[Commentary] (1) Concrete structures requiring water tightness is the structures greatly affectedby the permeation of water on their structure safety, durability, functionality, maintenance,
appearance, etc. The examples are storage facilities, underground structures, hydraulic structures,water tanks, sewage facilities, tunnels, etc. It is also known that the leaching of calcium fromconcrete over a sustained period of time can also impair the required performance of concrete
structure. The provisions of this Section may be ignored if water-tightness is not one of the required
performance parameters.
(2) The verification of water-tightness must be carried out not on the structure in a whole but oneach part, with the only verification index to be the transmissibility. In order to secure the watertightness of a concrete structure, measures such as using a waterproofing sheet especially in part(s)requiring water tightness, inducing crack at pre-designed locations (joints, and then taking suitablewater-proofing measures for such locations may also be considered. It should, however, be notedthat since the effectiveness of such measures could vary largely depending on the materials used
(during construction), the methods of construction adopted, etc., it is important that the details ofsuch measures are worked out only after appropriate evaluation and consideration of various factors,
including the structure maintenance plan.
(3) In the case of tank structures, the reduction rate of stored liquid in the tank can be treated as
the verification index aiming at the whole structure. For example, the water level in the PC
egg-shape digester (sewage digestion tank) must vary just within 5mm from the specified waterlevel in 24 hours. Permeation amount within 0.1% of water in water tank during circulation can bedisregarded. In addition, the allowable water permeation is governed by the structure function, theprocessing capacity of drainage system and the evaporation of water from structure surface.
The water-tightness of a concrete structure is related to not only the water-tightness of thenormal concrete used in the structure, but also the discontinuity arising at particular positions suchas cracks, joints etc.. In general, the extent of water permeation through a crack or verticalconstruction joint is much larger than that of sound concrete. Therefore, it is desirable to avoid theoccurrence of cracks when the water tightness of structure is required. It should be noted that theprovision of adequate and appropriate steel reinforcing bars is an effective means of controllingcrack with and preventing cracking in concrete. The use of expansive material serves a similar
purpose. It may be noted that carrying out an appropriate treatment for construction joints andinstalling water-sealing plates in the direction perpendicular to the joint are very effective incontrolling water permeation through these surfaces.
The transmissibility through sound parts shall be evaluated based on the permeability coefficient
using Darcy's law. The water permeability coefficient is a constant of proportionality to varylinearly with the hydraulic gradient. This coefficient may be obtained using the method given by theUnited States Reclamation Bureau (referred to as the “Output Method”), or, the method given in
DIN1048 (referred to here as the “Input Method”). The permeability coefficient can be estimatedindirectly from its empirical relationships with water-cement ratio or with compressive strength, orfrom characteristic values of micro-pore structure such as the coefficient of air permeability or the197

Standard Specifications for Concrete Structures-2007, Design

total porosity of concrete. In such a case, a suitable factor of safety should be used, depending upon
the accuracy of the method(s) used. The following equation which expresses relationship between
water-cement ratio and permeability coefficient is obtained from previous research results. The
safety factor of 1.0 may be selected for this equation.
log K p  4.3  W / C  12.5

(C 10.6.1)

Where, w/c is water-cement (binder) ratio.
In the event that water penetration through discontinuous surfaces such as cracks and joints
cannot be prevented, the verification for transmissibility shall be carried out with duel considerationon the influence of crack or joint as main items of verification. When the water permeation throughstructure members is considered a one-dimensional process, Eq. (10.6.2) shall be used to evaluate
the total transmissibility through sound parts and from cracks or joints. Appropriate permeability
tests shall be carried out for obtaining the transmissibility through cracks and joints.
Prevention of cracking or permissible crack width for water-tightness shall meet therequirements of examination of water-tightness. In general, Table C10.6.1 may be used as areference depending upon the required level of water-tightness and dominant force acting on the
cross-section.

Table C10.6.1

Reference values for permissible crack width for water-tightness (mm)Requiredlevel
water-tightnessofDominant
Axial tension
force actingon
the Flexural
2)
cross-section moment

High

Normal----1)

0.1

0.1

0.2

1) Concrete stresses due to stress resultant should be in compression at whole
sectional area.
Minimum compressive stress should be greater than2
0.5N/mm . In cases when detailed analysis is carried out the value may be
determined differently.
2) Under the action of reversed cyclic loading, the permissible crack width
should be determined in a manner similar to that under axial tension.

Here, past test data used to set the permissible crack width have all been obtained frommembers with fully penetrating cracks. In these tests, it has been reported that the amount of
permeating water is very little when the applied water pressure is below 0.9N/mm2 and the crack
width is less than 0.1mm. In Table C10.6.1, it has been assumed that that water-tightness can beeasily achieved under flexural moment because part of the section is in compression.

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Chapter 10

10.7

Verification of Serviceability

Verification for Fire Resistance(1) The required performance of a concrete structure shall not be impaired by the fire.
(2) In case when the concrete meets criteria for fire resistance, the structure may be
assumed that its performance will not be impaired on account of fire.

[Commentary] (1) It is important to ensure that the performance of normal civil engineering
structures during their designed service life will not be affected by the deterioration of concrete or
the quality degradation of reinforcing materials on account of fire.
(2) Since the fire resistance of concrete structures is basically determined by that of the coverconcrete, it is considered sufficient by ensuring that the requirements for the fire resistance of thecover concrete are satisfied. The verification for the fire resistance of cover concrete shall be carriedout at the mix design stage as stipulated in “Construction”. Prestressed concrete structures andmembers may degrade rapidly, so the investigation on the fire resistance must be carried carefully
once the rapid degradation under fire is anticipated.
In general, when the minimum cover depth is 20mm larger than the cover depth required fornormal environment in 8.3.6., the verification for fire resistance can be omitted.

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Standard Specifications for Concrete Structures-2007, Design

CHAPTER 11 SEISMIC DESIGN

11.0

m
Mm
Mn
η

11.1

Notation::::rotation angle of member at the maximum strength
maximum moment
yield moment of tensile reinforcement
coefficient of decreasing gradient

General(1) The verification of earthquake resistance shall be carried out not only to ensure thesafety of a structure but also to prevent fatal structural damage that has adverse effects
on the daily civil life.
(2) In the verification of earthquake resistance, seismic performance shall be definedas verification limit values to ensure comprehensively for safety against an earthquake
and usability and restorability after the earthquake.
(3) In principle, the seismic performance shall be defined not only to ensure the safetyof structures for ground motion but also to consider such factors as the ensuring human
life, the evacuation, rescue activities and secondary disaster prevention activities, thebasic infrastructure and economic activities, the degree of difficulty in restoration andconstruction cost. Generally, the seismic performance is classified as follows:(i) Seismic Performance Grade 1: The structure is able to keep the function for anearthquake without restoration.
(ii) Seismic Performance Grade 2: The functions of the structure can be restored in ashort period of time after an earthquake.
(iii) Seismic Performance Grade 3: The structural system does not collapse for anearthquake.
(4) The verification of the earthquake resistance of a structure shall be conducted inorder to ensure the required seismic performance for the assumed ground motion. In
general, verification shall ascertain the follows:(i) Seismic Performance Grade 1 is applied to Level 1 ground motion.
(ii) Seismic Performance Grade 2 or Seismic Performance Grade 3 is applied to Level 2
ground motion.
(5) Limit values for the seismic design of a structure shall be determined appropriately.
In principle, limit values for Seismic Performance Grades 1 and 2 shall be determinedtaking into consideration the influence of the damage state to structural members on theentire structure, and limit values for Seismic Performance Grade 3 shall be determinedtaking into consideration the relationship between the stability of the structure and the200

Chapter 11

Seismic Design

load-carrying capacity of members. In general, it may be assumed that the structure
satisfies seismic performance requirements if the limit values for members listed below
are satisfied.
(i) Seismic Performance Grade 1: yield displacement or yield rotation angle ofmembers(ii) Seismic Performance Grade 2: shear strength and torsion strength and ultimate
displacement or ultimate rotation angle of members(iii) Seismic Performance Grade 3: shear strength of vertical members and self-weightbearing capacity of a structure(6) Structural planning shall take into consideration the topographical, geological andgeotechnical characteristics of the construction site and the influence on adjacentstructures so that the structural system can have the required seismic performance. In
general, the following should be taken into consideration in structural planning:(i) Coupling with adjacent structures should be taken into consideration.
(ii) Attention should be given to the center of stiffness of the structure and the centerof loads so that they coincide as much as possible.
(iii) The plastic hinge regions in members should be designed to have sufficientductility.
(iv) Seismic isolation and structural response control technologies are taken into
consideration.
(v) Soil flow resulting from liquefaction should be taken consideration in design not tohave adverse effects on the structure.
(vi) In the case of an underground structure, consideration should be given to prevent
water infiltration into the structure and joints, leakage of the content of the structure, uplift
due to soil liquefaction, and so on.
(vii) If the location of an active fault is clearly known and a structure is constructedacross the fault, not only the structure should have safety for ground acceleration but
also system redundancy should be taken into consideration.
(viii) The safety of the people around the structure during an earthquake should betaken into consideration.

[Commentary] (1) In general, infrastructures are base of life of people and social and production
activities. When deciding on seismic performance for a structure, it should be considered not only
the dynamic response of the structure according to the magnitude of assumed earthquakes, but also
the post-quake restorability. In connection with a strong earthquake whose probability ofoccurrence for the service life time is very low, it is necessary to prevent fatal structural damage,but it is also necessary, from the view of social and economic activities, to minimize functional
degradation of the structure so that the daily civil life, social and production activities can berestored as soon as possible.
(2), (3) Seismic Performance Grade 1 refers to the performance that ensures residual201

Standard Specifications for Concrete Structures-2007, Design

deformation of the structure is kept within a small deformation range. It may be thought that thisseismic performance requirement is satisfied if the dynamic response of the members is before theiryielding.
Seismic Performance Grade 2 refers to the performance ensuring that load-carrying capacity
does not decrease. In general, it may be thought that this seismic performance requirement issatisfied if none of the structural members fails in shear and the response displacement of themembers does not reach the ultimate displacement. In special cases, residual displacement may be
specified. In such cases, it is necessary to calculate residual displacement by an appropriate
method and verify that the calculated values are within tolerance. In general, the residual
displacement of the foundation including the ground tends to be larger than the residual deformationof the structure. An appropriate evaluation method of the residual displacement of the foundationis necessary. Structures in which seismic force acts mainly as in-plane force such as wall
structures cannot be expected to have large deformation capacity. In seismic design of such
structures, it is necessary to have sufficient shear capacity in order to prevent brittle failure.
Seismic Performance Grade 3 refers to the performance that ensure that even if the structure isdifficult to repair, the structural system does not collapse because of the self-weight of the structure,soil pressure and water (fluid) pressure, and so on. Generally, a concrete structure satisfies
Seismic Performance Grade 3 if its members are sufficiently safe from shear failure. Dependingon the type of structure, however, the displacement of the structural system may become
excessively large and the deformation of the members due to the self-weight and additional moment
increase until collapse. It is necessary to verify by an appropriate method for such case.
The terms "repair" and "strengthening" used in this chapter indicates the purpose of restoration
work carried out after a structure is damaged. "Repair" means restoration work carried out torestore the original state, and "strengthening" means restoration work carried out so that structuralcharacteristics such as strength and deformation capacity satisfies seismic performancerequirements.
(4) When verifying the earthquake resistance of a structure, it is necessary to define seismic
performance requirements for a structure corresponding to the magnitude of ground motion and its
return period. Such requirements must be determined in view of such factors as the purpose andfunctions of the structure, the degree of contribution to or influence on the local community andsociety, asset value, the degree of influence of damage on the surroundings, the availability ofalternatives and the degree of difficulty in restoration.
The verification, with respect to the combinations mentioned above, is applicable for ordinary
civil engineering structures. For special structures, for example, LNG in-ground storage tanks, it
is recommended that Level 2 ground motion is further classified into two levels as shown below for
verification purposes:i) Strong ground motion the probability of occurrence for the service life time is relatively lowii) Extremely strong ground motion the probability of occurrence for the service life time is verylow(5) In order to verify the seismic performance of a structure, it is necessary to determine thelimit values of response that ensure the predetermined seismic performance. Although the seismic
performance of a structure depends on the structural characteristics of its members, the seismic
performance requirements specified for the structure do not need to be applied as are to structuralmembers. A two-layer rigid-frame pier, for example, does not collapse even if the intermediatelevel beams have failed in shear. Since the relationship between the seismic performance of astructure and the damage level of its members is usually unknown, limit values are set for structural
202

Chapter 11

Seismic Design

members described above.
(i) If the reinforcement does not yield during an earthquake, usually Seismic Performance Grade
1 is satisfied. On the assumption that shear failure does not occur, therefore, it is required that theyield displacement or yield rotation angle of structural members is used as a limit value for Seismic
Performance Grade 1. Usually, the concrete stress does not yet reach the compressive strength
before the reinforcement yielding. If, however, the amount of reinforcement is large, it may benecessary to use the compressive strength of concrete as a limit value. If two structures are locatedclose together so that they might crash with each other or if it is necessary to check whether passing
vehicles are safe, it is recommended to use the limit displacement determined from the viewpoint offunctional protection. In general, in cases where a structure is required to have Seismic
Performance Grade 2 or Seismic Performance Grade 3 against Level 2 ground motion, if thestructure has the safety requirements with respect to shear force, then it is safe against shear force
even under the Seismic Performance Grade 1 criteria. Usually, therefore, the verification of safety
against shear force under the Seismic Performance Grade 1 criteria is not necessary. However,satisfying Seismic Performance Grade 2 against Level 2 ground motion, it is necessary to verify theshear strength for some of members if these are to satisfy the Seismic Performance Grade 1 criteria.
(ii) Concerning Seismic Performance Grade 2, it is required that limit values can be set
appropriately within the range beyond the yield displacement until reaching the ultimate
displacement while preventing shear failure and torsion failure, in view of the degree of difficulty inrepairing the structure and the influence of the damage to the structural members, in order to restore
the functions of the structure in a short period of time after an earthquake.
This means that in order to achieve Seismic Performance Grade 2 (the functions of the structure
can be restored in a short period of time after an earthquake), the designer must determine limit
values appropriately within the range beyond the yield displacement until reaching the ultimate
displacement, taking into consideration the damage conditions of the structures and the difficulty ofrepair.
Many experimental tests have shown that the load-carrying capacity decrease clearlycorresponding to the spalling of cover concrete. Moreover, the damaged members can be repairedby such as crack grouting in many cased before the spalling of cover concrete. However, it isdifficult to repair the damaged member after the spalling of cover concrete. In the case of an
ordinary column, spalling of cover concrete tends to occur at a displacement close to the ultimate
displacement. This indicates that repair can be done in a short period of time, if the limit value isdefined as the displacement related to near the maximum strength.
For the members, such as the bottom of bridge piers, underground beams and piles, members
supporting overburden loads such as upper beams of rigid-frame viaducts and girders of prestressed
concrete bridges, cannot be inspected and repaired in a short period of time after an earthquake. In
this case, the limit values for Seismic Performance Grade 2 shall be defined before the maximum
strength point.
(iii) In the case of a concrete structure, in general, if vertical members are sufficiently safe fromshear failure, the structure satisfies Seismic Performance Grade 3. However, there are cases thatthe displacement of the structural system becomes so large because of the deformation of members
due to their weights and additional moment, and structure system fails. Using dynamic analysis isnecessary to verify that the structure does not collapse because of its own weight.
(6) In order to satisfy the required seismic performance as a structural system, seismic design ofa structure should generally take the following into consideration:(i) If the dynamic characteristics, type of foundation structure, ground conditions, and so on are203

Standard Specifications for Concrete Structures-2007, Design

different between adjoining structures, the response of one structure may affect that of the otherstructures and unexpected damage may be caused. Structural planning needs to take this into
consideration.
(ii) It is important that the center of stiffness of the structure coincide with the center of load
action as much as possible to minimize the horizontal torsion of the structure. It is necessary toenhance the seismic performance, if the both of center cannot coincide.
(iii) In order to prevent excessive deformation and stress concentration and prevent thecollapsing of the structure, it is important to give the sufficient ductility by reinforcing with asufficient amount of hoop reinforcement in plastic hinge regions. To be more specific, it isrecommended to have two times shear capacity to flexural capacity in plastic hinge regions. Fromthe viewpoint of seismic performance, statistically indeterminate structures are superior in terms ofdeformation capacity to statically determinate structures because forces can be redistributed instatically indeterminate structures.
(iv) In order to enhance the seismic performance of a structure, it is recommended to consider
the use of seismic isolation or structural response control technologies. Seismic isolation enhances
the damping of a structure with a relatively short period of vibration. A structural response control
system with an energy absorption mechanism enhances the damping of a structure with a long
period of vibration.
(v) It is important to consider that soil flow caused by liquefaction does not subject to thestructure. Soil liquefaction and the resultant lateral flow of soil greatly affect the earthquake
resistance of underground structures. In seismic design, it is necessary to carefully examine thestability of soil.
(vi) The displacement and deformation behavior and stability of the surrounding ground areimportant in the seismic design of underground structures. For a structure with a large crosssection, the three-dimensional displacement distribution, that is the distribution not only in a plane
but also in the direction of depth, is important. For a buried pipeline with a small cross section,
the displacement distribution along the pipeline is important. It is necessary, therefore, to fully
understand the seismic response of the surface layer of the ground. In order for an undergroundstructure to maintain the required seismic performance, it is recommended to consider the use ofstructures and materials designed for enhancing flexibility.
(vii) For the surface structure, if the location of an active fault is clearly known, constructing
continuous structures and increasing the strength may be effective for forced displacement causedby the fault. For the underground structures, large cross sections, double-wall structures, flexible
structures, and isolating structures from internal facilities may be effective. If the forced
displacement is so large as to introduce these technologies, it is necessary to consider the system
planning such as using alternative structures in order to minimize functional degradation in civil
life.
(viii) Depending on the dynamic behavior of a structure, the safety of the people using thestructure and the people living near the structure may be threatened. For example, even if damage
to a bridge structure is not serious, large deformation or displacement of the structure may causesuch problems as derailment of trains or falling of vehicles. If vehicles fall, people living near the
structure may be endangered. In structural planning, it is necessary to take into consideration
methods for preventing such consequences.

204

Chapter 11

11.2

Seismic Design

Definition of Limit Values(1) Yield displacement of member can be given at the yielding of center of tensile
reinforcement.
(2) Ultimate displacement of member can be given at the maximum displacement whichis greater than yield strength.
(3) Shear strength and torsion strength are given by referring to Chapter 9.

[Commentary] (1), (2) Capacity of displacement and strength are given by referring to Chapter 9.
For the multi arrangement of reinforcement, the reinforcement yielding from the outside
sequentially, and the clear yielding of member does not appear on the load-displacement
relationship. The yield displacement can be given as described above.
The load-carrying capacity of flexural member decreases after the spalling of cover concreteand buckling of longitudinal bars. As the load-carrying capacity undergo the yield strength,
serious damage as crush of the core concrete and fracture of longitudinal bars occur. The ultimate
displacement is defined as the maximum displacement greater than yield strength. Typicalload-displacement relationship of member is shown in Fig. C11.2.1. If the load-carrying capacity
has sustainable performance in the cyclic large deformation under the yield strength, the ultimate
displacement can be defined as the other limit value.

Load

Yield strength

Displacement
Yield displacement

Fig. C11.2.1

Ultimate displacement

Limit values of member

Calculating by beam element method, response displacement is related to the rotation angle.
The yield rotation angle of member can be given by Eq. (C7.2.1). The ultimate rotation angle has
to be evaluated for each member by appropriate method. In general, the ultimate rotation angle
can be given by Eq. (C11.2.1).

 n   m   1  M n M m 

(11.2.1)

where, m : rotation angle of member at the maximum strength given in Eq. (C7.2.5)
Mm : maximum moment given by referring to Section 9.2.1, where member factor of 1.0
is used.

205

Standard Specifications for Concrete Structures-2007, Design

Mn : yield moment of tensile reinforcementη : coefficient of decreasing gradient, where 0.1 is used in general.
It is necessary to model the post-peak behavior shown in load-displacement relationship in
verification of Seismic Performance Grade 2 and 3. It is difficult to evaluate the post-peak
behavior of concrete members, then, the decreasing gradient of skeleton of load-displacement
relationship is assumed to be constant. In the case of high axial loading or the case that shear
capacity is similar to flexural capacity, it is recommended that coefficient (η) is determined as smallvalue.
(3) It is known that the shear strength and torsion strength decrease under cyclic loading in large
deformation. However, it is difficult to evaluate the decreasing gradient of these strengths, and thedecreasing gradient is considered by increasing member factor as described in Section 11.4.

11.3

Verification(1) For structural members not significantly affected by torsional moment and thosesubject to only compatibility torsional moment, the verification for torsion may not be
carried out if the member satisfies the requirement of shear capacity.
(2) For the plate members significantly affected by out-plane shear, the verification forin-plane shear, in Seismic Performance Grade 3, may not be carried out.
(3) Verification may be referring to limit values described in Section 11.2.
(4) The verification for self-weight of a structure, in Seismic Performance Grade 3, may
not be carried out if the dynamic analysis indicates that a structure does not fail against
the earthquake.

[Commentary] (1) Generally, the torsion stiffness of member decreases clearly after the yieldingof reinforcement by shear force and flexural moment. If the member has sufficient ductility after
yielding of reinforcement, compatibility torsional moment also decreases as well as torsion stiffness.
In this case, the verification for torsion may not be carried out.
(2) For members significantly affected by in-plane shear force, for example, the undergroundstorage tank, the out-plane shear action is not corresponding to the main shear resistance region
even if the local out-plane shear force is caused. In this case, out-plane shear behavior is usually
not brittle, and the verification may not be carried out.
(3) For the analysis of linear members by using finite element method, the verification of thatthe dynamic response displacement is not exceed the ultimate displacement can be replaced withthe verification of that the equivalent sectional stiffness is not exceed the value at the ultimate
displacement. In general, it is related to the ultimate displacement when the equivalent sectional
stiffness ratio becomes 50% of the initial property. Where, the equivalent sectional stiffness ratio
is defined as the average of stiffness ratio of gross concrete section for each member. The
equivalent sectional ratio is described in Section 5.2.3.
For the analysis of plate members by using finite element method, the verification of that the
dynamic response displacement is not exceed the ultimate displacement can be replaced with theverification of that the compressive strain of plate surface is not exceed the two times strain at the
maximum compressive strength. In addition, the verification of that vertical member is not failed
in shear can be replaced with the verification of that the compressive strain of plate surface is not
206Chapter 11

Seismic Design

exceed the tree times strain at the maximum compressive strength. Though large strain causes inlocal region in linear members, the strain in plane and shell members is distributed constantly,
moreover, the strain is distributed constantly in thickness of plate. The strain of plate surface canbe used as limit value appropriately.
(4) For the verification of Seismic Performance Grade 3, it is necessary to prevent not only
shear failure of member but also structural collapse. Such verifications may be replaced with the
dynamic analysis, if the calculated results show that the structure is not failed and the dynamic
response converges after ground motion.

11.4

Safety Factors

Safety factors used for verification related to earthquake resistance shall be
determined appropriately according to verification methods, taking into consideration the
purpose of safety factors described in Section 4.5.

[Commentary] Safety factors used for verification related to earthquake resistance may betreated as follows:
For Seismic Performance Grade 1, the yield displacement or the yield rotation angle of amember is used as a limit value. Because the member receives little damage even if this limit
value is exceeded slightly, a safety factor of 1.0 may be used.
For Seismic Performance Grade 2 and Seismic Performance Grade 3, it is necessary to verify
that the load-carrying capacity of the structure does not decrease clearly. In general, if themembers of a structure are designed to prevent shear failure and torsional failure, the structure loses
very little of its load-carrying capacity even after the members fail in bending, and shows highly
ductile behavior.
The dynamic response of a structure is depends on the characteristics of its members as well as
ground motion. The stiffness of members greatly affects response displacement, but when
response displacement reaches the yield displacement or flexural strength of a member, shear force
corresponding to the yield load or flexural strength of the member acts. The purpose of thematerial characteristic values, material factors and member factors used for the verification of safety
from member failure described in Chapter 9 is to calculate the lower limit of flexural strength. If
this is used for earthquake resistance verification, the stiffness, yield load and flexural strength ofmembers are underestimated. Consequently, response displacement is overestimated in response
analysis, but shear force is underestimated. It is generally known that the shear capacity of amember decreases when the member is subjected to reversal cyclic loading in large displacement.
In order to verify safety from earthquake-induced shear force appropriately, it is necessary to
calculate the working shear force by using design values for the materials used based on the actual
strength of the materials and evaluate shear capacity reduction due to reversal cyclic loading.
The principle is to conduct more than one dynamic response analysis using different material
characteristic values, materials factors and member factors for the case where response
displacement is to be verified and the case where it is to be verified that shear failure does not occur.
In this Specification, safety factors are determined as shown in Table C11.4.1.
(i) A material factor of 1.0 is used to calculate all response values for structures.
(ii) In the verification related to the displacement and deformation of a structure, characteristic
values assuming lower limits are used as the design strength of the materials used, and design
values of the tensile yield strength of steel are calculated by using lower limit values of207

Standard Specifications for Concrete Structures-2007, Design

JIS-specified yield strength as characteristic values.
Among the member factors used for limit value calculation, the member factor for the limit
value of deformation is 1.0. In the case of a member whose behavior is significantly affected bybending, because a clear decrease in load-carrying capacity does not occur even if the ultimate
displacement as defined in this Specification is slightly exceeded, a member factor for displacementof 1.0 may be used. For members whose ultimate state is caused by shear failure after flexural
yielding, a member factor for displacement of 1.0 may be used because increasing the member
factor for shear capacity as described in Item (iv) below has the effect of increasing the amount oftransverse reinforcement and preventing a clear decrease in load-carrying capacity.
(iii) If it is to be verified that shear failure of a member does not occur, the actual strength ofsteel is used as design strength. If JIS-conforming steel is used, the value obtained by multiplying
the lower limit value of JIS-specified yield strength used as a characteristic value by the material
modification factor m may be used as the design value of tensile yield strength. In general, thematerial modification factor m of 1.2 may be used. The characteristic strength value and thematerial factor for concrete may be similar to the values used for the verification of thedisplacement and deformation of a structure. This is based on the understanding thatcharacteristics of concrete such as strength do not affect the response values of the structure as
much as those of steel.
The member factor used for shear capacity calculation is to be in accordance with Section
9.2.2.2.
(iv) In view of safety from shear capacity reduction due to reversed cyclic loading and fromexcessively large earthquake, when calculating shear capacity with large deformation cycles
exceeding the maximum strength point, it is necessary to use member factor values greater than themember factors indicated in Section 9.2.2.2. In general, the member factor should be increased bya factor of 1.2. The effect of reversal cyclic loading on plastic hinge regions also needs to be taken
into consideration. In this connection, Section 11.1 (6)(iii) should be followed. If, however, it
has been verified by an appropriate method such as an experiment that a clear decrease in strength
does not occur even if the ultimate displacement of a member is exceeded, the member factor does
not need to be increased.
When trying to make verification through a single response analysis using a material
modification factor (ρm) of 1.0 in order to allow for an increase in response shear force due to thedifference between the characteristic value and the actual value of reinforcing steel strength, theconventional method of calculation is to make corrections as mentioned above and then evaluate thevalue obtained by multiplying the response shear force by 1.2 as design shear force. In thisrevised Specification, in principle, in order to allow for the influence of the actual strength ofreinforcing steel, verification based on an analysis using a material modification factor (ρm) of 1.2
be conducted separately from deformation verification using ρm1.0.
(v) Uncertainty associated with structural analysis includes the uncertainty of groundcharacteristics, ground motion, and accuracy of analysis methods themselves. When using astandard analysis method described in this Specification, usually a structural analysis factor of 1.0
may be used.
These are summarized in Table C11.4.1.

208Chapter 11

Table C11.4.1
Safety factor
Modification
factorSeismic DesignStandard values of safety factors and modification factors
Material factor γmConcrete

Steel

γc

γs

1.0

1.0

Material
Structural
Member factor
analysis factorγbγaLoad factor

Structure factor

γfγiSeismic

Seismic
Performance
Grades2 and 3

Response
valued andlimit value

Response
value

1.0

1.0

1.0

1.0

value

1.0

Displacement :
1.0
1.0

1.0

1.0

1.0-1.2

1.0-1.2
1.0-1.2

Limit

factor for steel
strengthρm

Seismic performance

Performance
Grade 1

modification

Shear force :
1.2

1.0 *
1.3

1.0 or 1.05

1.0
1.1-1.3 *** Limit value of displacement** The shear capacity of beam and column subjected to reversed cyclic loading is calculated by multiplying by about 1.2; hence, 1.31.2
1.56 for the part to be carried by concrete (Vcd) and 1.11.21.32 for the part to be carried shear reinforcement (Vsd). Shear capacity, however,in the evaluation of the flexural shear capacity ratio in accordance with Section 11.1 (6) (iii) does not need to be increased.

11.5

Verification by Experimental Tests

When structural details are determined by the experimental trials, it is necessary tosatisfy the better performance for the specimens than those made according to Chapter
13. The tests of performance confirmation are carried out as follows:(1) Shape of member, the size of cross section, the size and interval of the steel, and soon shall be corresponded to the real member.
(2) In principle, reversed cyclic loading tests with displacement control system arecarried out, taking into consideration loading to imitate the real member.

[Commentary] Structural details are base of the verification in design, it is important thestructural details shall be satisfied.
It is natural that the technological improvement makes it to be able to verify the required
performance by alternative method. It may be determined the structural detail, if it is ensured tohave better performance according to Chapter 13 by experimental tests.
(1), (2) When the structural details are determined by experimental trials, it is necessary toensure that the specimens have better performance than the standard specimen. Also, it isnecessary to use the specimens, whose size of cross section is corresponding to real member, andthe loading tests imitate the real stress distribution. In principle, reversed cyclic loading tests shallbe carried, because the positive and negative loading subjects to the structural members during anearthquake. In addition, it is necessary to imitate the loading pattern and stress distribution caused
in real structures. To determine the structural details, it is recommended in cyclic loading tests to
set the upper displacement between maximum strength point and ultimate displacement, and to set
the loading cycles for each displacement from 5 to 10 times.
When it is difficult to prepare the real scale specimens and to imitate the load pattern and stress209

Standard Specifications for Concrete Structures-2007, Design

distribution, it may be determined the structural details from the experimental results undermanagement of responsible engineer.

210

Chapter 12 Verification Related to Initial Cracking

CHAPTER 12 VERIFICATION RELATED TO INITIALCRACKING

12.1 General(1) It shall be verified that initial cracks in a structure do not affect the required
performance of the structure.
(2) In general, verification related to settlement cracking and plastic shrinkage cracking
may be omitted. For structures that are known to be free from problems from past
construction experience, verification related to cracking due to heat generated byhydration and autogenous shrinkage may be omitted.
(3) If a structure is provided with crack-inducing joints for the purpose of crack control,
their structure and locations shall be determined so that the functions of the structure are
not impaired.

[Commentary] The influence of cracks that occur in a structure at the construction stage on
various performance attributes of the structure during its design service life has not been fully
explained. It goes without saying, however, that the verification of durability, safety, serviceability
and earthquake resistance described in the previous chapters is based on the assumption that initial
cracks that affect the required performance of the structure do not occur at the construction stage. It
is true that ascertaining that initial cracks occurring at the construction stage do not affect therequired performance of the structure is a good way to make us assured that the required
performance can be maintained during the design service life of the structure. Cracks caused byvolume changes occurring at the construction stage can be controlled variously, and it is possible tocontrol them by using certain construction procedures or curing methods even after mix proportions
and structural details have been finalized. Another characteristic of cracks occurring at theconstruction stage is that they, unlike cracks that occur after the structure goes into service, can beeasily detected in the acceptance inspection of the structure. A method for evaluating the influenceof cracks resulting from the hydration of cement on the performance of the structure is described in
the Design: Standards, Part 4, of this Specification (Fig. C12.1.1).
As mentioned above, the verification of the durability, safety, serviceability and earthquake
resistance of a structure is based on the assumption that initial cracks that affect the required
performance of the structure do not occur. The verification related to initial cracking described inthis chapter, therefore, is meant to be conducted at the design stage. There may be cases, however,where it is more rational to conduct verification related to initial cracking at the construction stage.
There may also be cases where verification related to initial cracking needs to be done at bothdesign and construction stages. This chapter has been written assuming that it can be consulted inconnection with verification related to initial cracking either at the construction stage or at bothdesign and construction stages.

211

Standard Specifications for Concrete Structures-2007, Design

Initial crack

Shrinkage crack

Crack due tocement hydration

Settlement crack

Verification(Section 12.3)

Plastic shrinkage
crack

Verification is not necessary in general
Based on the previous construction
record, crack does not apparently
occur.

YES

Verification is not necessaryNO
Verification(Section 12.2 and Standard for “thermal stress analysis”)
START

Environmental condition, determination of shape and size ofstructure, construction method, mix proportion of concrete
Limit value of probability of crack(Section 12.2.2)
Limit value of crack width(Section 12.2.3)

Determination of limit value

Calculation of predictive value (Section 12.2.4)
Thermal analysis(Standard part 4 “2. Thermal analysis”)

Stress analysis(standard part 4, “3. stress analysis”)

Design value of material properties for heattransfer analysis (Chapter 5, Standard part 4“4. material properties))

Design value of mechanical properties ofconcrete (Chapter 5, Standard part 4, “4.
material properties”)

Predictive value
satisfies limit value?

NO

YES
END

Fig. C12.1.1 Flowchart for verification related to initial cracking212

Chapter 12 Verification Related to Initial Cracking

This chapter deals with main types of cracks that occur at the construction stage, namely, cracks
caused mainly by the segregation of ingredients before hardening or by rapid drying and cracks
caused mainly by changes in volume of concrete resulting from hydration or shrinkage. Settlement
cracks may occur in regions over reinforcing bars or regions with non-uniform cross sections
because of the settlement of aggregates or the segregation of ingredients, but these cracks canusually be prevented by carrying out tamping at appropriate timing. Plastic shrinkage cracks may
occur when the rate of evaporation of water from the surface is higher than the rate of ascent of
bleeding water, but usually these cracks can also be prevented by preventing rapid drying of thesurface of newly placed concrete. In short, because problematic settlement cracks and plastic
shrinkage cracks can be prevented by placing concrete in accordance with the Construction sectionof this Specification, verification related to those types of cracks may be omitted. Even verification
related to cracks caused by the hydration of cement may also be omitted if such cracks are so smallthat they are thought to pose no problem as a result of careful evaluation from the viewpoints ofsafety, serviceability, durability, appearance, etc. Construction is carried out without following theConstruction section of this Specification, it is necessary to verify by an appropriate method thatthese types of cracks do not have adverse effects on the structure.
In cases where, as in the construction of, for example, a reinforced concrete viaduct, many
structures of the same type are constructed, verification as described in this chapter may be omitted
if it is known from past construction experience that initial cracks occurring at the construction
stage do not affect the required performance of the structures.
The dimensions of structural members to be treated as mass concrete structures because ofconcern about the possibility of cracking due to the hydration of cement are difficult to determine
uniformly because they vary depending on the type of structure, materials used and construction
conditions. As a rule of thumb, a relatively large slab having a thickness of 80 to 100 cm or more
and a wall with a restrained bottom having a thickness of 50 cm or more may be thought of as massconcrete structures. If, however, rich mix concrete is used as in the construction of prestressed
concrete structure, a thinner member may need to be treated as a mass concrete structure dependingon the restraint conditions. Dam concrete, however, is outside the scope of this chapter because it isdealt with in the Dam Concrete section of this Specification.
In general, it is often difficult to control thermal cracks occurring in a massive wall or wall-likestructure by means of material- and mix-proportion-related control measures alone. For concretethat is required to be watertight, cracks hampers the achievement of the purpose of the structure.
One method that can be used in such cases is to provide reduced-cross-section regions at certain
intervals in the longitudinal direction of the structure in order to induce cracks in those regions,
thereby preventing cracking in other regions and facilitating remedial measures taken in crack
regions. In order to induce cracking at the intended locations, the cross-sectional reduction ratio at
crack-inducing joints needs to be 30% or higher. Since the required spacing of crack-inducing
joints is greatly affected by such factors as the size of the structure, the amount of reinforcing steel,placing temperature and the placing method, spacing needs to be determined in view of thosefactors. It is also necessary to carefully consider details such as methods for preventing steel
corrosion at joints, methods for maintaining the required concrete cover and the selection of joint
filler materials. By providing crack-inducing joints, cracking can be controlled with relative ease inwalls and wall-like structures. Since, however, crack-inducing joints might become structural weak
spots, it is necessary to determine their structure, locations, etc., appropriately by referring torelevant data such as past construction records.

213

Standard Specifications for Concrete Structures-2007, Design

12.2 Verification Related to Cracking Caused by Hydration of Cement
12.2.1 General(1) In the verification related to cracking, it shall be judged, by verifying that cracking
does not occur in a structure or crack width is not larger than the limit value, that therequired performance of the structure is not lost because of cracking.
(2) If cracking is not permitted, a limit value for the probability of occurrence of cracking
shall be set and verification shall be made.
(3) If cracking is permitted but restricted so that the required performance of thestructure is not lost because of cracking, a limit value for crack width shall be set andverification shall be made.
(4) Verification related to cracking shall be made on the basis of concrete stresscalculated through stress analysis incorporating the temperature change from the initialstate calculated through thermal analysis and the volume change of concrete due toautogenous shrinkage, both of which are determined in advance.

[Commentary] (1) Cracking due to the hydration of cement is affected by a combination ofvarious interacting factors such as the environmental conditions, the dimensions and shape of thestructure, thermal and mechanical properties of materials and construction methods. It must be
verified, therefore, that cracks impairing the required performance of the structure do not occur by
evaluating those factors appropriately. Permitting the occurrence of cracking is not synonymouswith permitting initial cracking unlimitedly. This is based on the philosophy that trying to prevent
very fine cracks that are judged, as a result of careful evaluation from the viewpoints of safety,
serviceability, durability, appearance, etc., to pose no problem is an unreasonably inefficientapproach to the design and construction of a structure.
(2) and (3) If cracking due to the hydration of cement is permitted, verification is made byascertaining that crack width is not greater than the limit value of crack width. If the occurrence of
cracking is not permitted, it must be verified on the basis of the probability of occurrence of
cracking that cracking does not occur. In this case, the upper limit value of the probability ofoccurrence of cracking is used as the limit value for verification. If crack width is thought todifficult to calculate, verification may be made on the basis of the probability of occurrence of
cracking.
When making verification related to steel corrosion due to chlorides, it is necessary to verify inaccordance with Section 8.3 that crack width is not greater than the limit value and that chloride ion
concentration at the steel location is not higher than the critical concentration for steel corrosion.
(4) In the verification related to cracking due to the hydration of cement, usually a thermal
analysis incorporating the influence of the environmental conditions, the dimensions and shape ofthe structure, thermal characteristics of the materials used, construction method details, etc., isconducted as the first step. Then, the volume change based on the temperature change from theinitial state calculated through thermal analysis and the volume change due to autogenous shrinkage
is determined. After that, a stress analysis modeling the restraint conditions for the placed concrete214

Chapter 12 Verification Related to Initial Cracking

and the mechanical properties of the materials used is conducted, and concrete stress is calculated.
The strength/stress ratio (cracking index) is determined through comparison between the actual
strength of concrete and the calculated stress. Whether cracking occurs or not is checked in termsof the cracking index determined from the limit value of the probability of occurrence of cracking.
If crack width is to be restricted, it is verified that the crack width calculated on the basis of stressanalysis is not greater than the limit value of crack width or that the calculated cracking index is not
greater than the cracking index corresponding to the limit value of crack width determined on thebasis of the probability of occurrence of cracking. These methods are used to ascertain that initial
cracks occurring at the construction stage do not affect the required performance of the structure.
One method each of thermal analysis and stress analysis is described in Chapters 2 and 3 of the
Design: Standards, Part 4, of this Specification, and standard values of thermal properties andmechanical properties of materials are indicated in Chapter 4 of the Design: Standards, Part 4, of
this Specification.

12.2.2 Verification related to occurrence/nonoccurrence of cracking(1) The occurrence or nonoccurrence of cracking shall be verified in terms of thecracking index determined from the limit value of the probability of occurrence of cracking.
(2) If measures are taken to prevent cracking, the limit value of the probability ofoccurrence of cracking shall be set taking into consideration the environmental conditions,the dimensions and shape of the structure, construction methods and concrete mix
proportions.

[Commentary] (1) The ratio of the tensile strength (characteristic value) of concrete specimens to
the principal tensile stress (calculated value) in the structure is defined as a cracking index, and theoccurrence or nonoccurrence of cracking is checked by using the cracking index determined fromthe limit value of the probability of occurrence of cracking. If Eq. (C.12.2.1) is satisfied, structures
may be deemed to have been passed:
Icr(t)  γcr(C.12.2.1)

where,
Icr(t): cracking index
Icr(t) = ftk(t)/σt(t)ftk(t): tensile strength of concrete at age of t days
σt(t): maximum principal tensile stress in concrete at age of t days
γcr: safety factor for probability of occurrence of cracks. The factor maybe 1.0 to 1.8
The thermal cracking index has been conventionally used in the verification of cracking due tovolume changes caused by heat generated by the hydration of cement for mass concrete. The
thermal cracking index is defined as the ratio of the tensile strength of the concrete to the tensile215

Standard Specifications for Concrete Structures-2007, Design

stress in the concrete generated by heat generated by the hydration of cement. The larger thethermal cracking index, the lesser the possibility of crack occurrence and vice versa. Generally, as
the index becomes smaller, the number of cracks increases and the crack width tends to grow larger.
In cases where the distribution of generated stresses is more or less uniform, penetrating cracks areoften formed. In cases where stresses due to volume changes have a considerable gradient in themember cross section, surface cracks do not develop into penetrating cracks immediately and, if theconcrete has high fracture toughness, performance can be retained. Crack patterns in this case varywith the dimensions of the structure. Neither the fracture toughness of the materials nor stability of
the cracking process is considered in the thermal cracking index. Since, however, a relatively
strong correlation has been found between the thermal cracking index and the probability ofoccurrence of cracking, the index may be used for verification associated with the occurrence of
cracking.
In this specification, the cracking index is defined as the ratio between the tensile strength(characteristic value) of concrete specimens and the principal tensile stress (calculated value) in the
structure. In this case, it should be noted that the probability of occurrence of cracks corresponding
to the cracking index of 1.0 may not be always 50% because the probability of occurrence of cracks
is influenced by the accuracy of estimation methods and the difference between the tensile strengthof test specimens and that of the structure.
(2) For use when the calculation methods described in this chapter and Chapter 3 of the Design:Standards, Part 4, of this Specification are used, the relationship between the factor of safety γcr andthe probability of occurrence of cracking shown in Fig. C12.2.1 is available. For reference, typicalvalues of γcr and the probability of occurrence of cracking are shown in Table C12.2.1.
Table C12.2.1 Typical values (for reference) of the probability of occurrence of cracking andthe factor of safety γcr for ordinarily reinforced concrete structures
Table C12.2.1 Probability of occurrence of cracking and factor of safety

When cracking is to be prevented
When cracking is to be restricted as muchas possible
When cracking is permitted but
excessively large crack width is to beprevented

216

probability ofoccurrence of
cracking
5%factor of safety γcr

25%1.45 or greater85%

1.0 or greater

1.75 or greaterChapter 12 Verification Related to Initial Cracking

Probability of Cracking (%)

100
90
80
70
60
50
40
30
20
10
0

0.5

1.0
1.5
Safety factor, γcr

2.0

Fig. C4.2.1 Safety factor(γcr) vs. probability of cracking

What should be kept in mind here is that the probability of occurrence of cracking shown in Fig.
C12.2.1 is the result obtained by conducting thermal analysis by the two-dimensional finite element
method and using the CP (compact procedure) method of stress analysis. Under different
conditions for stress analysis, somewhat different cracking probability curves would be obtained.
The cracking probability curve shown above should be applied to a cross section in which stresschange occurs gently as in a wall or wall-like structure or a slab or slab-shaped structure. It should
be kept in mind that the curve should not be applied to corner regions, etc.
If the influence of autogenous shrinkage does not need to be taken into account, a simple, thecracking index Icr(t) may be conservatively calculated based solely on thermal analysis results using
Eq. (C12.2.2) and Eq. (C12.2.3).
When stresses due to the internal restraint are predominant:
Thermal cracking index Icr(t) = 15/ΔTi(C12.2.2)

When stresses due to the external restraint are predominant:
Thermal cracking index Icr(t) = 10/(R・ΔTo)(C12.2.3)

where,
ΔTi: temperature difference between the inside and outside of the member at the peaktemperature (oC),
ΔTo: difference between the maximum average temperature of the member and its equilibrium
temperature with the ambient air temperature (oC),
R: factor of the external restraint, which may be 0.5 when placed on relatively soft rock, 0.65
when placed on medium hard rock, 0.8 when placed on hard rock and 0.6 when placed on
the previous concrete.

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Standard Specifications for Concrete Structures-2007, Design

An example of a concrete member in which stresses due to internal restraint are predominant isa slab cast on soft ground, and an example of a concrete member in which stresses due to external
restraint are predominant is a slab cast on a rock or massive concrete base. In deriving the indicatedequations, the critical tensile strain in the concrete of 100x10–6 was used, and autogenous shrinkage
was ignored.

12.2.3 Verification of crack width(1) Crack width shall be verified by an appropriate method.
(2) If crack width is to be restricted, the limit value of crack width shall be determinedtaking into consideration the environmental conditions, the dimensions and shape of thestructure, construction methods and concrete mix proportions. In general, the limit valuesof crack width associated with steel corrosion indicated in Section 8.3.2 may be used.
(3) If it is difficult to calculate crack width, verification may be made in terms of theprobability of occurrence of cracking.

[Commentary] (1) Methods of crack width calculation include statistical methods, the CP Crack
Width Method proposed by the committee on temperature and stress in mass concrete of the Japan
Concrete Institute, and FEM in which the bond characteristics of reinforcing steel are taken into
consideration. The method in which the post-cracking behavior of concrete is modeled is anattempt at faithful reproduction.
(2) Even if the occurrence of cracking is permitted, cracks must not be allowed to affect therequired performance of the structure. It is therefore necessary to keep crack width within an
acceptable range so that the performance of the structure is not impaired. The most important thing
to be careful about when considering the influence of cracks on the structure is the corrosion ofinternal reinforcing steel. With respect to initial cracking, the limit values of crack width associatedwith steel corrosion indicated in Section 8.3.2 may be used as in the verification related to flexural
cracking. This does not apply, however, if the limit value of crack width is determined by theappearance of the structure.
If the occurrence of cracking is permitted, attention needs to be given to cracking patterns. For
example, in a wall or wall-like structure or a box culvert, longitudinal cracks directly over the main
reinforcement might cause the adhesion with the reinforcing bars to decrease so that the strength of
the structure decreases. The occurrence of such cracking, therefore, should not be permitted.
(3) Fig. C12.2.2 shows the relationships among crack width, the thermal cracking index and thereinforcement ratio based on experiment results. The figure shows the relationship between the
maximum crack width and thermal cracking index for actual wall-type structures and specimens fordifferent reinforcement ratios in the full cross section of the retrained body. L/H ranges from 10.0
to 15.0 (L and H: length and height of the restrained body). The longitudinal factor of the external
restraint at the mid-height of the wall is 0.5 to 0.7. The maximum reduction in mean temperature in
the cross section is in the range between 20C and 54C.

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Chapter 12 Verification Related to Initial Cracking

Reinforcement
ratio
鉄筋比
0.25～0.30％
0.55～0.65％
0.85～0.95％

Maximumcrack width (mm)
最大ひび割れ幅(mm)

0.5
0.4
0.3
0.2
0.1
0

0.2 0.4

0.6
0.8
1.0
Cracking
index
ひび割れ指数1.2

1.4

Fig. C12.2.2 Relationship between maximum crack with and cracking index

The width of the crack due to hydration of cement converges to a certain value as the tensilestress accumulated in the concrete is released due to cracking. The crack width is determined by theshrinkage of the concrete and the restraining forces of the restraining body and reinforcing steel thatprevent the deformation. The crack width may become extremely large in cases where thereinforcement ratio is small. If temperature falls after the occurrence of cracks, the concrete isdeformed further due to shrinkage. Then, the crack width increases unless new cracks occur. To
control the crack width, therefore, the deformation of concrete due to shrinkage should becontrolled. To that end, maximizing the thermal cracking index by changing the materials, mix
proportion and construction method is effective. If concrete-related measures alone are not enoughto control crack width, the method of controlling crack width by use of reinforcing steel may be
used. Then, it is recommended to use reinforcing steel of smaller diameter as long as the ease of
construction is ensured.

12.2.4 Calculation of stress and crack width(1) The thermal analysis of concrete shall be conducted using adequate methods inaccordance with factors such as the type and configuration of the structure and.
(2) Stresses due to volume changes of concrete shall, in general, be calculated, bydetermining volume changes of restraints such as concrete, reinforcing steel and rock, soil
or foundation, so that the boundary and compatibility conditions and the equilibrium
condition are satisfied.
(3) If the occurrence of cracking due to the hydration of cement is expected, crack width
shall be estimated by an appropriate method.

219

Standard Specifications for Concrete Structures-2007, Design[Commentary] (1) The methods of the thermal analysis of concrete include numerical methods
such as finite element method, finite difference method, simplified numerical method such as
Schmidt or Carlson method, and simplified calculation methods with the use of figures and tables,
whichever can be used. Thermal analyses of concrete can also be classified into linear analyses,
which assume that heat generation characteristics and thermal properties are not dependent on
temperature, and nonlinear analyses, which allow for temperature dependence. However, sinceeach method has limitation in its application, it is necessary to select the most adequate method
considering the required accuracy of the analysis and various conditions of the structures subjectedto the analysis. In thermal analysis, it is necessary to determine a valid analytical model andboundary conditions in accordance with environmental and other conditions of the objective
structure. Calculation of temperature changes and thermal stresses may be conducted until thetemperature change becomes practically stationary.
The determination of boundary conditions is as fundamental as that of the analytical model andhas a significant influence on the results of the analysis. The heat transfer boundary is a boundary
where heat is transferred between the concrete and atmosphere and the fixed temperature boundary
is a boundary where the temperature is kept constant. In general, radiation can be ignored in thethermal analysis of concrete.
The rate of heat generation in concrete is strongly influenced by temperature. Since
temperatures in a structure are usually not uniform, different parts of the structure usually generateheat at different rates. In a thermal analysis, therefore, it is desirable that thermal properties be
determined from mix parameters such as the type of cement, chemical and nonchemical admixtures,cement content and water-cement ratio, and calculated rates of heat generation reflecting
temperature dependence be used.
(2) Since mass concrete structures are usually more rigid than ordinary concrete structures,simplification of the compatibility conditions including the boundary conditions may result in lower
accuracy of analysis. It is desirable, therefore, to use an analysis method in which both thecompatibility and equilibrium conditions are satisfied and volume changes and unsteady mechanicalproperties of concrete can be considered (e.g., finite element method). Results of finite element
analysis may vary depending on element resolution, analytical domain and boundary conditions,and the properties of the restraining body and the restrained body. If the finite element method isused, therefore, it is important to determine these parameters carefully, paying attention to past
analysis data, so that the required level of accuracy is achieved.
There are various approximation methods that can be used as a means of calculating stresses inmass concrete structures in which volume changes due to temperature changes are predominant
over those due to autogenous shrinkage. In general, volume change at the construction stage ismost greatly affected by temperature change. Depending on the type of cement or admixture or mix
proportions, however, autogenous shrinkage due to hydration may become too large to ignore. In
such cases, it may be possible to enhance the accuracy of stress analysis by taking the effects of
those factors into consideration.
When the minimum member size is smaller than about 400 mm, temperature changes,
autogenous shrinkage and drying shrinkage, which occurs later than the first two, may become too
great to ignore. In such cases, it is desirable to consider the effect of drying shrinkage as well as
autogenous shrinkage.
(3) Methods for calculating crack width include statistical methods, the CP Crack Width
Method proposed by the Committee on Thermal Stress in Mass Concrete of the Japan Concrete
220

Chapter 12 Verification Related to Initial Cracking

Institute, and an FEM-based method that takes into consideration the bond characteristics ofreinforcing steel.

12.3 Verification Related to Cracking due to Shrinkage
It shall be verified that cracks caused by the shrinkage of concrete such as drying
shrinkage do not affect the required performance of the structure.

[Commentary] (1) Cracks caused by the shrinkage of concrete such as drying shrinkage mar theappearance of concrete structures and cause the airtightness of concrete to decrease. Shrinkage ofconcrete includes not only drying shrinkage resulting from the dissipation of the moisture in theconcrete but also autogenous shrinkage resulting from the hydration of the cement in concrete.
Usually, the two types of shrinkage occur in combination. These types of shrinkage cracks may
occur as shallow cracks found at the surfaces of a structure or deep cracks that reach reinforcing
bars or even cracks penetrating the full depth of members depending on such factors as the concretematerials used, mix proportion, the shape and dimensions of the structure, restraint conditions, andenvironmental conditions such as temperature and humidity. The influence of shrinkage cracks in a
structure, therefore, on the performance of the structure varies widely. Conventionally, it has been
believed that the influence of cracks caused by drying shrinkage on the performance of a structure isminor mainly because cracks of this type often occur in members with relatively low degrees ofimportance in a structure, because they tend to close when wetted, and because water is not supplied
to the reinforcing bars inside when cracks are open because of dryness. Since, however,excessively large shrinkage cracks may affect the stiffness or deflection of structural members, it isdesirable that it be verified at the design stage that the required performance of the structure is notaffected. Autogenous shrinkage and drying shrinkage of concrete are dealt with in this chapter
because most of these types of cracks are thought to occur before the structure goes into service.
Depending on the dimensions of members, mix design conditions, environmental conditions,etc., cracks may occur because the concrete in a structure is exposed to a dry environment whilestress caused by volume changes due to temperature changes and by autogenous shrinkage isaccumulated in the concrete. It is desirable, therefore, that stress introduced into the concrete in the
structure be evaluated in view of volume changes of concrete due to temperature changes,
autogenous shrinkage and drying shrinkage, and the occurrence of cracking be predictedaccordingly.

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Standard Specifications for Concrete Structures-2007, Design

CHAPTER 13 STRUCTURAL DETAILS OF REINFORCEMENT

11.0

Notation

i
b

:
:
N 'd :
f 'yd :
f 'cd :pb:
 'cu :fyd:Es:
Aw min :bw:s:
Mtwd :
Am
:
fwd
:
u
:

:
fbod :
c
:
At
:

13.1

structure factor
member factor
design compressive strength of concrete
design compressive yield strength of reinforcement
design compressive strength of concretebalanced reinforcement ratio
ultimate strain of concrete
design tensile yield strength of reinforcement
modulus of elasticity of reinforcement
minimum amount of vertical stirrups
web width of concrete section
stirrup spacing
design torsional capacity given in Section 9.2.3.2.
effective torsional area
design yield stresses of transverse reinforcement
length of the centerline of transverse reinforcement
diameter of reinforcing bar
design bond strength of concrete
concrete coverarea of transverse reinforcement

General(1) General structural details described in this chapter shall be observed in the designof reinforced concrete structures.
(2) If the structural details determined for each structural types in other specifications,
it shall be also observed in the design.

[Commentary] (1) This chapter is described about the structural details of reinforcing bars in
reinforced concrete structures. The structural details are based on the design method described in
Chapters 7, 8, 9, 10, 11 and 12. Standard construction performance laid down in the Standard
Specifications for Concrete Structures "Materials and Construction" are the prerequisite for the
structural details in this chapter.
(2) Structural details in other chapters are only applied to members or structures that aredescribed in those chapters. In cases when there is a conflict in the provisions in other chaptersand those given in this chapter, the former provisions shall be followed. However, the common
structural details in this chapter, except the special provisions for each structural types (i.e.
prestressed concrete, steel-concrete composite structures), shall be followed.

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13.2

Structural Details of Reinforcement

Concrete CoverConcrete cover shall be determined to ensure the bond strength that is the prerequisite
for structural performance of a reinforced concrete structure, and the requirements for fire
resistance, durability, social importance of the structure, and errors in construction.
Minimum concrete cover shall be larger than the summation of diameter of reinforcing bar
and construction error margin.

[Commentary] The bond strength, ensured by structural detail of concrete cover described in thissection, is the prerequisite for verification of usability and safety of a structure. Minimum
concrete cover shall be larger than the diameter of reinforcing bar. It is necessary to ensure thesufficient concrete cover for preventing steel corrosion and enhancing fire resistance, and so on.
Concrete cover shall be determined taking into consideration material quality of concrete, diameterof reinforcing bars, surrounding environment of a structure, something of harmful on the concretesurface, dimension of member, construction error, social importance of a structure, and so on. As
far as the protections against fire and corrosion of reinforcement are concerned, the concrete covershall be determined in a manner given in Section 10.7 and 8.3, respectively. Concrete cover
should be more than the maximal values of diameter of bars, concrete cover from verification ofdurability and fire resistance, considering construction error margin.
Provisions of this section shall be applicable to cases, which use steel reinforcing bars.
Concrete cover for other materials than steel may be based upon different requirements. As theresults, designed concrete cover is larger than the either diameter of reinforcing bars and one thatsatisfies durability and fire resistance, considering the construction error. The concrete cover islarger than diameter of bars, and it can satisfy the durability and fire resistance performance.
In this chapter, the provisions are applied to steel reinforcing bars.
another manner for other materials.

13.3

It is necessary to consider

Clear DistanceIn order to ensure that concrete surrounds the reinforcement appropriately, clear
distance shall be determined taking into consideration type of member, maximum size ofaggregate, diameter of reinforcing bars, construction error, and so on.

[Commentary] Clear distance shall be determined to satisfy enough workability. Workability ofconcrete construction is evaluated by relationship between concrete slump and clear distance ofreinforcing bars.
Therefore, the construction workability shall be verified by slump assumed from concrete
mixing. The relationship between concrete slump and clear distance of reinforcing bars are given
in Chapter 4 in the Standard Specifications for Concrete Structures "Structural Performance
Verification".

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Standard Specifications for Concrete Structures-2007, Design

13.4
13.4.1

Arrangement of Reinforcement
Arrangement of longitudinal reinforcement(1) Minimum reinforcement(i) For a reinforced concrete member under the action of a predominantly axial force,
longitudinal reinforcement of not less than 0.8% of concrete area shall be provided.
The concrete area mentioned here is the minimum concrete area required to resist only
the applied axial force.
In case the provided concrete area is greater than the minimum defined above, it isdesirable that the longitudinal reinforcement is at least 0.15% of the actual concrete area.
(ii) For a linear member under the action of predominantly flexural moments, at least
0.2% of concrete area shall be provided as longitudinal tensile reinforcement in principle.
For a T-shaped cross-section, it is necessary to use the effective width of concrete
compressive area in the verification. For a T-shaped cross-section at least 0.3% ofeffective concrete area, which is defined as the product of the effective depth d of thecross-section and the web width bw, shall be provided as longitudinal tensile
reinforcement.
(2) Maximum reinforcement(i) For a reinforced concrete member under the action of a predominantly axial force,the provided longitudinal reinforcement shall not exceed 6% of concrete area in principle.
(ii) For a linear member under the action of predominantly flexural moments, theprovided longitudinal tensile reinforcement shall not exceed 75% of the amount requiredfor balanced failure in principle.
(3) Arrangement(i) Additional reinforcement shall be provided in concrete where cracks due totemperature gradient, shrinkage, and so on are anticipated.
(ii) Additional reinforcement to prevent concrete cracking shall be distributed aroundthe cross-section. The diameter and spacing of reinforcement shall be as small as
possible.
(iii) Maximum spacing of longitudinal and transverse reinforcement shall not exceed
300mm in principle.

[Commentary] (1)(i) For a reinforced concrete member under the action of a predominantly axial
force, the provision of minimum longitudinal reinforcement is the same as that has been
conventionally used.
There is a probability of cracking in a concrete member due to shrinkage, temperature gradient,etc. To keep width of such cracks within harmless limits, the present specification stipulates theuse of at least 0.15% of the concrete area as longitudinal reinforcement even in cases where theprovided concrete area is greater than that required from calculations.

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Structural Details of Reinforcement

In arranging reinforcement according to this provision, it is preferred to use reinforcements thathave smaller diameter compared with dimension of members and can bond with surrounding
concrete satisfactorily. As far as the layout of the reinforcement is concerned, it is desirable that itshould be distributed around the cross-section of the member. The minimum concrete area (Ac)required to resist the applied axial force may be obtained using Eq. (C13.4.1).

Ac   i  b N d' 0.008 f yd'  0.85 f cd'

(C13.4.1)

where, i : structure factor

b : member factor
N’d : design compressive strength of concrete (N/mm2)
f'yd : design yield strength of longitudinal reinforcement in compression (N/mm2)
f'cd : design compressive strength of concrete (N/mm2)(ii) The intent of this provision is to ensure that designed linear reinforced concrete members
have the desired flexural characteristics. When the ratio of tensile reinforcement becomes
extremely small, the load to cause yielding of the provided reinforcement may become smaller thanthat to cause onset of flexural cracking in concrete. In such a case, the member failure may bebrittle and the reinforcing bars yield or fracture immediately after initiation of cracking. In somecases, members may fail with only a single localized crack much like a plain concrete member
without reinforcement. Provision of nominal tensile reinforcement, not less than 0.2%, prevents
this type of failure when normal concrete having a characteristic strength of about 30 N/mm2 or lessand reinforcement with a design yield stress of about 350 N/mm2 are used.
When high strength concrete is used, the minimum reinforcement to prevent brittle failure inflexural members should be determined in accordance with Eq. (C13.4.2).
When high strength reinforcement is used, a lower reinforcement ratio may be used.
This rule may be relaxed when extremely excessive reinforcement is used than that is derived
by computation. However, in the case when tensile reinforcement ratio is extremely low, desirable
structural characteristics already are not shown. In this case, reinforcement ratio is not to be lessthan 0.15%.
In order to prevent brittle failure of a linear reinforced concrete flexural member, the amount ofreinforcement must be large enough to prevent simultaneous occurrence of onset of flexural
cracking and failure of member. The minimum reinforcement ratio at which cracking moment
does not exceed the flexural moment at yield of main reinforcement may be calculated using Eq.
(C13.4.2).
23h f
pmin  0.058   c
 d  f sy
2

(C13.4.2)(2)(ii) If the section is excessively reinforced, not only the actual placing of the reinforcement isdifficult, but also the failure of the member is governed by compressive failure of the concrete, andis brittle. Hence, an upper limit on the reinforcement ratio is stipulated in relation to the balanced
reinforcement ratio, which may be obtained using Eq. (C13.4.3) for ultimate state. The coefficient in the equation is an approximate value in the case when the stress-strain relationship shown in
Fig. 5.2.1 is used.
pb  

 'cu

 'cu ＋f yd / Es



f 'cd
f yd

(C13.4.3)

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Standard Specifications for Concrete Structures-2007, Design

where, pb : balanced reinforcement ratio  0.88  0.004 f ck , where   0.68
'cu : ultimate strain of concrete, for which value shown in Fig. 5.2.1 may be used
fyd : design tensile yield strength of reinforcement (N/mm2)
Es : modulus of elasticity of reinforcement, usually 200 kN/mm2(3)(i) The harmful cracking for durability may be occurred in concrete member due totemperature gradient, shrinkage, and so on. Adaptive reinforcement shall be arranged at thesurface of member, concrete joint, and so on to prevent harmful cracking.
(ii) With the same amount of reinforcement, crack width is decreased by using small diameterand small spacing of reinforcement. To minimize cracking, it is prefer to use the reinforcementwith small diameter and to arrange it in small spacing.
(iii) The spacing of reinforcement prefers to be less than 300mm from view of the crack
distribution characteristics.

13.4.2

Arrangement of transverse reinforcement(1) Arrangement of stirrup(i) In the case of a linear member, stirrups not less than 0.15% of the concrete area
shall be provided throughout the length of the member. The spacing shall exceed neither
3/4 the effective depth of the member, nor 400mm in principle. This provision may not beapplied to planar members.
(ii) In the case of a linear member, if calculations indicate the need for shear
reinforcement, the spacing of stirrups shall exceed neither 1/2 the effective member depth,
nor 300mm. The same amount of shear reinforcement shall be provided over a distanceequal to the effective member depth from the end of the zone where the need for shear
reinforcement is indicated from the calculations.
(2) Arrangement of ties(i) The spacing of ties shall exceed neither 12 times diameter of longitudinal bar, nor
the minimum dimension of the section in principle. In the plastic hinge region, thespacing of ties shall exceed neither 12 times diameter of longitudinal bar, nor 1/2 times theminimum dimension of the section. The ties shall be enclosed longitudinal bars.
(ii) Using the ties in the rectangle section, the interval distance of ties in the section
shall exceed neither 48 times diameter of ties, nor 1m. The intermediate ties shall bearranged, for that interval distance between ties and intermediate ties in the section does
not exceed these limit values.

[Commentary] (1)(i) Diagonal cracking in members without shear reinforcement is often
accompanied by a sudden reduction in member strength. When the behaviors of the whole
structure are affected by the sudden failure of members, it is necessary to consider the improvementof member ductility and the re-establishment of load carrying mechanism. Therefore, even whenshear reinforcement for a linear member is not necessary according to computation, the minimum
amount of vertical stirrups by Eq. (C13.4.4) should be arranged in order to avoid sudden failure due
226

Chapter 13

Structural Details of Reinforcement

to diagonal cracks caused by shrinkage of concrete, difference of temperatures, etc.
Aw min bw s   0.0015(C13.4.4)

where, Aw min : minimum amount of vertical stirrups
bw : web widths : stirrup spacing
With the arrangement of reinforcement specified by Eq. (C13.4.4), the increase in the shear
capacity by the shear reinforcement due to Eq. (9.2.6) becomes approximately equal to Vcd, ingeneral.
This minimum value required is based on deformed bars. When plain bars with small yieldand bond strengths are used, it is desirable to arrange them approximately 1.5 times the volume byEq. (C13.4.4).
(ii) In order to ensure the effective performance of stirrups as shear reinforcement, the spacingof stirrups need to be determined so that the stirrups must intersect with the diagonal cracks in web
concrete. The spacing shall not exceed one half the effective depth of member cross sections nor
300mm in order to ensure that stirrups function as additional reinforcement to avoid cracking due toshrinkage and others.
Considering the shear cracking diagonal to the member axis, the range where stirrups and tie
reinforcement shall be arranged in the range as a calculated necessary length plus outer sub-ranges
with the same distance as the effective depth of member cross section. In this case the required
amount of shear reinforcement in the sub-ranges may be taken as that at the edge of the range
considered necessary by computation.
(2)(i) Transverse reinforcement, ties and spiral hoops, is effective to prevent shear cracking andbuckling of longitudinal bars. Also, transverse reinforcement enhances the shear strength andconfining the core concrete. The amount of reinforcement shall be verified in Chapter 11 and thespacing of ties shall not exceed the limit values described in this section.

a b
Ties

s  a/2 and s  12 lTies (diameter :  t)Longitudinal bars
(diameter :  l)

Fig. C13.4.1

Arrangement of ties enclosing longitudinal bars(ii) When concrete members have large cross-sections, concrete may not be sufficiently
confined by ties at the distance from the corner. The intermediate ties shall be arranged.

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Standard Specifications for Concrete Structures-2007, Design

13.4.3

Arrangement of torsion reinforcement(1) The minimum torsion reinforcement for a linear member shall be calculated using
Eq. (13.4.1).

Atl  M tud u 3 Am f ld (longitudinal reinforcement)

Atw  M tud s 3 Am f wd (transverse reinforcement)(13.4.1)

where, Mtwd : design torsional capacity given in Section 9.2.3.2.
Am : effective torsional area (rectangular section: b0d0, circular or cylinder
section: πdo2/4)
ftd, fwd : design yield stresses of longitudinal and transverse reinforcement,
respectivelys : longitudinal spacing of transverse reinforcement that works effectively as
torsion reinforcementu : length of the centerline of transverse reinforcement (rectangular section:2(b0+d0), circular or cylinder section: πd0)(2) The torsion reinforcement comprises closed transverse reinforcement andlongitudinal reinforcement perpendicular to the transverse reinforcement, as shown in
Fig. 13.4.1.
(3) The longitudinal reinforcement which works effectively as torsion reinforcement
shall be arranged symmetrically with respect to the vertical and horizontal axes of thecross section of a member.
(4) The transverse reinforcement which works effectively as torsion reinforcement
shall have acute or semicircular hooks at the ends, enclose the longitudinal
reinforcement, and be anchored to the inner concrete. In cases when the distance
between the position of the transverse reinforcement and the outer perimeter of the crosssection exceeds 0.2 times the member width, the transverse reinforcement should not be
considered as effective torsion reinforcement in principle.

Transverse
横方向鉄筋
reinforcement

Longitudinal
reinforcement
軸方向鉄筋

do

Longitudinal
reinforcement
軸方向鉄筋

do

do

Transverse reinforcement
横方向鉄筋

bo

do

S
(a)長方形断面(b)円形断面(a) Rectangular cross section
Fig. 13.4.1

S(b) Circular cross section

Arrangement of torsion reinforcement
228

Chapter 13

Structural Details of Reinforcement(5) For a rectangular cross section, at least one longitudinal reinforcing bar shall be
provided at each corner of the cross section, as shown in Fig. 13.4.1(a). In the case of acircular cross section, at least six longitudinal reinforcing bars shall be arranged at equalintervals, as shown in Fig. 13.4.1(b).
(6) The transverse reinforcement for a box section shall be provided as shown in Fig.
13.4.2.

(a)板厚が薄い場合(b)板厚が厚い場合(a) Concrete flange and web are thin. (b) Concrete flange and web are thick.

Fig. 13.4.2

Arrangement of transverse reinforcement for a box section(7) Appropriate amount of torsion reinforcement shall be provided in portions whererequired. The same reinforcement shall also be extended into adjacent segments up to alength equal to the overall height or the diameter of the cross section of the member. In
the remaining portions of the member, the minimum amount of reinforcement shall be
provided.

[Commentary] (1) According to the existing experimental data, it has been confirmed that thetorsional failure characteristics are greatly improved when torsion reinforcement with the torsional
capacity corresponding to that of concrete is provided. However, if the amount of reinforcement
corresponding to it is specified as the minimum reinforcement, excessive amount of reinforcement
may be given when the design torsional moment slightly exceeds the negligible torsion. Therefore,
the torsion reinforcement corresponding to one-half of the torsional capacity provided by theresistance of concrete is specified as the minimum amount. Also, for the torsional moment
exceeding this value, the reinforcement corresponding to the design torsional moment may beprovided.

(2) The most effective arrangement of torsion reinforcement is such that torsion reinforcement
crosses the member axis at an angle of 45 degrees. However, if torsional moment subject in cyclic
pattern, the reinforcement arrangement becomes complex and also bending of reinforcement
becomes difficult. Meanwhile, the combination of longitudinal reinforcement and closed
transverse reinforcement perpendicular to the longitudinal one, as shown in Fig. 13.4.1, has a shapesimilar to the vertical stirrup against shear forces, and the fabrication and the bending of
reinforcement is simple, although the effectiveness for torsion reinforcement is reduced to someextent. Therefore, it may be considered practical and is specified as the basic arrangement
configuration of torsion reinforcement. Also, this is the arrangement configuration which is used
to derive the equation for the torsional capacity.
(3) When the reinforcement for flexure satisfies the requirements for the arrangement
configuration of torsion reinforcement, it may be considered as torsion reinforcement.
(4) If the ends of transverse reinforcement are not sufficiently anchored to the inner concrete,they are not adequate as torsion reinforcement. Hence this requirement is provided. If thereinforcement for shear forces satisfies the codes for the arrangement of torsion reinforcement, it

229

Standard Specifications for Concrete Structures-2007, Design

may be considered as torsion reinforcement. If more than one set of transverse reinforcing bars for
torsion reinforcement are used, the side length of the transverse reinforcement may be the centerlineof the transverse reinforcement group. When the distance between the transverse reinforcement
and the outer member surface is more than 0.2 times the member width, it may not be considered astransverse reinforcing bars for torsion reinforcement. This is because the transverse reinforcement
arranged in the central region of the cross section does not work effectively against torsion.
(7) The region reinforced by torsion reinforcement is extended beyond the length required from
calculation by the height of member for ensuring safety, because unexpected loading and growth ofcracks may be caused.
Also, the longitudinal and transverse reinforcement when torsional reinforcement is required
from calculation should be spaced so that the torsional cracks always cross the reinforcement andthe diagonal compression of concrete should be effectively maintained.

13.5

Bend Configurations of Reinforcement(1) When bended reinforcement is used, bend configuration and arrangement shall be
determine taking into consideration the bearing stress of the concrete.
(2) Configuration of standard hooks is followed with Section 13.6.2.

[Commentary] (1) Inner radium of bend configuration of reinforcement shall be determined not
to provide large bearing stress to concrete.

13.6
13.6.1Development of Reinforcement
General(1) In order to achieve their full strength, reinforcing bars shall be firmly anchored inconcrete so that the bar ends are not pulled out of the concrete.
(2) Ends of the reinforcing bars shall be sufficiently embedded into concrete by thematter shown as below.
(i) Bars are developed through bond stress between the reinforcement and theconcrete.
(ii) Bars are developed by provision of a hook.
(iii) Bars are developed by suitable mechanical device.
(3) If the method described in Item (2) (i) or (ii) is used, basically the shapes of standard
hooks shall be in accordance with Section 13.6.2, and the development length shall becalculated in accordance with Section 13.6.3, and the bar ends shall be anchored taking
into consideration the type of structure or member, the state of loading, arrangement ofreinforcement, the state of stress at the anchoring location, etc.
(4) If a method other than those mentioned in Item (3) is used, the method shall satisfy
the required anchoring performance taking into consideration the type of structure or
member, the state of loading, arrangement of reinforcement, the state of stress at the230

Chapter 13

Structural Details of Reinforcement

anchoring location, etc.
(5) Longitudinal reinforcement shall be anchored in view of the stress state of thereinforcing bars in the anchoring zone and the characteristics of the member.

[Commentary] (1) In reinforced concrete, reinforcing bars and concrete must act together inresisting external loads. Thus, under the action of external loads, the anchorage of reinforcement
in concrete is very important. Since the effects of local bond can be neglected with sufficientanchorage of reinforcement, only the anchorage of ends of the bars is described in this section.

(2) In order to allow development of the full strength of reinforcing bars, either the end of thebars should be sufficiently embedded in the concrete, or provisions for hooks, appropriately made,so that the reinforcing bars do not get simply pulled out of the concrete.
Hooks may not be provided in the anchored regions in the case of deformed bars, but sufficient
reinforcement in the perpendicular direction should be provided to enable development of bond.
However even when deformed bars are used, it is recommended that hooks are provided in casessuch as fixed end in members, both ends of tensile reinforcement in footing, tensile reinforcement atfree end of cantilever beam, to ensure that even onset of large cracks does not cause the bars to bepulled out.
(3) If the bar ends are anchored by the method described in Item (2) (i) or (ii) and no special
examination is conducted, the reinforcing bars may be anchored in accordance with the Design:Standards, Part 5, of this Specification.
(4) For example, other anchoring methods are shown below.
(a) Out of specification such as, high-strength reinforcing bars, large diameter reinforcing bars,
special deformed bars, etc. These are embedded in concrete with the development length.
(b) Ends of reinforcing bars with special bend configurations(c) End of bars welded with steel plate, nut, metal, and so on. In addition, end of bars welded
into steel members.
(d) The development length is shortened by improving the bond strength between reinforcing
bars concrete.
If an anchoring method other than those described in Item (3) is used, the method must satisfy
the required performance according to the type of structure and load characteristics. In general,
performance requirements include those listed below. Anchoring performance details andverification methods shall be in accordance with the Recommendations for Design, Fabrication and
Evaluation of Anchorages and Joints in Reinforcing Bars (2007).
1) Static load capacity
2) High-stress cyclic load capacity
3) High-cycle load capacity
4) Reliability attributable to construction5) Others (performance at low temperature, etc.)(5) The anchoring of longitudinal reinforcement varies depending on the stress state ofreinforcing bars in the anchoring region and the characteristics of the member. It is therefore
231Standard Specifications for Concrete Structures-2007, Designnecessary to determine the development length of reinforcing bars, taking into consideration theinfluence of these factors. If no special examination is conducted, the Design: Standards, Part 5,of this Specification should be followed.

13.6.2Standard hooks(1) Standard hooks are defined as semi-circle hooks, rectangular hooks, andacute-angled hooks.
(2) The configurations of standard hooks shall be as specified in Items (i) to (iii) below(see Fig. 13.6.1).
(i) Semicircle hook is defined as one having the end of the bar bent through 180
degrees and has a straight extension which measures neither less than 4 times bar
diameter nor less than 60mm.
(ii) Acute-angled hook is defined as one having the end of the bar bent through 135
degrees and has a straight extension which measures neither less than 6 times bar
diameter nor less than 60mm.

Not less than 4 nor 60mm

Semicircular hook(for plain bar and deformed bar)Not less than 6 nor 60mm

Acute-angled hook(for deformed bar)

 : Diameter of reinforcement
Fig. 13.6.1

Rectangular hook(for deformed bar)Not less than 12

(iii) Rectangular hook is defined as one having the end of the bar bent through 90
degrees and has a straight extension which measures not less than 12 times bar diameter.

r : Inside radius bent

Configuration of hook at free end of bar(3) Standard hooks for the longitudinal reinforcement shall satisfy the requirements
specified in Items (i) to (iii) below.
(i) When using plain bars as longitudinal reinforcement, the semicircular hook shall be
used as the standard hook.
(ii) Inside radius of bend for hook shall not be less than that given in Table 13.6.1,
where  is diameter of the bar.
(4) Standard hooks for stirrups and hoops shall satisfy the requirements specified in
Items (i) to (v) below.
(i) A standard hook shall be provided at the end of stirrups, ties and hoops.

232Chapter 13

Structural Details of Reinforcement(ii) In cases stirrups, ties and hoops are made using plain bars, semicircular hooks
shall be used.
(iii) In cases stirrups are made using deformed bars, rectangular or acute-angled hooks
can be used.
(iv) In case ties are made using deformed bars, semicircular or acute-angled hook shallbe used.
(v) Inside radius of bend for stirrups and ties shall not be less than the values shown in
Table 13.6.1. For stirrups made with bars of diameter less than 10mm, however, insideradius of bend may be taken as 1.5, where  is diameter of the bar.
Table 13.6.1

Inside radius of bend for hook
Inside radius of bars (r)TypeLongitudinal bars

Stirrups and ties

SR235

2.0

1.0

SR295

2.5

2.0

SD295A, B

2.5

2.0

SD345

2.5

2.0

SD390

3.0

2.5

SD490

3.5

3.0

Plane bar

Deformed bar[Commentary] (2) The length of the straight extension of the hook has been determined to ensurethat the hook is effective and to facilitate the making hook. For reinforcement bent at less than 90
degrees, provisions in Section 13.6.3 should be followed.

(3) The inside radius of bend of hooks here is slightly greater than that specified for the bending
test in JIS G 3112 "Steel Bars for Concrete Reinforcement", considering the need to appropriately
distribute concrete, and ensuring that the reinforcement is not damaged and that the hooks are
effective. The fracture of reinforcing bars may be occurred with the small inside radius of bend.
The radius of bend of hook shall not be less than the verified value described in this section.
(i) The bond strength between plain steel bars and concrete is considerably lower than thatbetween deformed steel bars and concrete and varies widely depending on the surface properties ofplain bars, the properties of the concrete around the plain bars, etc. According to pull-out test
results, reinforced concrete members reinforced with hookless plain bars usually fail because of theslipping out of reinforcing bars. For these reasons, semicircular hooks must be installed at theends of plain bars in order to achieve reliable anchoring.
(4) Ties serve to confine the core concrete and to prevent buckling of the longitudinal
reinforcing bars. In order to satisfy the required performance, the ties shall be arranged at closeintervals, and anchored sufficiently.
(5) Smaller inside radius of bend for stirrups and ties have been provided for facilitating thearrangement of reinforcing bars within the cross section. It is necessary to ensure that thereinforcing bars are not damaged by bending.

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Standard Specifications for Concrete Structures-2007, Design

13.6.3

Basic development length(1) Basic development length (ld) shall be calculated using Eq. (13.6.1) and modified by
Items (i) to (iii) below. However, modified ld shall not be less than 20.

ld  

f yd
4 fbodφ(13.6.1)

where,  : diameter of reinforcing bar
fyd : design tensile yield strength of reinforcement
fbod : design bond strength of concrete, which may be obtained using Eq. (5.3.2),
assuming c to be 1.3, and with the condition that fbod  3.2 N/mm2.

  1.0 (in case of kc  1.0)
 0.9 (in case of 1.0 < kc  1.5)
 0.8 (in case of 1.5 < kc  2.0)
 0.7 (in case of 2.0 < kc  2.5)
 0.6 (in case of 2.5 < kc)
where, k c 

c

φ



15 A tsφc : concrete cover of reinforcing bar or half of the clear distance between
reinforcement, whichever is smaller.
At : area of transverse reinforcement arranged perpendicular to theassumed splitting failure surfaces : distance between the centers of transverse reinforcement(i) Basic development length, ld, is given by Eq. (13.6.1).
provided with standard hooks, may be reduced by 10.

Basic development length,(ii) The basic development length in compression reinforcement may be taken as 0.8 ofthat obtained as shown in accordance with Eq. (13.6.1). It shall not be reduced in case ofusing standard hooks.
(iii) In cases the anchored reinforcing bar is located at a depth less than 300mm fromthe concrete surface, and at an angle less than 45 degrees from the horizontal, the basic
development length shall be give by Item (i) or (ii).
(2) In cases when the provided area of steel (As) is larger than the amount required fromcomputations (Asc), the development length, l0, may be estimated using Eq. (13.6.2).

l 0  l d   A sc A s (13.6.2)

where, l0  ld /3, l0  10,  : diameter of reinforcement234

Chapter 13

Structural Details of Reinforcement(3) Development length in the case of reinforcement, which is bent in the anchoredportion shall be taken as given below (see in Fig. 13.6.2).
(i) In cases when the inside radius of bend is not less than 10 times the diameter of thebar, the entire length of the reinforcement including the bent portion shall be consideredeffective.
(ii) In cases when the inside radius of bend is less than 10 times the diameter of the bar
and the straight portion beyond the bend extends more than 10 times diameter of the bar,the straight portion shall be considered effective.

Not lessthan
10Bend is effective

:Diameter of reinforcementr : Inside radius

in development

Fig. 13.6.2

Development length of reinforcement with bend[Commentary] (1) The required development length for reinforcing bars depends on the type ofthe bar, strength of concrete, cover thickness, and condition of transverse reinforcement. These
factors shall be appropriately considered when calculating the required basic development length.

The required development length, lo, in cases when transverse reinforcement is provided may be
given using Eq. (C13.6.1).


f yd

 13.3 φ 1.25 f 
cdl0  
 c 15 At 
0.318  0.795 φ sφ (C13.6.1)

where, fyd : design yield strength of reinforcement (N/mm2)
f'cd : design compressive strength of concrete (N/mm2), which may be obtained using Eq.
(C13.6.2), with c of 1.3.
f 'cd f 'ck

(C13.6.2)

cwhere, c/  2.5.
It is very difficult to take into account of the effect of all the factors such as type of the bar,strength of concrete, cover thickness, and condition of transverse reinforcement. The factor  hasbeen introduced to take into account these effects.
The required development length for tensile reinforcement provided with standard hooks has
been reduced as the length of the hook is added to the development length, and, the bearing stress of235

Standard Specifications for Concrete Structures-2007, Design

the concrete confined within the hook is also expected to transfer forces. Though, in principle, theextent of reduction in the development length of tensile reinforcement with standard hooks should
vary depending upon the type of bar, strength of concrete, etc., a uniform simplified value of 10 in
all cases has been recommended on the basis of provisions in standards in other countries. In
compression reinforcement, the development length shall not be reduced on account of presence ofhooks.
(2) The development length should be calculated using the basic development length ld
determined on the basis of the size of the bars and their arrangement, and the strength of theconcrete, and modified in taking into consideration the actual condition of use.
In cases that the amount of reinforcement exceeds that required by computation, the basic
development length may be reduced. However a certain minimum basic development length, l0,
should be determined to ensure the safety for additional forces.
13.7

Splices in Reinforcement(1) Appropriate splices shall be provided in the reinforcement taking into accountfactors such as the type and diameter of the bars, state of stress, and location of splices,and so on.
(2) To the extent possible, splices shall not be located at cross-sections of members
subject to high stresses.
(3) Splices shall not be clustered at the same cross-section of a member, and the
maximum number of joints permitted in the same cross section shall be one in every twobars. To ensure that splices do not cluster at the same section, in general, the standard
distance between two staggered splices in the longitudinal direction shall not be less than
the sum of the splice length and 25 times the bar diameter.
(4) Clear distance between two adjacent splices or between a splice and a bar shall not
be less than the maximum size of coarse aggregate.
(5) When splicing is provided after distributing reinforcing bars, adequate allowanceshall be made for operation of jointing machines.
(6) Concrete cover of splices shall be provided in accordance with requirements ofSection 13.2.
(7) If lap jointing is used, in general, the lap length is determined by the basic
development length indicated in Section 13.6.3, and joints shall be provided taking into
consideration such factors as the type of structure or member, the state of loading,arrangement of reinforcement, the stress state at the joint location, etc.
(8) If joints other than lap joints are used, the joints shall satisfy joint performancerequirements according to the type of structure, the state of loading, arrangement ofreinforcement, the stress state at the joint location, etc.

[Commentary] (1) Strength and reliability of splices depend on such factors as kind of splices,
construction methods, the type of bars, state of stress, and location of splices. Therefore,
appropriate splices shall be provided so that their performance can be well exhibited in response to
the above-mentioned factors.
236

Chapter 13

Structural Details of Reinforcement(2) Splices in reinforcement could become weak points, and become the cause for reduction instrength of the structural members that contain splices, when the splices are provided in regions
subject to high stresses. Thus, splices at cross sections subject to high tensile stresses, such as the
mid-spans, are preferably avoided.
(3) In cases when splices with weak points are concentrated in a single cross-section, thestructural performance of the member may be seriously decreased. In addition, certain types ofsplices provided in a certain area also hamper proper compaction of concrete, and therefore, thelocation of splices should be staggered. The recommendation for the splices to be staggered by adistance equal to the sum of the splice length plus 25 times the bar diameter, has been madeconsidering this requirement may ensure adequate strength of the joint through bond action, even if
some of the splices are poor. The adverse effects of splices on compaction of concrete may also be
considered to be minor provided the provisions for staggering the splices are followed.
If splices cluster at the same cross-section in a less favorable condition, an appropriate joint
strength must be determined. The performance of joints and verification methods are as describedin the Japan Society of Civil Engineers' Recommendations for Design, Fabrication and Evaluationof Anchorages and Joints in Reinforcing Bars (2007).
(4) Requirements have been waived from the practical consideration that the amount ofreinforcing steel increases at joints in comparison with normal cross sections and that a requirementof too much clear distance may cause difficulty in proportioning of members because of increase inspacing of reinforcement. However, in the case of splices, the maximum possible spacing has
been recommended, as concrete tends to spread unevenly in the neighborhood of splices.
(5) When splices are fabricated after arranging the reinforcing bars, the required clear distances
may be considerably greater than the maximum size of coarse aggregate to allow for the operationof a jointing machine. Therefore, it is important to consider the method and procedure offabrication of splices at the design stage itself, in order to avoid problems in the construction stage.
(6) This requirement has been included from the consideration that splices using sleeves,couplers, gas pressure welding joints and others should have adequate concrete cover, at the samelevel as reinforcing bars.
It is noted that concrete cover to stirrups or ties at joints shall conform to provisions of Section
13.2.
(7) If lap joints are used and no special examination is conducted, joints may be provided inaccordance with the Design: Standards, Part 5, of this Specification.
(8) If joints other than lap joints are used, the joints must satisfy joint performance requirements
according to the type of structure, the state of loading, arrangement of reinforcement, the stress stateat the joint location, etc. Commonly specified performance requirements are listed below.
Details of performance requirements for joints and verification methods are referred to the
Recommendations for Design, Fabrication and Evaluation of Anchorages and Joints in Reinforcing
Bars (2007).
1) Static load capacity
2) High-stress cyclic load capacity
3) High-cycle load capacity
4) Reliability attributable to construction5) Others (performance at low temperature, etc.)
237

Standard Specifications for Concrete Structures-2007, Design

13.8

Reinforcement of Members

Each member shall be provided with necessary reinforcement, taking into
consideration the shape and stiffness of the member, boundary conditions, load
characteristics, the state of loading, an unexpected situation such as steel corrosion,
concrete cracking, initial defect, construction workability, and so on.

[Commentary] Reinforcement for concrete members includes not only reinforcement calculated
through the performance verification described in this chapter but also nonstructural reinforcement
and reinforcement provided according to empirical judgment.

The arrangement of reinforcement shall be determined taking into consideration the shape andstiffness of members such as beams, columns, rigid frames, arches, slabs, footings, shells and walls,
the ratio to the stiffness of adjoining members, boundary conditions such as the type of joint
structure, load characteristics, and the state of loading. It is also necessary to consider theconstruction ability as well as member characteristics and the risks of problems such as steel
corrosion, unexpected cracking of concrete, unexpected initial defects, etc.
These types of reinforcement must be arranged according to the results of numerical analysis orexperimental tests. The special examination should be managed by the responsible engineer.
If no special examination is conducted, arrangement of reinforcement may be provided
according to the Design: Standards, Part 5, of this Specification.

238

Chapter 14

Other Structural Details

CHAPTER 14 OTHER STRUCTURAL DETAILS

14.1

GeneralGeneral structural details of reinforced concrete structures, prestressed concrete
structures and steel-concrete composite structures shall be provided in accordance withthis chapter.

[Commentary] This chapter specifies common structural details of reinforced concrete structures,prestressed concrete structures and steel-concrete composite structures that are not directly related
to verification methods, such as items specified to make up for structural weaknesses. If structuraldetails relevant to this chapter are specified separately in other parts of this Specification, thosespecifications must be followed.

14.2

Beveling

Corners of the reinforced concrete members shall be beveled. Especially in cases
when the member of structures in cold regions or structures likely to be subjected tosevere weather action, beveling shall be carefully considered at the design stage, and thechamfers or fillets shall be clearly indicated in design drawings.

[Commentary] Since corners of the reinforced concrete member tend to be damaged by freezing
or impact, it is important to provide appropriate chamfers or fillets, as may be required. Especially,in case of members in cold regions or otherwise subjected to severe weather action, larger chamfers
or fillets should be provided.

14.3

Additional Reinforcement for Exposed Surfaces

Additional reinforcement shall be provided near large exposed surfaces in order toprevent occurrence of harmful cracks due to shrinkage and changes in temperature.

[Commentary] Use of closely spaced small diameters reinforcing bars is recommended asadditional reinforcement. Such reinforcement is more effective to prevent the cracking of concrete.
In the case of retaining wall, use of more than 500mm2 (sectional area of bars) of additional
horizontal reinforcement per one-meter height of wall is recommended with spacing not exceeding
300mm. The concrete cover should be provided in accordance with the provisions of Section
13.2.

14.4

Reinforcing for Concentrated Reactions

Additional reinforcement shall be provided in portions under concentrated reactionand excessive stress concentration.

[Commentary] Concentration of stresses occurs in structural components such as mid supports ofcontinuous slabs or beams, connections of columns and footings, where they are subjected toconcentrated reactions, or portions where the cross-sectional area changes drastically. Since it is239

Standard Specifications for Concrete Structures-2007, Designdifficult to actually calculate stresses in such portions, appropriate additional reinforcement should
be provided on the basis of test results or cracks in similar existing structures.

14.5

Reinforcing for Openings

Appropriate additional reinforcement shall be providing around all openings instructural members, such as slabs and walls, to safeguard against cracks due to stressconcentration.

[Commentary] Cracks due to stress concentration tend to occur around openings in such
structural members as slabs and walls. Occurrence of these cracks depends on specific local
conditions, and therefore methods of reinforcement are based on available results, such as
approximate calculations, experimental tests describing the actual conditions, and past cracking
records. The additional reinforcement is generally provided as shown in Fig. C14.5.1. Suchreinforcement should be extended to allow for appropriate development length in the bars beyond
the corners.
The primary and distribution reinforcement which cannot be provided because of the openings
should be arranged around the openings in a manner that requirement for the amount ofreinforcement at any cross-section is satisfied.

Fig. C14.5.1

14.6
14.6.1

Additional reinforcement around opening

Construction Joints
General(1) Location and direction of construction joints shall be decided so as not to have any
detrimental effects on the strength, the durability and external appearance of structures.
(2) Construction joints shall not be located on the portion subjected to large shear
force, and it is recommended that direction of construction joints is crossed at rightangles to the direction of compressive force in member. In the case construction joints
are located on the portion subjected to large shear force, the notch shall be provided orconstruction joints shall be reinforced appropriately.
(3) It is not recommended to locate the construction joints for the concrete structuresin coastal environments. If the construction joints are located, the durability shall beconsidered.
(4) Construction joints shall be located with appropriate spacing for the water-tightstructures.
(5) It is desirable that construction joints are indicated in design drawings.
240

Chapter 14

Other Structural Details[Commentary] (1) Since the location and direction of construction joints affect the strength of
the structure, they should be located in portions where the shear force is less and, at right angles tothe direction of compressive force, according to the requirements specified herein. In the case ofconnections of columns and beams, considering the settlement of concrete, the construction joints
may be located at the top of columns connected with beams. Since construction joints render thereinforcement susceptible to corrosion, it is advisable not to locate these joints in a region where
corrosive material may penetrate through such joints.
(2) Construction joints may be weak-points for shear force. It is necessary to locate theconstruction joints on the position subjected to small shear force, and it is recommended that thedirect of construction joints is crossed at right angles to the direction of compressive force inmember to enhance the shear strength of construction joints. In the case that construction joints
are located on the portion subjected to large shear force, the notch shall be provided or construction
joints shall be reinforced with appropriate reinforcing bars.
(4) If the large mass concrete is constructed without joints, the structure could not have thewater-tight performance by large cracking. The verification is to ensure the water-tightperformance requirement.

14.6.2

Construction joints of columns or walls integrated with slabs

Construction joints of column or wall integrated with slab is located near the boundarywith slab in principle. Haunches shall be constructed with slab continuously. Also,
structure with coving shall be constructed with slab continuously.

[Commentary] The concrete of haunches in slab cannot shrink and sink with columns and walls,
because it is supported by formwork directly. Considering the haunches behave with slab,
haunches shall be constructed with slab continuously.

14.6.3

Construction joints of slab

Construction joints of slab are located near the center of span of slab or beam inprinciple. In the case that main beam crosses transverse beam at the center of span,
construction joints of beam shall be located at distance of two times width of transverse
beam. Construction joints shall be reinforced by diagonal tensile steel bars to enhance
the shear strength.

[Commentary] In general, shear action is small and direction of construction joints is crossed atright angles to the direction of compressive force near the center of span. Construction joints arelocated near the center of span because the decreasing of strength of slab and beam are not serious.
However, in the case that the main beam crosses the transverse beam at the center of span, it isappropriate that construction joints of beam shall be located from distance of two times width oftransverse beam. In this case, large shear force subjects to the construction joints, and it isrecommended that the construction joints shall be reinforced by diagonal tensile steel bars through45 degree (see Fig. C14.6.1).

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Standard Specifications for Concrete Structures-2007, Design

Construction joint

Transverse beam

Fig. C14.6.1

14.6.4

Reinforcement of construction joins

Construction joints of arches

The direction of construction joints shall be crossed at right angles to axis of archmember in principle. In the case that direction of construction joints is crossed atparallel to axis of arch member, it is necessary to provide the construction joints taking
into consideration the location, the method of reinforcement, and so on.

[Commentary] In the case that construction joints are not located in direction at the right angles
to axis of arch member, shear force subject along the construction joints and it may become astructural weak point. This provision is to prevent such shear action.
When the direction of construction joints crosses at the parallel to axis of arch member,construction joints are subjected to shear force from eccentricity of live load, and sufficientconsideration is needed.

14.7

Expansion Joints(1) Location and the function of expansion joints shall be decided in a manner thatprovides the most effective protection against cracking, and, to make the movements due
to shrinkage or expansion as free as possible. These shall be clearly indicated in design
drawings.
(2) Expansion joints shall not be confined by both sides of structures.
(3) Joint sealer and water stop shall be provided in expansion joints when needed.
(4) In the case that expansion joints is to be moved in the longitudinal direction, it isrecommended that the notch is provided and dowel bar is used.

[Commentary] (1) In the case of structures like retaining walls cracks may occur on account ofhigh stresses due to restraining movements induced by changes in temperature or moisture, or highstresses due to inconstancy of the changes in a section. Therefore, the location and structure of
expansion joint shall be determined as specified herein, and, shall be indicated in design drawings.
(2) Locating expansion joints, there are a case to separate both sides of structures and member
completely and a case to separate only concrete and to be strung by reinforcing bar (see Fig.
C14.7.1).
(3) It is recommended to use the joint sealer when sand might enter the space of expansion
joints. The joint sealer and filler are made of the asphalt, the rubber, the resin, and so on. The
242

Chapter 14

Other Structural Details

stretch water stop is recommended to use for the water-tight structures. The water stop is made of
the sheet copper, the stainless plate, the vinyl chloride resin, and rubber, and so on.

Releasingconcretebond
by byasphalt,
Releasingconcretebondasphalt,etc.
etc.

(a)-(d):Expansion joint for wall, etc.

Dowel bar

Water stop

SealerFillerSealer

Water stop

Water stop
FillerAsphalt membrane(e),(f) :Expansion joint for watertight of wall and slab
FillerFiller(g),(h):Expansion joint for bottomof water tank

Synthetic rubber ring

Hinge

Fig. C14.7.1 Expansion joints

14.8

Crack Inducted Joints

When crack inducted joints is located to control cracking, the type and location of
crack inducted joints shall be determined not to decrease the strength and function of thestructure.

[Commentary] The deformation of concrete structure might be caused by the heat hydration of
cement, the temperature change, the drying shrinkage, and so on. The concrete crack might occur
if the deformation is restricted. Therefore, the crack inducted joints are installed at prescribedintervals to concentrate the concrete crack on the predicted location. When the crack inductedjoints are provided, the sufficient consideration is necessary as for the interval and rate of sectionalloss caused by the crack inducted joints, the maintenance method of reinforcing bar for steel
corrosion, the ensuring the prescribed concrete cover, the selection of material for the joint filler.
In general, it is recommended that the interval of crack inducted joints is one to two times the heightof cross section and that the rate of sectional loss is 30 to 50%. Figure C14.8.1 shows the exampleof the crack induced joints. These examples show that a notch in vertical direction on both
surfaces of the wall and that bond of concrete surface is released by parting agent. In addition, avinyl chloride pipe, precast concrete or the iron plate, and so on, with the concentration of stress,
are embedded into the wall section. The ratio of sectional loss is defined as the ratio of the total
length, given as the summation of notch depth and unbond depth, to the original wall thickness.

243

Standard Specifications for Concrete Structures-2007, Design

When the crack induced joint is provided in the water-tight structure, it is recommended that waterstop is used. When the water leak from the crack induced joints and the steel corrosion ofreinforcing bar are concerned, the treatments shall be done as shown in Fig. C14.8.2.

0.5 ～
0.7

Water
stop
止水板

Spacing of crack
隔
induced joints地間（a）0.15 ～
0.25

壁高Height of wall

Water
stop
止水板

chloride pipe（c）Releasing
はく離剤
agent

（d）
プレキャストPrecastコンクリートconcrete

Releasing
はく離剤
agent

Half pipe
半切パイプ

（e）

0.15 ～
0.25

一 般 図

（b）

Vinyl
塩ビパイプ

0.5 ～
0.7

目
誘発

（f）

溝の形の例
Example断面of notch

Steel plate with
= 0.6～1.2㎜の鉄板
0.6-1.2mm
thickness
止水板stop
Water

0.15 ～
0.25

Additional
配力鉄筋
reinforceme

充てん材（シーリング材，樹脂モルタル等）
Filler, Sealer, Resin mortar, etc.（g）Fig. C14.8.1

Example of crack induced joints

Crack
ひび割れ
(Fillingof epoxy resin)（エポキシ樹脂注入）

止水板
Water
stop

Crack
ひび割れ
(Fillingof epoxy resin)（エポキシ樹脂注入）

Water
stop
止水板

Joint
board
目地板
接着剤塗布
Adhesionbond
樹脂モルタルResin mortal

Backup
バックアップ材
弾性シーリング
Elastic sealing(a)Fig. C14.8.2

14.9

(b)

Example of details of crack inducted joints

Water-Tight Structures

When water-tightness is required for reinforced concrete structures, arrangement ofreinforcement, spacing and arrangement of construction or expansion joints, or otherdetails shall be determined so as to prevent harmful cracks.

[Commentary]

For reinforced concrete structures that require water-tightness, it is necessary to244

Chapter 14

Other Structural Details

construct watertight concrete. It is especially important that steps are taken to minimize cracking
at the design stages. Therefore, changes in temperature, shrinkage, differential settlement offoundation, will appropriately accounted for in the design stage, so as to decrease possibilities ofcracking by such ways as appropriate detailing of reinforcement, limiting stresses in reinforcement,
providing expansion or construction joints with appropriate spacing and location. Also in thedesign stage, provisions for water-stops, etc. at construction joints and expansion joints should bemade to ensure water-tightness of the structure.

14.10

Drainage and Water Proofing(1) For structures in contact with water, provisions for drainage and waterproofing
shall be considered when needed.
(2) Water proofing shall, as a rule, be provided on the face subjected directly to waterpressure.

[Commentary](1) For reinforced concrete structures requiring water-tightness, before
considering waterproofing, the possibility of providing appropriate drainage should be considered.
For such structures as underpasses, for example, drainage may be the best way for maintaining
water-tightness. Therefore, it is recommended that for such structures drainage should beconsidered first, and for cases where the objective is not satisfied with drainage alone,waterproofing may be considered to maintain the water tightness of the structure.
For structures in which water pressure act directly on one face and the other face is required tobe dry, appropriate waterproofing should be provided considering cracking of concrete and otherdefects during construction.
(2) When waterproofing is provided at the face not directly subjected to water pressure, water
may seep through the concrete and fill the space between the waterproofing and concrete face, andcause some damage to former. Therefore, waterproofing should, in principle, be provided on theface directly subjected to water pressure.
If the water between waterproofing and concrete face freezes, the affects are likely to be worse
compared to a case without waterproofing. In cases where the structure is subjected to freezing
and thawing, water proofing shall not be provided on the face not subjected to water pressure.

14.11

Protection of Concrete Surface(1) In order to provide durability to portions subjected to abrasion, deterioration,
impact, or other severe actions, concrete surfaces shall be protected using appropriatematerials.
(2) Concrete surfaces exposed to environmental deterioration factors such as chloride
attack, freezing and thawing actions and chemical attack should be protected withappropriate materials such as polymeric materials.

[Commentary] (1) For structures subject to running water with suspended sand, wave action,
impact of traffic, or subject to chemical erosion, concrete surfaces need to be protected by suchmaterials as timber, good quality stone, steel plates and polymer materials so that the portions
subject to abrasion, corrosion, impact, or other severe actions may be rendered especially durable.
When the actions are not severe, providing an additional concrete cover of 10mm may be
245

Standard Specifications for Concrete Structures-2007, Design

considered as the countermeasure.
(2) Methods for enhancing the durability of structural components subjected to chloride attack,freeze-thaw cycles or chemical attack, include increasing the concrete cover over reinforcing bars
and protecting the concrete surface with appropriate materials such as polymeric materials. In thiscase, it is necessary to substitute the surface protection for the appropriate time.

14.12

Haunches

Haunches shall be provided, in portions such as connections of rigid framed members,
supports of fixed slabs or beams and supports of continuous slabs or beams. The
effective height in design of the section where a haunch is provided may be determined,
considering the dimension of the haunch. In general, only the portion of the haunch withan inclination less than 1/3 shall be considered effective.

[Commentary] Haunches are recommended to provide in portions such as connections of rigid
framed members, supports of fixed slabs or beams and supports of continuous slabs or beams
because stress-concentration tends to occur there.

14.13

Joint part of Members

The joint part of the columns, beams, and other members should be designed toensure the sufficient load-carrying capacity before the members indicate plastic behavior.

[Commentary] It is assumed that the some members indicate plastic behavior in the seismic
design to verify the Seismic Performance Grade 2 or Seismic Performance Grade 3. The structure
cannot have required seismic performance if the joint part loses the load-carrying capacity before
the members indicate plastic behavior. Therefore, the joint part of columns and beams isnecessary to have higher load-carrying capacity than that of structural members. It is necessarythat the dimension of cross section of the joint part is enlarged, the haunches are located, and thetransverse reinforcing bars are arranged sufficiently, etc.
In addition, the longitudinal
reinforcement that enters the joint part from each member should be embedded into concrete
sufficiently.

14.14

Structural Details of Members

Structural details of members shall be determined through examinations taking into
consideration such factors as the shape and stiffness of the members, boundary
conditions, load characteristics, the state of loading and construction workability.

[Commentary] Structural details and the minimum dimensions of members for beams, columns,
rigid frames, arches, slabs, footings, shells and walls must be determined taking into consideration
the shape and stiffness of the members, boundary conditions, load characteristics, the state ofloading, construction workability, etc. The verification should be managed by the responsible
engineer.
If such examinations are not conducted, structural details and the minimum dimensions ofmembers may be determined in accordance with the Design: Standards, Part 1, of this Specification.
246

Chapter 15

Prestressed Concrete Structure

CHAPTER 15 PRESTRESSED CONCRETE STRUCTURE

15.0

NotationAc: total cross-sectional area of concrete

Acc : area of concrete in compressive zone of shear plainAp: cross-sectional area of prestressing tendonAs: cross-sectional area of tension reinforcement

As ' : cross-sectional area of compression bar
Ak: area of shear key

B: outer diameter of steel shear key or width of concrete shear keyd': distance from compression edge to compression bar

dp: distance from compression edge to prestressing tendond: distance from compression edge to tension bar

Ec: Young's modulus of concrete

E p : Young's modulus of tendon
e p : distance between the centroid of member and the centroid of prestressing
tendones: distance between the centroid of member and the centroid of tension bar

es ': distance between the centroid of member and the centroid of compression bar

f puk : characteristic value for tensile strength of prestressing tendonf vk : limit value of shear stress that steel shear key can carryIc: total cross-sectional moment of inertia of concreteL: embedment depth of steel shear keyl: length of tendon

l: setting lengthN: number of shear keyN: number of tensioning times (number of groups of the tendon)np: Young's modulus ratio of prestressing tendon to concrete ( E p Ec )ns , j , ns , k : Young's modulus ratio of tension bar and compression bar to concrete at age
247

Standard Specifications for Concrete Structures-2007, Designt j , tkn ps : Young's modulus ratio of prestressing tendon to reinforcing bar

 E / E ps

P(x) : prestressing force of considered cross sectionPi: prestressing force at prestressing work at the tensioning end of tendon

P : loss of tension force due to set of tendon
Pi ( x) : loss of prestressing force immediately after prestressingPt ( x) : time dependent variation of prestressing force

Tc: total tension force in concretet: height of shear key

Vk: shear capacity of shear key

Vks: shear capacity of steel shear key

: angular change of the tendon in radian : equivalent angular change per meter of a length of the tendon.

: coefficient that indicates shear plain configuration (0–1)

: apparent relaxation ratio of tendon

b: member factor

 'cs : shrinkage strain of concrete: friction coefficient of unit length: average friction coefficient of solid contact

a: bearing stress that acts to single shear key at execution or ultimate limit state

 'cdp : compressive stress of concrete at the location of prestressing tendon bypermanent load 'cpg : concrete compressive stress due to prestressing at the centroid of prestressing
tendons

 'cpt : compressive stress of concrete at the location of prestressing tendon by
prestress force just after prestressing

l: diagonal tensile stress nd : average compressive stress which acts to shear plain vertically pt : tensile stress of prestressing steel just after prestressing
 sl : maximum permissible value for tensile stresses in tension reinforcement248Chapter 15

xPrestressed Concrete Structure: normal stress y : stress perpendicular to  x p : prestress loss in prestressing tendon

 pr : loss of tensile stress due to relaxation
 pcs : stress loss of prestressing tendon by creep and shrinkage of concrete: angle between shear key and vertical line: creep coefficient of concrete j ,  k : creep coefficient of concrete loaded at age t j ,and tk


15.1: shear stress due to shear and torsion

General(1) Provisions of this chapter describe general guidelines especially needed for designof ordinary prestressed concrete structures or their members.
(2) Level of prestressing shall be determined such that the structure or member fulfills
its desirable functions and discharge its function in a safe and economical manner.

[Commentary] Use of prestressed concrete enables improvement in the crack characteristics atthe serviceability limit state, and reduces the required cross sectional area with use of high strength
steel, and thus, affords a wide range of options for many types of structures and construction
methods. The designer of a prestressed concrete structure must follow the requirements of thisSpecification and verify, in accordance with the provisions of this chapter concerning requirements
specific to prestressed concrete structures that the performance requirements related to safety,
serviceability, etc., are met.

As far as treatment of the prestressing force introduced to concrete members for the purpose ofdesign calculations is concerned, it may, in general, be treated as a load in the consideration of theserviceability limit state. At the ultimate limit state, only the indeterminate force may beconsidered as the effect of the prestressing force is included in calculating the ultimate strength ofthe cross-section.
When calculating response values, it is necessary to take moment redistribution into
consideration and to model the prestressing force by a method suitable for the purpose ofverification and for the analysis method used. In general, methods such as the method of treatingprestressing force as a fixed external force and the method of directly modeling tendons as chordmembers (one-dimensional linear elements) can be applied. It is necessary to perform modeling,taking into consideration such factors as the anchoring locations of tendons and whether concrete
members and tendons are bonded, so that the prestress that introduced into the concrete members
can be allowed for appropriately.
(1): Provisions of this chapter shall be applicable to ordinary prestressed concrete structures ormembers using prestressing tendons. If high-strength materials outside the scope of Chapter 5 areused as when concrete having a characteristic compressive strength exceeding 100 N/mm2 is used,
design values for the materials must be considered separately. But provisions of this chapter are249

Standard Specifications for Concrete Structures-2007, Design

not to be applied to the following structures or members:i) structures or members where the prestressing force is transferred by a method other thanprestressing tendons. For example in cases where jacks are used to prestress, e.g. in archedmembers or in concrete pavement, or in cases where concrete is cast on the tension side of a steel
girder, in which prior flexural moment has been induced, and which is released after hardening of
the concrete.
ii) prestressed steel reinforced concrete structures or members; prestressed composite structures
or members consisting of rolled sections, steel plates or built-up sections and concrete.
iii) prestressed concrete structures or members exposed to abnormal temperature. A range ofthe normal temperature may be considered from 0°C to 40°C.
iv) factory products such as prestressed concrete piles, prestressed concrete pipes, etc.
Means of introducing permanent prestress into concrete members can be classified, according to
the timing of tensioning of tendons, into two types: the pretensioning method and thepost-tensioning method. The post-tensioning method can be further classified into three types: theinternal tendon method, the external tendon method and the combined use of the two methods.
In the internal tendon method, tendons are placed through concrete members. They are either
tendons bonded to the concrete by use of grout to integrate the tendons with the concrete or tendons
unbonded to the concrete. Structure or member prestressed by unbonded tendon is separated fromthose prestressed by external tendons, because the relative distance between concrete and unbonded
tendon does not vary, and because unbonded tendon arrangement differs from the external tendon
system. However, additional considerations should be required to the structure or member withunbonded tendon, such as the increase of crack width, reduction of flexural capacity, minimum
amount of tendon, fatigue characteristics of anchorage, etc.
On the other hand, in the external tendon system described in this chapter the tendons areprovided outside of the concrete member and transfer the prestress through anchorages anddeviators. Arrangements for permanent rust-proofing and corrosion protection treatment oftendons are provided. In this chapter, tendons that can be used for the external tendon method arereferred to as "external tendons," and this chapter deals external tendons whose effective depth is
not greater than the depth of the member. Therefore, the provisions of this chapter may not beenough for the treatment of temporary prestressing during construction, additional external tendons
for repair or reinforcement without prior planning, stay-cable of cable-stayed bridges whose stressis regulated because of the large stress change by fluctuated load. Furthermore, it may also not beenough for large eccentric tendons such as tendon's location excesses the effective height of girder,
for fatigue by vibration, which is caused by direct effects of wind, is severe. For such cases,
reference should be made to other codes or papers.
Furthermore, in the case of structures or members using external tendons, considerations otherthan those described in this chapter are required for the following cases.
 The increase of crack width because external tendons have no bond to the concrete member The fact that plane sections remain plane is not adopted to the external tendon
 Change in the prestressing force and change in the effective depth in the external tendon
because of deformation in the concrete member
 Minimum tendon content

250Chapter 15

Prestressed Concrete Structure Fatigue of tendon
 Protection and rust-proofing of tendon(2): The level of prestress may generally be determined from considerations of flexural cracking
limit state corresponding to the function of structure.

15.2

Classification of Prestressed Concrete(1) This chapter classifies prestressed concrete structures into PC (prestressed
concrete) structures and PRC (prestressed and reinforced concrete) structures, anddescribes standard verification methods applicable to these structures.
(2) PC structures do not permit cracking in serviceability-related verification and are
structurally designed to control the edge stress in concrete by introducing prestress.
(3) PRC structures permit cracking in serviceability-related verification and are
structurally designed to control crack width by installing deformed reinforcing bars andintroducing prestress.

[Commentary] (1): The behavior of a prestressed concrete structure may be radically different
before and after the occurrence of cracking. Therefore, depending on whether cracking is permitted
under normal service conditions, methods of calculating stress in materials and methods ofstrengthening to resist bending moment such as the use or nonuse of reinforcement for crack
distribution vary considerably. Therefore, prestressed concrete structures are classified, according
to the definitions of Items (2) and (3), into PC (prestressed concrete) structures and PRC(prestressed and reinforced concrete) structures, and it is verified, by the method described in thischapter, that the degree of prestressing has been determined appropriately.

Flexural and other behavior at failure of prestressed concrete structures varies depending onwhether tendons are installed inside or outside the concrete members. Similarly, flexural and otherbehavior varies depending on whether the tendons used are bonded to the concrete members.
Therefore, it is necessary to classify prestressed concrete structures into PC structures and PRC
structures and to classify verification methods according to tendon arrangement and whether
tendons are bonded to the concrete. Therefore, this chapter classifies tendons into three types,
namely, internal tendons, unbonded prestressing tendons and external tendons, and also classifies
prestressed concrete structures according to the concept shown in Fig.C15.2.1. In this case,prestressing tendons used in the pre-tensioning method can generally be classified as internaltendons because those prestressing tendons can be treated like internal tendons used in the
post-tensioning method. Pregrouted prestressing tendons are made by filling sheaths with slowand cold-setting resin in place of ordinary grout used for prestressed concrete, keeping theunbonded state until prestress is introduced, bonding after resin set over time. The tendons canalso be classified as internal tendons because after the filling material sets, those tendons can betreated like internal tendons used in the post-tensioning method.
Prestressed concrete structures should be classified each member or each cross section. By
using PC structures and PRC structures together according to the purpose and performancerequirements, rational prestressed concrete structures can be constructed.

251

Standard Specifications for Concrete Structures-2007, Design
Classification of structures

Classification of prestressing tendonsClassification of prestressing time

Internal tendon (bonded)

Pre-tensioning method

Unbonded prestressing tendon (unbonded)

Post-tensioning method

PC structure

PRC structure
External tendon (unbonded)

Fig. C15.2.1

Classification of prestressed concrete structures(2): Serviceability verification for PC structures does not permit the occurrence of cracking. In
PC structures, the edge stress and diagonal tensile stress in the concrete are restricted in accordancewith the requirements specified in Section 15.7.2 by introducing prestress. Stress of material may
be calculated by assuming a fully effective cross section. As a general rule, the restraining effectof reinforcement is taken into account as an influence on the creep and shrinkage of concrete.
However, in general, the restraining effect of reinforcement does not need to be taken into
consideration because the amount of reinforcement is relatively small.
(3): Serviceability verification for PRC structures permits the occurrence of cracking. In PRC
structures, crack width is controlled by placing deformed bars and introducing prestress. To be
more specific, as in reinforced concrete structures, crack spacing is controlled by using the crack
distribution effect of deformed bars, and increases in steel stress are controlled by prestressing.
Therefore, as a general rule, examinations for flexural cracking look at the tensile reinforcement
located closest to the concrete surface, and flexural crack width is calculated by using the value of
1.0 for the factor ( k1 ) expressing the influence of the steel surface configuration on crack width in
Eq. (7.4.4). The restraining effect of both prestressing tendons and reinforcing bars is taken into
consideration as an influence on the creep and shrinkage of concrete.
For PRC structures, in theory, any degree of prestressing can be specified by setting load state tobe verified by stages according to such factors as the frequency and duration of variable loads andaccidental loads, the percentage of permanent loads in all loads, determining the limit state at thetension edge in each load state. PRC structures cover the entire intermediate range in the spectrum
between reinforced concrete structures and PC structures. In general, if a highly accurate
verification method taking into consideration the influence of cracking is as-needed used, the scopeof application of the method is very wide.
However, no verification method has been proposed that makes it possible to allow for the
influence of cracking over time at the loading stages and the subsequent stages and examine
different limit state by stages. There is as yet no highly accurate verification method capable ofallowing for those factors. There is as yet no highly accurate verification method capable ofallowing for those factors. If a special verification method capable of allowing for the influence of
cracking over time is not used, it is recommended that a limit state in which the tensile stress in theconcrete does not exceed the limit value is set by assuming that cracking does not occur because ofpermanent loads, and it is verified by using, for example, a formula for calculating the amount ofdecrease in tensile stress in prestressing tendons derived by assuming a fully effective cross sectionof concrete that the degree of prestressing has been determined appropriately. The limit value ofthe tensile edge stress may be determined according to the flexural crack strength of concrete.
By determining such limit state, the occurrence of cracking at an early age of concrete can beprevented. Therefore, the growth over time of the width of cracks caused by variable loads, etc.,
can be controlled. If a limit state with a limit value of the tensile stress of zero (a state ofdecompression in which the occurrence of tensile stress at the tension edge is prevented) is chosen,
252

Chapter 15

Prestressed Concrete Structure

it can be thought that even if cracks occur because of variable loads, etc., the cracks practicallyclose under permanent loads. Therefore, the limit value of the tension edge stress in the concreteshould be set appropriately according to the frequency and duration of variable loads and accidentalloads the percentage of permanent loads in all loads, etc., as mentioned earlier. If the influence ofrestraint on the shrinkage of concrete is thought to be great, it should be taken into consideration.

15.3

Prestressing Force(1) Prestressing force shall be calculated from Eq. (15.3.1).

P( x)  Pi  [Pi ( x)  Pt ( x)]where, P (x ) :Pi:(15.3.1)

prestressing force of considered cross section
prestressing force at prestressing work at the tensioning end of
tendonPi ( x) : loss of prestressing force immediately after prestressing to be
calculated taking into account the influence of the following:I) elastic deformation of concreteII) friction between tendon and sheathIII) Set during anchoring of tendon
IV) othersPt ( x) :time dependent variation of prestressing force; to be determinedtaking into account the influence of the following:V) relaxation of prestressing tendonVI) creep of concreteVII) shrinkage of concrete
VIII) restraint by reinforcement(2) If statically indeterminate force occurs because of prestressing force, the response
value may be calculated by using the prestressing force calculated from Eq. (15.3.1) as thecharacteristic value of the load.

[Commentary] (1): The items whose influence needs to be taken into account when calculating
the loss in prestressing force, Pi ( x) and Pt ( x) , are as follows:

I ) Influence of elastic deformation of concrete
In the pretensioning method, usually, prestress is introduced by releasing more than one tendon
pretensioned to a predetermined level. Therefore, loss of tension force in the tendons due to theelastic deformation of the concrete must be taken into consideration. The loss in the averagetensile stress in the prestressing tendons may be calculated from Eq. (C15.3.1).
In construction carried out by the post-tensioning method, usually, tendons are tensioned one by
one or group by group. Consequently, the concrete undergoes elastic deformation each time atendon or tendon group is tensioned, and the tension force in the previously tensioned tendons
gradually decreases under the influence of the tendons tensioned subsequently. In such cases, the253

Standard Specifications for Concrete Structures-2007, Design

loss in the average tensile stress in the internal tendons and unbonded prestressing tendons may be
calculated from Eq. (C15.3.2). The amount of decrease in the average tension in the externaltendons may be calculated from Eq. (C15.3.3) by assuming that it does not vary among anchoring
points.
(i) For prestressing tendon in the pretensioning method
 p  n p ' cpg(C15.3.1)(ii) For internal tendon and unbonded prestressing tendon
1
N 1
n p ' cpg
2N p 

where,  p :np :(C15.3.2)

prestress loss in prestressing tendon
Young's modulus ratio of prestressing tendon to concrete n p  E p Ec

 'cpg : concrete compressive stress due to prestressing at the centroid of prestressing
tendons:N

number of tensioning times (number of groups of the tendon)(iii) For external tendon

Pp 

1
l N  1
E p Ap2
l N(C15.3.3)

where， Pp ：loss of prestressing force in external tendon
E p ：Young's modulus of external tendon

Ap ：cross-sectional area of external tendon
l ：amount of movement of concrete member between anchoring points due toinitial tension Pil：distance between anchoring points

N ：number of tensioning times (number of groups of the tendon)

However, if the anchoring point of the external tendon is located at or near the centroid andlongitudinal deformation is not restrained, the strain between anchoring points, l l , in Eq.
(C15.3.3) may be calculated from Eq. (C15.3.4).
l
P

l
Ec Ac

where,(C15.3.4)

P：prestressing force introduced into external tendon

Ec：Young's modulus of concrete

254

Chapter 15

AcPrestressed Concrete Structure：total cross-sectional area of concreteII) Influence of friction between tendon and sheath
In the post-tensioning method, as the distance from the tensioning end (jack location) increases
mainly, tensile force in the tendon decreases because of the friction between the tendon and thesheath and the friction between the external tendon and the protection tubes at the deviators. In
general, factors causing such decreases in tension can be classified into those related to changes in
the angle of the centroidal line and those related to tendon length. Therefore, the tensile force inthe tendon in the design cross section may be calculated from Eq. (C15.3.5) in view of these
influences. In the external tendon method, all external cables other than those in the anchorage
zones or the deviator zones are placed outside the concrete member. Therefore, the influence offriction in this section does not need to be taken into consideration.
Px  Pi  e  (   x )(C15.3.5)

where, Px : tension force in tendon in design cross sectionPi: tension force in tendon at jack location: friction coefficient per radian of angle change: angular change (radian) (See Fig. C15.3.1).

: friction coefficient of unit lengthx: length of tendon from tensioning end to design cross section

Pi
α3

α4
α２

α１

α5

Px

α = ∑n１αi = α1+ α2+ α3+ α4+ α5+・・・・・・・・・ +αnFig. C15.3.1 Angular change of centroidal line of tendon

Usually, the values of  and  need to be determined experimentally because they varydepending on such factors as the state of the inside surface of the sheath and the type of prestressing
tendon. However, if steel sheaths are used, the values shown in Table C15.3.1 may be used. For
the friction coefficient in the anchorage and deviator zones of external tendon, the values shown in
Table C15.3.2 may be used according to the type of protection tube material. However, if a special
type of sheath or spacer is used to reduce friction, or if prestressing tendon with special surface
processing with resin, coating film, etc. is used, or if friction is cut off by impacting the prestressing
tendon, the friction coefficient may be determined separately by referring to relevant data such as
conventional experiment results.

255

Standard Specifications for Concrete Structures-2007, Design

Table C15.3.1 Friction coefficient (steel sheath)Type
Prestressing tendon,prestressing strand
Prestressing bar (unit: l/m)

0.30

0.004

0.30

0.003

Table C15.3.2 Friction coefficient of prestressing steel and protection tube(prestressing tendon, prestressing strand)
Steel pipe
Polyethylene pipe

0.30
0.15

 (unit: l/m)
0.004
0.004

In the internal tendon method, if the length of tendon is about 40 m or less and the angularchange of the tendon is about 30 degrees or less, Eq. (C15.3.6) may be used as an approximation:
Px  Pi (1    x)(C15.3.6)

It is also possible to calculate Px by replacing the term  to allow for the influence of tendon
length in Eq. (C15.3.6) with the additional angular change per meter of tendon length. In this case, may be calculated from Eq. (C15.3.7).

  

(C15.3.7)

where, Δα : additional angle change per meter of a length of the tendon (radian).
III) Influence of set during anchoring of tendon
The term "set" means the movement of the tendon drawn to the anchorage with anchoring
wedges. If set occurs when a tendon is anchored, the loss of the tension force in the tendon mustbe allowed for. Because anchoring wedges cause a relatively large setting length, it is necessary tocheck on the setting length in advance, and to examine the loss of tension force in the tendon andthe zone of influence of the set by assuming a somewhat larger-than-expected length of set to be on
the safe side. Since the setting length varies among anchorage elements, it is necessary to
determine the setting length for each anchoring device by referring to literature such as the
Recommendations for Design and Construction of Prestressed Concrete Structures (1991).
If there is no friction between the tendon and the sheath when internal tendons or unbonded
prestressing tendons are used, the loss of tension force is constant over the length of the tendon asshown in Fig. C15.3.2 (a). In this case, the area enclosed by a', b', o', o'', b'' and a'' can becalculated as P × l , and the loss of tension force in the tendon due to set can be calculated directlyfrom Eq. (C15.3.8):
P l
E p Aplwhere, P(C15.3.8): loss of tension force due to set of tendon

l: setting lengthl: length of tendon

E p : Young's modulus of tendon
256Chapter 15

Prestressed Concrete Structure

Ap : cross section area of prestressing tendon

If there is friction between the tendon and the sheath, the loss of tension force in the tendon may
be determined by the graphical method by following the Steps 1) to 4) described below assumingthat the friction during the tensioning operation and the friction that occurs when the tendon isrelaxed because of set are the same.
1)

Determine from Eq. (C15.3.5) the distribution a', b' and o' of the tension in the tendon
immediately before anchoring when assuming that the initial tension force at the tensioning
end is Pi , taking into account the friction between the tendon and the sheath.

2)

Assume the location c under the influence of set and find a'', b'' and c that are symmetricwith a', b' and c with respect to the horizontal axis c-e.

3)

Calculate the area enclosed by a', b', c, b'' and a'', find the location c at which
Aep  E p Ap l (see Eq. (C15.3.9)) holds and determine the distribution of a'', b'', c and o'of the tension force in the tendon immediately after anchoring.

4)

l 

Find the tension in the tendon in an arbitrary design cross section from the distribution a'',b'', c and o''. The tension force in the tendon at the tensioning end is Pi immediately
after anchoring.
Aep(C15.3.9)

Ap E pwhere, Aep ：area of the shaded region shown in Fig. C15.3.2 (b) (= area enclosed by a', b', c, b''
and a'')

CL
b

o

a”

b’

Aep

b”

b

緊張材の配置Tendonarrangement

Aep
o’
o”

緊張材引張力Distribution of tensionの分布
force in tendon

緊張材の配置Tendonarrangement

b’
c

e

x：緊張材の長さ
Tendon length（a）In the case where there is no friction

o

a’

b”

Pt

Pi

Pt

ΔP

a’

CL

a

Pi

a

o’

緊張材引張力Distributionof tension
の分布
force
in tendona”
x：緊張材の長さ
Tendon length（b）In the case where there is friction

between tendon and sheath

between tendon and sheathFig. C15.3.2 Distribution of tension force in internal tendon and unbonded prestressing
tendon after the occurrence of set

The loss of tension force due to set that occurs when an external tendon is anchored may be
calculated by a method similar to the method used for internal tendons. However, since the freepart of the tendon is not affected by friction, the tension force in that section decreases uniformly
because of set. In general, the length of the section in which an external tendon is in contact withdeviators (Section B1–B2 in Fig. C15.3.3) is short. Therefore, the influence of set may reach the
halfway point of an external tendon (Location c) as shown in Fig. C15.3.3 (b) if angular change of257

Standard Specifications for Concrete Structures-2007, Design

the centroidal line of the external cable is small or if the setting length is large. When considering
the influence of set in connection with an external tendon, the tension force in the tendon in anarbitrary design cross section can be determined by calculating the area enclosed by a', b1', c, b1''
and a'' or the area enclosed by a', b1', b2', o', o'', b2'', b1'' and a'' on the basis of Eq. (C15.3.9) (see Fig.
C15.3.3), paying careful attention to the considerations mentioned aboveaCL
b 1 b2

Aepb 1 b2Tendonarrangement外ケーブルの
配置

b 1’
b 1”

b2’

x： 緊張材の長さ
Tendon length（a）In the case where c is located

b 1’

e
b 1”

a”

Pi

a”

Aep

b2’
b2”

o Tendonarrangement外ケーブルの配置o’

外ケーブル引張力cの分布o”
Distribution of tension
force in tendonPteo’ 外ケーブル引張力の分布of tension
Distribution
force in tendon

ΔP

a’
c

Pt

Pi

ΔP

a’

o

CL

a

x： 緊張材の長さ
Tendon length（b）In the case where c is not locatedin section b1– b2

in section b1– b2Fig. C15.3.3 Distribution of tension force in external tendon after the occurrence of set

IV) Other influences
Other influences such as the deformation (plastic deformation) of precast concrete block joints
should be taken into consideration.
V) Influence of relaxation of prestressing tendon
The prestress loss in prestressing tendon due to relaxation may be calculated from Eq.
(C15.3.10):
 pr   pt(C15.3.10)

where,  pr : prestress loss in prestressing tendon due to relaxation of prestressing steel: apparent relaxation ratio of prestressing steel (See Table 5.3.1.)

 pr: tensile stress of prestressing steel just after prestressing

If the external tendon method is used, usually the loss of prestressing force due to the creep andshrinkage of concrete is smaller than in the internal tendon method. In such cases, the apparent
relaxation ratio tends to become greater than the values shown in Table 5.3.1. For this reason, if
the initial tensile stress is between 50% and 75% of the tensile strength, the apparent relaxation ratio
γ of an external tendon used to calculate the loss of prestressing force should be calculated from Eq.
(C15.3.11) after determining the net relaxation ratio γ0 from Table C5.3.2 and Fig. C5.3.1.

   0 1  2Pt  Pe  Pt 
where,(E15.3.11)

 : apparent relaxation ratio of external tendon

258

Chapter 15

0Prestressed Concrete Structure: net relaxation ratio of prestressing steel

Pt  Pe : loss of prestressing force due to creep and shrinkagePt: tension force in external tendon immediately after prestressingPe: prestressing force in external tendon determined to allow for the influence of
creep and shrinkage

6) Creep of concrete, 7) Shrinkage of concrete
As a general rule, the loss of tensile stress in a tendon due to the creep and shrinkage of concrete
is to be determined through an appropriate creep analysis taking the influence of reinforcement into
consideration. The loss of tension force in an external tendon may be calculated from Eq.
(C15.3.12):
Pe  Pt n p ρ p  φ  Pt  E p  A p  ε cs

(C15.3.12)

1  n p ρ p 1  χφ 

where, Pe ：prestressing force in external tendon determined taking into account the
influence of creep and shrinkage

Pt ： prestressing force immediately after introducing into external tendon
np：

Young's modulus ratio of prestressing tendon to concrete; n p  E p E c

 p ： cross-sectional area ratio of tendon;  p  Ap Ac c：creep coefficient of concrete：

aging factor; usually,   0.8

 cs ： shrinkage strain of concrete
E p ： Young's modulus of external tendon
E c ： Young's modulus of concrete

Ap ： cross-sectional area of external tendon
Ac ： total cross-section area of concrete
For the purpose of deriving this equation, it is assumed that the tension changes in the externalcable due to flexural strain in the cross section can be ignored because Navier's hypothesis cannot
be applied to external tendons. It is also assumed that the strain changes in external tendon is thesum of the shrinkage strain  cs in the concrete and the longitudinal creep strain in the whole crosssection of concrete due to prestressing force. In this case, the strain changes in concrete and thestrain changes in external tendon can be expressed by Eq. (C15.3.13) and Eq. (C15.3.14),
respectively, and Eq. (C15.3.12) is an equation derived by developing these equations.

259

Standard Specifications for Concrete Structures-2007, DesignΔε c t    Pt
P  Pe1  χφ  ε cs
φ t
E c AcE c Ac(C15.3.13)

Pt  Pe  c t   
E p Ap(C15.3.14)

 p t    

where,  c t    ： strain change in concrete since immediately after introducing until t   p t    ：strain change in external tendon since immediately after introducing untilt

Equation (C15.3.12) allows only for the influence of the creep and shrinkage of concrete on theprestressing force in external tendons. If both internal and external tendons are used, it is necessary
to calculate the prestressing force in the external tendons by an appropriate method, taking into
account the influence of the creep of the concrete due to the prestressing force in the internaltendons.
If the loss of the prestressing force in an external tendon due to the creep and shrinkage ofconcrete is to be calculated exactly, it is necessary to determine the strain change at the centroid of
the external tendon due to the creep and shrinkage of the concrete member over the entire length ofthe external tendon and calculate, from the average strain thus determined, the loss of the tension
force in the external tendon. This requires very complex and laborious calculation, but recently it
has become possible to model a structure or an external tendon according to the configuration of thestructure, support conditions, etc., and calculate the prestressing force in the external tendon
through structural analysis. The three methods shown in Fig. C15.3.4 are widely used, and they
are briefly described below. Because these methods can also be used for other applications such as
the calculation of design sectional forces, those methods should be used rationally according to thelimit states considered at the design stage.
(i) In the member evaluation method, an external tendon is modeled as a chord member, and theinitial tension force is given as an equivalent axial strain. Because the deformation of the chordmember follows the deformation of the girder, the influence of the creep and shrinkage of concreteand the influence of loads can be analyzed directly as the tension changes in the chord member.
(ii) In the external force evaluation method, prestressing force is let to act as a concentrated
load or a distributed load at the anchoring locations and the deviator locations of external tendon.
The action point of each load and the action direction are clearly indicated, and the prestressing
force can be clearly evaluated as an external force in the free part of the tendon.
(iii) In the internal force evaluation method, prestressing force is let to act in the analysis model
as internal forces (axial force N , eccentric moment M ), and statically indeterminate forces due tothe prestressing force are calculated. This is based on the conventional internal tendon method,and prestressing force (internal force) due to the external tendon and negative shear force need to beconsidered separately.
Each type of analysis model and the external tendon prestressing force calculation approaches
described in this section are summarized in Table C15.3.3.

260

Chapter 15
Anchoring location

定着位置

Prestressed Concrete Structure
Deviator member

偏向部材Centroid of cross-section

断面図心

外ケーブル
External
tendonGirder member
はり部材
ダミー部材
Dummy member

Chord member (External tendon)
弦部材（外ケーブル）(1) Member evaluation method①部材評価法Prestressing force
プレストレス力

Prestressing force
プレストレス力

Force at deviatorlocation
偏向力

Force
at deviator location
偏向力(2) External②外力評価法
force evaluation method
Axial
軸力forceNN

Eccentric
moment
偏心ﾓｰﾒﾝﾄMM(3) Internal ③内力評価法
force evaluation method

Fig. C15.3.4

Modeling of member with external tendon(2): In the case of a statically indeterminate structure, it is possible to prevent the occurrence ofstatically indeterminate force due to prestressing force by using appropriate prestressing steel
arrangements. However, if this method is used, the deformation of the member due to prestressing
force is restrained so that statically indeterminate force occurs. Therefore, when considering
stresses in materials, this statically indeterminate force must be taken into consideration. Staticallyindeterminate force due to prestressing force may be greatly affected by a cross-sectional change if
the member has a non-uniform cross section. This needs to be kept in mind.
If prestressing force is given at different times or if the degree of redundancy of the structurechanges during the prestressing period, statically indeterminate force changes with the progress ofcreep of concrete. In such cases, the influence of such changes must be taken into consideration.
To be more specific, for example, if a continuous girder is constructed by connecting together anumber of simple girders erected earlier or if a continuous girder is constructed by joining the ends
of cantilever girders erected earlier, the degree of redundancy changes during the construction of thestructure. If the structural system changes during construction in this way, the creep deformationof the structural system before the change is restrained so that new statically indeterminate forces
may occur or may changes with the progress of creep. These need to be taken into considerationin the verification process as the influence of the creep and shrinkage of concrete as indicated in
Chapter 6. In the case of a prestressed concrete structure, it is also necessary to take the influenceof prestressing force into consideration.

261

Standard Specifications for Concrete Structures-2007, Design

Table C15.3.3 Analysis models and external tendon prestressing force calculation approaches
in different evaluation methods(1) Member evaluation
method(2) External force evaluation
method(3) Internal force evaluation
methodEq. C15.3.3, Eq. C15.3.4
Eq. C15.3.5
Eq. C15.3.9

Ditto
Ditto
Ditto

Ditto
Ditto
Ditto

This can be allowed for asaxial strain (thermal load),but the relaxation ratio is
calculated from Eq.C15.3.11.

Eq. C15.3.10, Eq. C15.3.11

Ditto2) Creep of concrete
3) Shrinkage of concrete

The influence of the creep
and shrinkage of concrete
can be analyzed directly as
tension changes in a chordmember.

Eq. C15.3.12

Ditto4) Restraint by reinforcement

This can be allowed for byusing a model and analytical
tools capable of analyzing
the influence ofreinforcement.
Expressed as axial strain(thermal load)

To be considered separately

Ditto

Expressed as concentrated
load or distributed load

Prestressing forces (N, M)
are simply added together.
Statically indeterminate
force is determined byletting prestressing force act
as internal force.

Automatic calculation can bedone by letting theprestressing force calculatedin (1) act in accordance with
(3).

The prestressing forces
calculated in (1) and (2) are
let to act in accordance with
(3).

(1) Loss of prestressing force
immediately after prestressing1) Elastic deformation of concrete
2) Influence of friction
3) Set during anchoring(2) Loss of prestressing force overtime1) Relaxation of external tendon(3) How to express prestressing
force in analysis model(4) Calculating method ofprestressing force in design
cross section

15.4
15.4.1

Ditto

Calculation of Response Values
General(1) Response values used for the performance verification of a prestressed concrete
structure shall be calculated in accordance with Chapter 7 after classifying the structure
either as a PC structure or a PRC structure.
(2) Design response values used for verification related to serviceability or verification
related to fatigue failure may be calculated by the methods describing in this section byusing design sectional forces, etc.

[Commentary] This section describes methods for calculating design stresses for materials anddesign crack width from design sectional forces among the response values used for verification
related to the serviceability and fatigue failure of prestressed concrete structures. If sectional
forces are calculated from the results of analyses such as finite element analyses using theconstitutive equations for the stress–strain relationship for materials when calculating design crack
width, Section 7.4.2 must be followed.

Other response values such as the displacement and deformation of members must be calculated
in accordance with Section 7.4.5, etc., taking the influence of prestress into consideration.
262

Chapter 15

15.4.2Prestressed Concrete Structure

Design stresses for materials due to bending moment and axial force(1) Design stresses for concrete and steel due to bending moment and axial force may
be calculated on the basis of the assumptions listed below. Stress in concrete and thetendon under variable load should be considered as acting in addition to those calculatedin (2).
(i) Fiber strain is proportional to the distance from the neutral axis of the member crosssection.
(ii) Concrete and reinforcing bar are generally treated as elastic solid.
(iii) In the case of PC structure, the gross cross section of concrete is effective.
(iv) In the case of PRC structure, tensile stress in concrete may generally be neglected.
(v) Young’s modulus of concrete and reinforcing bar is calculated in accordance with
Section 5.2.5 and 5.3.4, respectively.
(vi) In the case of tendons bonded with concrete, any increase in strain as the same asthat for concrete at the same location.
(vii) Area of sheath in the longitudinal direction shall not be considered to be effective
cross section.
(viii) The modulus of the composite section made of the prestressing tendon andconcrete shall be calculated considering the ratio of Young's modulus of the prestressing
tendon to concrete.
(2) Stresses in concrete and the tendon under permanent load shall be calculated
considering the effect of the tendon's relaxation, creep and shrinkage of concrete, and therestraint due to reinforcing bars.

[Commentary] (1): As in the conventional method, design stresses for the materials of a PC
structure due to bending moment and axial force may be calculated by a method based on the elastic
theory assuming a fully effective cross section of concrete. Cross-sectional parameters after
prestressing tendons and concrete are integrated are determined taking into account Young's
modulus ratio of the prestressing tendons and the concrete as mentioned in Item (viii) of this section.
In general, the influence of reinforcement does not need to be taken into consideration because theamount of reinforcement is relatively small.

For PRC structures, it is recommended that a limit state in which cracking of concrete does notoccur because of permanent loads be set. In this case, the stress due to permanent loads andprestress calculated by assuming a fully effective cross section of concrete and the stress due tovariable loads calculated for a cross section with flexural cracks cannot be added together.
Therefore, it is necessary to calculate design stresses for the materials of a PRC structure after theoccurrence of flexural cracking by assuming a state in which the cross section with flexural cracks
is being acted upon simultaneously by prestress, permanent loads and variable loads. In general,the calculation method described below may be used.
In a PRC structure before the occurrence of flexural cracking, usually, tensile stress is occurringin the prestressing tendons and compressive stress is occurring in the reinforcement. Therefore,
design stresses for the materials of a PRC structure after the occurrence of cracking may be
263

Standard Specifications for Concrete Structures-2007, Design

calculated as for a reinforced concrete structure reinforced with prestressing tendons and reinforcing
bars, assuming that the axial force in each tendon in the state in which the concrete stress at eachtendon location is zero acts externally as an eccentric axial force. This calculation may be done by
the method described in Items 1) to 4) below.
In this method, in view of the basic assumption that cracking does not occur because ofpermanent loads, axial force in each tendon in the state in which concrete stress is zero is calculated,assuming that the state in which permanent loads are acting is the initial state. Because it may be
assumed that the prestress acting in the cross section remains constant, calculation can be done
regardless of the action of loads. Therefore, this method is practical and easy to use.
1) How to find the neutral axis
The location of the neutral axis is determined by using Eq. (C15.4.1):
M  N d p  d N   P1d s  d p   P1 d p  d s N  P1  P0  P1

where, x：d s , d p , d s ：I cx  n s  I sx  n p  I px  n s  I sx
Qcx  n s  Q sx  n p  Q px  n s  Q sx d p  x (C15.4.1)

distance from compression edge to the neutral axis
distance from compression edge to the centroid of compression bar, the centroidof prestressing tendon and the centroid of tension bar

M：acting bending momentN：

acting axial forcedN：

distance from compression edge to the point at which axial load acts

P0

： prestressing force in tendon in the state in which concrete stress at the centroid of
the prestressing tendon is zeroP1, P1 ：compression bar reaction and tension bar reaction in the state in which concrete
stress is zero at the centroid of compression bar and the centroid of tension bar

Qcx , I cx ： geometrical moment of area and geometrical moment of inertia of concrete in thecompression zone with respect to the neutral axis
Qsx , I sx ：geometrical moment of area and geometrical moment of inertia of compression
bar with respect to the neutral axis

Q px , I px ：geometrical moment of area and geometrical moment of inertia of prestressing
tendon with respect to the neutral axis

Qsx , I sx ：geometrical moment of area and geometrical moment of inertia of tension bar
with respect to the neutral axis

ns：

Young's modulus ratio of reinforcing bar to concretenp：

Young's modulus ratio of prestressing tendon to concretens  Es Ec
n p  E p Ec

Reaction forces from the compression bar, prestressing tendon and the tension bar are calculated
from Eq. (C15.4.2). However, as in the bending stress formula for ordinary reinforced concrete
264

Chapter 15

Prestressed Concrete Structure

structures in Eq. (C15.4.1),  s0 is regarded as positive if the stress in the compression bar iscompressive, and  p 0 and  s 0 are regarded as positive if the stresses in the prestressing tendon
and the tension bar, respectively, are tensile. In such cases, as shown in Fig. C15.4.1, the reaction
force P1 of the compression bar acts as an eccentric tensile axial force, and the reaction forces P0
and P1 of the prestressing tendon and the tension bar, respectively, act as eccentric compressive
axial forces.

Fig. C15.4.1 Flexural stress distribution in a PRC structure  ns   cds 
P1  As   s0  As  scs
P0  A p   p 0  A p  pd  n p   cdp (C15.4.2)

P1  As   s 0  As  scs  ns   cds where, As , Ap , As： cross-sectional area of compression bar, prestressing tendon and tension bar s0 , p 0 , s 0：

stresses in compression bar, prestressing tendon and tension bar

under permanent loads after all prestress losses end
 ,  scs ： stress variations in compression bar and tension bar by the creep
 scsand shrinkage of concrete (see Eq. (C15.4.8) and Eq. (C15.4.9)).

 pd ：

prestressing tendon stress under permanent loads calculated taking into
consideration the influence of the relaxation of prestressing tendon and thecreep and shrinkage of concrete, and restraint by reinforcement

 , cdp , cds ： concrete stress at the centroid of compression bar, the centroid of prestressing
 cds

tendon and the centroid of tension bar under permanent loads
Because the left-hand side of Eq. (C15.4.1) is known and the right-hand side is a function along
the neutral axis x , x can be calculated by solving a cubic equation. However, since the crosssection to be considered is usually complex in shape, solving Eq. (C15.4.1) analytically is laborious.
A method that can be used in such cases is to calculate the geometrical moment of area and thegeometrical moment of inertia by assuming x and repeat calculations until the right-hand side ofthe equation is equal to the left-hand side.
265

Standard Specifications for Concrete Structures-2007, Design

2) Concrete stress
Concrete stress  c is calculated by substituting x in Eq. (C15.4.3).

c 

N  P1  P0  P1   x(C15.4.3)

Qcx  ns  Qsx  n p  Q px  ns  Qsx

3) Stress variation in reinforcement
Stress variation in the compression bar,  s , and stress variation in the tension bar,  s , fromthe state in which concrete stress at the centroid of the reinforcement is zero are calculated from Eq.
(C15.4.4) and Eq. (C15.4.5), respectively.
 s  n s   c x  d sx

(C15.4.4)

 s  n s   c 

ds  xx(C15.4.5)

4) Tensile stress variation in prestressing tendon
Tensile stress variation in prestressing tendon,  p , from the state in which concrete stress at
the centroid of the reinforcement is zero is calculated from Eq. (C15.4.6):
 p  n p   c 

dp  x(C15.4.6)x

The calculation of the increase in strain in unbonded prestressing steels or external tendons must
be considered separately by using, for example, the member evaluation method shown in Table
C15.3.3 because Bernoulli-Navier's hypothesis cannot be applied. If these methods are not used,concrete stress may be calculated by regarding as a PC structure or PRC structure acted upon by
eccentric axial force due to prestressing force, ignoring the increase in stress in the unbonded
prestressing steels and external tendons.
(2): If internal tendons are used, in order to calculate the stresses in the concrete and steel of a
PC structure or PRC structure due to permanent loads, the decrease over time in the tensile stress inthe prestressing tendons may be calculated by either of the methods described in Items 1) and 2)
below.
If unbonded prestressing steel or external tendons are used, in theory, it is possible to calculate
the strain variation at the centroid of the tendons due to the deformation of the concrete member andthen calculate the decrease over time in the tensile stress in the tendons from the average strain thus
determined. If all tendons are used as external tendons, the decrease in the tensile stress in theexternal tendons may be calculated in accordance with Section 15.3. However, if unbonded
prestressing tendons or external tendons are used or if these are used in conjunction with internaltendons, in general the decrease in the tensile stress in the tendons may be calculated by using themethods described in this section for the three reasons listed below:(i) Calculation by the theoretical method mentioned above would be very complex and laborious.
(ii) Under normal service conditions, the deformation of a member is very small. Therefore, theinfluence of strain variations at the tendon location is thought to be small.
(iii) The decrease in the tensile stress in external tendons due to the creep and shrinkage of concrete266

Chapter 15

Prestressed Concrete Structureis smaller than when internal tendons are used.
1) PC structure
For PC structure, too, it is a general rule to take the influence of reinforcement restraint into
consideration, but in general the influence of reinforcement restrain does not need to be considered
because only a small amount of reinforcing steel is used in a PC structure. In this case, thedecrease in the tensile stress in the prestressing steel may be calculated from Eq. (C15.4.7).
The standard method of calculation is to use the creep coefficient of plain concrete andshrinkage strain, but a creep coefficient and shrinkage strain determined taking into consideration
the influence of the relatively small amount of longitudinal reinforcement in the concrete may be
used. This is based on the empirical knowledge gained by using the verification method
combining these design values and Eq. (C15.4.7). For example, if a considerable amount of
empirical knowledge such as the knowledge about PC structures in prestressed concrete bridges isavailable, a creep coefficient and shrinkage strain determined appropriately according to such
empirical knowledge may be used.
 pcs 

n p   ( ' cpt  ' cdp )  E p   ' cs

(C15.4.7)

 ' cpt    1  1 n p  pt  2 

where,  pcs : loss of stress in the prestressing tendon due to creep and shrinkage of concrete: creep coefficient of concrete 'cs: shrinkage strain of concretenp: ratio of Young's modulus of prestressing tendon to concrete pt: tensile stress of prestressing tendon just after prestressing

 'cpt :n p  E p Ec

compressive stress of concrete at the location of prestressing tendon by
prestressing force just after prestressing

 ' cdp :compressive stress of concrete at the location of prestressing tendon bypermanent load2) PRC structure
For PRC structure, the effect of restraint due to reinforcing bars should, in principle, be
considered. If a limit state in which crack does not occur at tension edge of the concrete underpermanent loads is set, in general the decrease in the tensile stress in the prestressing steel and thestress variation in the tension bar and the compression bar may be calculated from Eq. (C15.4.8) byusing the creep coefficient and shrinkage strain of plain concrete. When the effect of shrinkage
before prestressing cannot be neglected, variation of stress in tendon due to creep until prestressing
may be calculated using Eq. (C15.4.9). In such cases, variation of stress in the tendon may be
calculated by adding the value calculated using Eq. (C15.4.8) and Eq. (C15.4.9).
Further, in the case of post-tensioned prestressing, the term relating to the prestressing tendon in
Eq. (C15.4.9) may be neglected.

267

Standard Specifications for Concrete Structures-2007, Design

 s 'sk   psk n ps  23  scs , k 
1   ssk   psk n ps  13
  n s,k   ss 'k   ps 'k n ps  13 1   s 's 'k   ps 'k n ps  23  s 'cs , k 

1 k  cps , k   cds , k   E c , k  ' cs , k  k  cps ', k   cds ', k   E c , k  ' cs , k  pcs , k  n ps 13 scs , k   23 s 'cs , k (C15.4.8) scs , j cs  s 'sj   psj n ps  23   j  css, j 
1   ssj   psj n ps  13
  ns, j   s 'cs , j cs   ss ' j   ps ' j n ps  13 1   s 's ' j   ps ' j n ps  23   j  css ', j 
1pcs , kwhere,

  n  
ps

cs

13

scs , k   cs

23

s ' cs , k 13  d p  d ' / d  d ' (C15.4.9)cs

 23  d  d p / d  d ' 







 ssk  ns , k As 1 / Ac  es 2 / I c J k ssj  ns , j As 1 / Ac  es 2 / I c J j s ' sk  ns , k As ' 1 / Ac  es 'es / I c J k

 s ' sj  ns , j As ' 1 / Ac  es 'es / I c J j

 psk  ns , k Ap 1 / Ac  e p es / I c J k

 psj  ns , j Ap 1 / Ac  e p es / I c J j

 ss ' k  ns , k As 1 / Ac  es es ' / I c J k

 ss ' j  n s , j As 1 / Ac  e s e s ' / I c J j

 s ' s ' k  ns , k As ' 1 / Ac  es ' 2 / I c J k s ' s ' j  ns , j As ' 1 / Ac  es ' 2 / I c J j ps 'k  ns , k Ap 1 / Ac  e p es ' / I c J k

 ps ' j  ns , j Ap 1 / Ac  e p es ' / I c J j







and, J k  1   k / 2 , J j  1  0.8 j , age j may be the intermediate age of age k.
where,  pcs , k: loss of tensile stress of prestressing tendon by creep and shrinkage ofconcrete after prestressing

 scs, k:

stress loss of tension bar by creep and shrinkage of concrete after
prestressing

 s 'cs , k: stress loss of compression bar by creep and shrinkage of concrete after
prestressing : stress variation of prestressing tendon by creep which occurs by shrinkage

pcs , j cs

before prestressingscs , j

 : stress variation of tension bar by creep which occurs by shrinkage beforecsprestressings ' cs , j : stress variation of compression bar by creep which occurs by shrinkage
cs

before prestressing j , k: creep coefficient of concrete loaded at ages, t j , and tk

 ' cs, k: shrinkage strain of concrete after prestressing at age tk
268

Chapter 15

n s , j , n s ,kPrestressed Concrete Structure: Young's modulus ratio of tension bar and compression bar to concrete atages t j , and tk
n s , j  E s E c , j , ns , k  E s Ec , k

Ec, j , E c,k :Young's modulus of concrete at ages t j , and tk . It may be consideredthat E c , k = E cn ps: Young's modulus ratio of prestressing tendon to reinforcing bar
n ps  E p E s

 cpp , k:compressive stress of concrete at age tk at the location of prestressing
tendon by prestressing force just after prestressing, and it may be
calculated by following equation.

 cpp, k  13 cps , k   23 cps ', k cps , k:compressive stress of concrete at age tk at the location of compression
bar by prestressing force just after prestressing cdp , k:compressive stress of concrete at age tk at the location of prestressing
tendon by permanent load, and it may be calculated by following
equation.

 cdp , k   13 cds , k   23 cds ', k
 cds , k:compressive stress of concrete at age tk at the location of tension bar bypermanent load cds ', k:compressive stress of concrete at age tk at the location of compression
bar by permanent load csp , j:tensile stress of concrete at age t j at the location of prestressing tendon
by shrinkage until prestressing, and it may be calculated by following
equation.

 csp , j   13 css , j   23 css ', j css , j:tensile stress of concrete at age t j at the location of tension bar byshrinkage until prestressing

 css ', j:tensile stress of concrete at age t j at the location of compression bar byshrinkage until prestressingAp:cross-sectional area of prestressing tendonAs:cross-sectional area of tension bar

269

Standard Specifications for Concrete Structures-2007, Design

:

As '

:

ep

cross-sectional area of compression bar
distance between the centroid of member and the centroid of prestressing
tendones:

distance between the centroid of member and the centroid of tension bar

es '

:

distance between the centroid of member and the centroid of compression
bard ',dp ,d :distance from compression edge to compression bar, prestressing tendon,
and tension bar

15.4.3Ac:

total cross-sectional area of concreteIc:total cross-sectional moment of inertia of concrete

Design material stresses caused by shear force and torsional moment(1) Design diagonal tensile stress of concrete caused by shear force and torsional
moment may be calculated, assuming a fully effective cross section, from Eq. (15.4.1):
l ( x   y )2

1( x   y ) 2  4 2
2

(15.4.1)

where,  l : design diagonal tensile stress of concrete x : normal stress y : orthogonal stress to  x
 : shear stress caused by shear force and torsional moment(2) Design stress of the shear reinforcement and design stress of the torsion
reinforcement of a PRC structure may be calculated in accordance with Section 7.4.3 (2)and (3), respectively.

[Commentary] (1) Diagonal tensile stress of concrete is calculated by using the normal stress andshear stress calculated by assuming a fully effective cross section of concrete. If prestressing
tendons are inclined, design shear force Vd may be calculated as Vpd + Vrd  Vprd, where Vprd is thevertical component of the tensile force of the prestressing tendons, and (Vpd + Vrd) is the loading
shear force. If the vertical component of the tensile force of the prestressing tendons is greaterthan the shear loading force after introducing the prestress, it should be take care of the direction ofshear force might be reversed.

In the design of a concrete structure, it is recommended to practice to draw up a structural planso that the influence of torsion can be ignored. If a structural system cannot be designed without
taking torsional stiffness into consideration, shear stress by the torsional moment must be taken into
account.
Shear stress by shear force and torsional moment may be calculated, according to the elasticity
theory, by the methods described below.
270Chapter 15

Prestressed Concrete Structure1) Shear stress caused by shear force may be calculated from Eq. (C15.4.10):

Vd  Qbw  I(C15.4.10)

where,  : shear stress caused by shear force
Vd : design shear force (= Vpd + Vrd  Vprd)
Q : first moment of area with respect to the neutral axis of the cross section outside theshear stress calculation location
bw : width of the main section of the member
I : second moment of area with respect to the neutral axis of the cross section2) Shear stress caused by torsional moment may be calculated as described in Items (a) to (c) below.
(a) In the case of a rectangular cross section (see Fig. C15.4.2), shear stress may be calculated
from Eq. (C15.4.11) and Eq. (C15.4.12):
 t1 

M td
k1  b 2  h(C15.4.11)

 t 2  k 2   t1

(C15.4.12)

where, t1 : shear stress along longer sides

t2 : shear stress along shorter sides
Mad: design torsional moment
B: length of shorter side
h: length of longer sideh

k1, k2 : coefficients shown in Table C15.4.1

bFig. C15.4.2

Rectangular cross section

Table C15.4.1

Coefficients k1 and k2

h/b

1.0

1.2

1.5

2.0

2.5

3.0

4.0

5.0

7.0

10

20

∞

k1

0.208

0.219

0.231

0.246

0.258

0.267

0.282

0.292

0.303

0.313

0.323

0.333

k2

1.000

0.930

0.859

0.795

0.766

0.753

0.745

0.743

0.742

0.742

0.742

0.742

271

Standard Specifications for Concrete Structures-2007, Design(b) In the case of a T-shaped cross section (see Fig. C15.4.3), shear stress may be calculated
from Eq. (C15.4.13):
 ti 

M td
 bi  i
It(C15.4.13)

where, ti : shear stress of each rectangular section
Mtd : design torsional moment
It : torsional second moment of area
I t  ki  ai  bi

3

ai : length of a longer side of each rectanglebi : length of a shorter side of each rectangle
ki : coefficient shown in Table C15.4.2

i : coefficient shown in Table C15.4.3

a1

b3

a3

b2

a2

b1

Fig. C15.4.3 T-shaped cross section
Table C15.4.2

Coefficient ki

ai/bi

1.0

1.2

1.5

1.75

2.0

2.5

3.0

4.0

5.0

10

ki

0.140

0.166

0.196

0.214

0.229

0.249

0.263

0.281

0.292

0.313 0.333

Table C15.4.3∞

Coefficient i

ai/bi

1.0

1.2

1.5

1.75

2.0

2.5

3.0

4.0

5.0

10

∞

i

0.675

0.759

0.848

0.895

0.930

0.968

0.985

0.997

0.999

1.0

1.0

(c) In the case of a box-shaped cross section (see Fig. C15.4.4), shear stress may be calculated
from Eq. (C15.4.14).
 ti   Si   Bi
 Si 

(C15.4.14)

M td
 bi   i
I t1
272

Chapter 15

 Bi 

Prestressed Concrete Structure

M td 2 A
I t1 C  t i

where, ti : shear stress of each rectangular section
Mtd : design torsional moment
It : torsional second moment of area
I t  I tS  I tB
I tS  ki  ai  bi

I tB 

3

4 A2
CA  bhC

h0 b0 h0 b0  
t1 t 2 t3 t 4

where, ai : length of longer side of each rectangle shown in Fig. C15.4.4 (a)bi : length of shorter side of each rectangle shown in Fig. C15.4.4 (a)ki : coefficient shown in Table C15.4.2

i : coefficient shown in Table C15.4.3

a5

a6

t4

t3

h

t1

b3

h0

b6

a3

b2
b1

b4

a1

b5

t2

a2

a4

b0
b

(a) When calculating Si and ItS(b) When calculating Bi and ItB

Fig. C15.4.4 T-shaped cross section(2) In general, only stirrups are used as shear reinforcement for prestressed concrete structures,and bent-up bars are not used. For this reason, design tensile stress of the shear reinforcement of a
PRC structure to resist shear force may be calculated from Eq. (7.4.1) and Eq. (7.4.2) shown in
Section 7.4.3.
Design tensile stress of the torsion reinforcement of a PRC structure to resist torsional moment
may be calculated from Eq. (7.4.3). If the tendons for a member subjected to torsional moment are
inclined, torsional moment Mtped by prestressing force may occur even in a statically determinate
structure. Design torsional moment Mtpd by dead loads may be calculated by subtracting the273

Standard Specifications for Concrete Structures-2007, Design

torsional moment Mtped from the torsional loading moment. When calculating design torsion
capacity Mtcd in the no-torsion-reinforcement case, the influence of prestressing force on the torsion
capacity must be allowed for nt in Eq. (9.2.26) shown in Section 9.2.3.2.

15.4.4

Design flexural crack width(1) Design flexural crack width wd in a PRC structure may be calculated in accordancewith Section 7.4.4.
(2) As a general rule, the reinforcing bars to be considered in connection with theverification related to flexural cracking shall be tension reinforcement bars closest to theconcrete surface, and reinforcement stress shall be calculated in accordance with Section
15.4.2.

[Commentary] Similarly to reinforced concrete structures, PRC structures described in thischapter are basically designed to control crack spacing by using the crack distribution effect of
deformed steel bars and control the increase in steel stress by use of prestressing. If internaltendons are used a structure of this type, deformed bars for crack width control are usually placed at
locations closer to the concrete surface than the internal tendons. If external tendons are used, rustpreventions for prestressing steel are considered. As a general rule, therefore, in the verification of
flexural crack width, only the deformed bars closest to the concrete surface need to be taken into
consideration. In Eq. (7.4.4), the coefficient k1, which allows for the influence of the surface
configuration of steel on crack width, may be assumed to be 1.0 to calculate flexural crack widthcorresponding to the increase of the stress of bars.

In Eq. (7.4.4),  'csd, which considers the creep and shrinkage and so on, needs to be determinedtaking into consideration the cross-sectional shape of the member, environmental conditions, themagnitude of stress, etc. Since the value of  'csd varies among verification items, it needs to be
calculated by using the values indicated in each chapter of this Specification. If the value for thelocation of the center of gravity of the tension reinforcement is used, 1.0 must be used for thecoefficient k3, which considers the influence of multilayer reinforcement, in Eq. (7.4.4) regardlessof the number of reinforcement layers.
However, in the case of a special type of structure, a structure in which the influence of
longitudinal restraint is great, a structure constructed by a special construction method is to be as a
PRC structure, it is recommended that not only the influence of the shrinkage and creep of concreteon crack width but also other influences such as the age at which cracking occurs be taken into
consideration to determine the value of  'csd in accordance with Section 5.2.8., and flexural crack
width should be calculated by  'csd.

15.5

Verification of Durability(1) Verification of durability should be made in accordance with Chapter 8, taking theinfluence of prestressing into consideration.
(2) As a general rule, verification of steel corrosion should be applied to reinforcing
steel and prestressing steel. Prestressing steel should be protected not to be damaged
with corrosion for the design service life.

274

Chapter 15

Prestressed Concrete Structure(3) When a PRC structure is constructed in chloride environment, as a general rule,
plastic sheaths should be used to protect the prestressing steel from corrosion. In thiscase, the verification of steel corrosion may be ignored.
(4) When external tendons and unbonded prestressing tendons are used, verificationof steel corrosion should be applied to the entire tendon system including anchorages
and deviators. However, the verification may be ignored if the durability performance forsteel corrosion has already been ensured by experimental tests.

[Commentary] (1) Similarly to the verification for a reinforced concrete structure, verificationof steel corrosion for a PRC structure considers flexural cracking, shear cracking and torsion
cracking.

In a PRC structure, the influence of shear cracking and torsion cracking on steel corrosion may
be ignored if the requirements described in Chapter 8 are satisfied. To be more specific, theinfluence of shear cracking may be ignored if the design shear force Vd (= Vpd + Vrd  Vprd) is lessthan 79% of the shear capacity Vcd calculated from Eq. (9.2.4). Similarly, the influence of torsion
cracking may be ignored if the design torsional moment Mtd is less than 70% of the design torsion
capacity of a bar member without torsion reinforcement calculated from Eq. (9.2.26). If theinfluence of shear cracking and torsion cracking on steel corrosion is taken into consideration, an
appropriate evaluation method must be used. However, more examinations may not be needed if it
is confirmed that the design tensile stresses of the shear reinforcement and torsion reinforcement
subjected to dead loads are less than the values shown in Table C8.3.1, respectively.
(2) If prestressing steel is damaged with corrosion, stress concentration occurred by decreasingof cross-sectional area of steel and hydrogen embrittlement may eventually cause the prestressing
steel to fracture, thereby degrading the structural performance considerably. Even in a normal
environment, it is recommended that resin-coated prestressing tendons, plastic sheaths, etc., capableof effectively protecting prestressing tendons from corrosion such as water, oxygen and chloride
ions be used.
As a general rule, the verification of steel corrosion must be made for the reinforcing bars andprestressing tendons closest to the concrete surface. In the verification of durability for internaltendons and unbonded prestressing tendons, design values of concrete cover of sheaths may be usedas design values cd of concrete cover.
If anchoring elements or couplers for prestressing tendons are located closer to the concretesurface than the prestressing tendons, verification needs to be made concerning their corrosion. It
is recommended that anchorage elements are appropriately protected in accordance with Section
15.9.6 in order to prevent corrosion.
(3) For the reason described in the commentary in Section 8.3.2 (2), limit value of crack width
has not been specified for prestressing tendons in chloride environment (see Table 8.3.2). When astructure is used in chloride environment, therefore, it is desirable that the concrete cracking is notoccurred in a PC structure. If a PRC structure is used, as a general rule, plastic sheaths capable ofprotecting prestressing steel from corrosion are used. If such sheaths are used, verification of
corrosion for prestressing steel may be ignored. It is also recommended, in order to enhance thecorrosion resistance of prestressing tendons, that plastic sheaths be used when a PC structure isconstructed in chloride environment. In such cases, only the reinforcing bars closest to theconcrete surface need to be taken into consideration in the verification.
If plastic sheaths are used, anchorage elements should be protected from corrosion by the grout
capping, that are comparable to sheaths in terms of shielding performance in order to enhance the275Standard Specifications for Concrete Structures-2007, Design

corrosion resistance of prestressing tendons. If steel sheaths and plastic sheaths of the same inside
diameter are used, usually the outside diameter of the plastic sheaths is greater than that of the steel
sheaths. Usually, members made with such sheaths are larger. The influence of such size
increases needs to be evaluated.
(4) This chapter assumes the use of permanently rust- and corrosion-proof tendons as externaltendons. It is necessary to conduct verification of steel corrosion for the entire tendon system
including anchorage elements and deviators and use tendons with corrosion resistance for thedesign service life.
A typical rust-proofing structure for external tendons consists of three layers, namely, a
protective sheath, filler material and prestressing tendons. Examples of external tendon
rust-proofing structures are shown in Table C15.5.1. An appropriate combination of elements
should be selected in view of the environmental conditions, etc. Case 7, in which resin-coatedprestressing tendons are used without protective sheathing, should be used only in a low-humidity
and mild environment.

Table C15.5.1

Examples of rust-proof structures for external tendons

Case

Protective sheathing

1

Polyethylene sheath2

Transparent sheath3
4
5

Filler materialType of prestressing
steel

Cement grout

Ordinary
prestressing steel

GreasePolyethylene sheath

None
Cement grout

6
7

Galvanizedprestressing steel

None
None

Resin-coatedprestressing steel*None* Type of resin-coated steel
1) Epoxy resin coated steel2) Polyethylene resin coated steel3) Epoxy resin and polyethylene resin coated prestressing steel

Unbonded prestressing tendons can be largely classified, according to the type of rust-proof
structure, into two types: coated unbonded prestressing tendons and sheathed unbonded prestressing
tendons. A tendon of the former type consists of a prestressing steel tendon coated with asphalt,
polymer or other rust-preventive material and covered with protective taping. A tendon of thelatter type consists of a prestressing steel tendon encased in polyethylene or other sheathing andgrease or other material filling the space between the steel and the sheath. Most of these tendons
are manufactured at factories. Recently, unbonded prestressing tendons using epoxy resin coatedsteel has been developed in order to enhance the rust-proof performance. Another type of recently
developed unbonded prestressing tendon is a pregrouted prestressing tendon, which uses slower
setting resin. This cold-setting resin remains unbonded until prestress is introduced, and bonding276

Chapter 15

Prestressed Concrete Structureis achieved as the resin hardens over time.
15.6
15.6.1

Verification of Safety
General(1) Verification of safety shall be done in accordance with Chapter 9.
(2) Verification of cross-sectional failure shall be made in accordance with Section 9.2,
taking into consideration the influence of prestress. With respect to the design flexuralstrength Mud of a member subjected to bending moment or to bending moment and axial
force, the flexural strength Mu may be calculated by the method described in this section.
(3) Verification of fatigue failure shall be made in accordance with Section 9.3, andresponse stresses in materials shall be calculated in accordance with Section 15.4.2,
taking the influence of prestress into account. Verification for steel in PC structures may
be ignored.

[Commentary] (2) In the verification of safety for flexural moment, PC structure is similar to RC
structure's behavior if the steel yielding occurs before crush of concrete cover. The verification for
PC structure may be done as reinforcing bars.

Plane conservation, however, can be applied neither to unbonded prestressing tendons nor
nearly-unbonded tendons such as external tendons. Consequently, the amount of increase in thetensile stress in a tendon at the failure is less than in an internal tendon. In the external tendon, theeffective height of an external tendon in a non-deviated free portion of the tendon becomes
relatively small as the deformation of the member increases. Flexural strength in such cases isusually less than in cases that effective height does not change. A member with internal tendonsand a member with unbonded prestressing tendons or external tendons require different evaluation
methods of flexural strength. Flexural strength of those members, therefore, should be calculatedby the each methods described in this section.
(3) In the case of that a concrete crack is not allowed in the verification of usability of PC
structures, the steel of prestressing stress is small and the verification of steel stress for fatigue
failure may be ignored.
Stress variation of unbonded prestressing tendons and external tendons is less than that ofinternal prestressing tendons. However, the stress may effect on the entire of prestressing tendons
through the anchor of tendons. The damage of local portion in tendons depends on the fatigue
strength. Therefore, it is necessary to care the fatigue failure of the unbonded tendons and externaltendon. Especially, it is recommended to use the structure of anchor and deviator, which are
ensured to have enough fatigue strength.
Also, it is necessary to care the resonant of external tendons with the member, vehicle vibrations,and mechanical equipments. Fatigue failure may occur in these cases. It is recommended toplace the vibration control equipment and to arrange the external tendons at the small spacing.
Fretting fatigue may occur at the deviator when the external tendons are used. The externaltendon has come in contact mutually, and the fatigue damage accumulated in the tendons by frictionof each other. It is recommended to care the corner breaking of prestressing tendons, and to fill the
grout cement in the sheath to restrain the displacement, and to protect the prestressing tendons withresin coating, and to prevent the tendons from coming in contact mutually with the spacer, etc.

277

Standard Specifications for Concrete Structures-2007, Design

15.6.2

Design flexural strength of PC members with internal tendons

The design flexural strength of a PC member with internal tendons subjected to
flexural moment and axial force may be calculated on the basis of the following
assumptions:(i) Strain is proportional to the distance from the neutral axis of the cross section.
(ii) Tensile stress of concrete may be ignored.
(iii) As a general rule, the stress-strain curve of concrete is shown in Fig. 5.2.1 in
Section 5.2.3.
(iv) The stress-strain curve for steel must be as shown in Fig. 5.3.1 in Section 5.3.3.

[Commentary] The flexural strength Mu of a member with bonded internal tendons may be
calculated in accordance with Fig. C15.6.1 by the methods described in Items 1) to 4) below if theneutral axis is located in the cross section. In cases where there is lateral reinforcement, its
flexural strength should be evaluated by other method.

Strain distribution
ひずみ分布
ε’cu

A’s
d’s

ds

dp

Neutral
axis
中立軸

b(y)

Stress応力分布
distribution
σc’(y)

Δε’s

x

T’st

β’x

C’
y

dN

M
N

図心軸
Centroid
axis
Ap

Δεp

εpe

Tp

Δεs
Tst
As

Fig. C15.6.1

Calculating the flexural strength Mu of a PC member with an internal tendon

1) Assume the location of the neutral axis and determine the strain distribution in the crosssection on the basis of the assumption in Item (i) above by regarding the concrete strain at thecompressive concrete surface as the ultimate compressive strain  'cu.
2) According to the strain distribution in the cross section, the compressive force resultant C ' ofthe concrete is calculated from Eq. (15.6.1) on the basis of the assumption in Item (iii). Similarly,
 's, p + p (p : strain caused by prestressing of internal tendon) and s is calculated on the basisof the assumption in Item (iv). The compressive force resultant T 'st of the reinforcement, thetensile force resultant Tp of the internal tendon, the tensile force resultant Tst of the reinforcement
are calculated from Eqs. (C15.6.2), (C15.6.3), and (C15.6.4), respectively.
C     c  y   b y   dy
0

(C15.6.1)

Tst  As   s(C15.6.2)

T p  Ap   p(C15.6.3)

x278

Chapter 15

Prestressed Concrete Structure

Tst  As   s(C15.6.4)

where, A's, Ap, As : cross-sectional areas of compression reinforcement, internal tendon andtension reinforcement
3) From the equilibrium of the forces in the cross section, Eq. (C15.6.5) can be given. Thisequation is a quadratic equation in which the neutral axis location x is an unknown. By solving
this equation, the location of the neutral axis is given.
(C15.6.5)

N d  C   Tst  T p  Tst

where, N 'd : design axial compressive force
4) If the neutral axis location x is determined, C ', T 'st and Tst can be calculated. The locationof the compressive stress resultant C ' of the concrete,  ' x, can be calculated from Eq. (C15.6.6),
and the flexural strength of the cross section is calculated from Eq. (C15.6.7):x σ '  y   b y   y  dyβ  x  x (C15.6.6)

M u  C d N     x   Tst d N  d s   Tp d p  d N   Tst d s  d N (C15.6.7)

0

c

C

In structural analysis including Eq. (C15.6.7), flexural moment is usually determined withrespect to the centroid of the cross section.
Except in the case where the strain of the cross section is completely compressive, thecompressive stress resultant C' of the concrete may be calculated in accordance with Section 9.2.1.1(3) by assuming an equivalent stress block. If f 'ck  50N/mm2 with a rectangular crosssection [b(y) = b : constant], then    x    x 2  0.4 x and C   0.68 f ck  b  x .

15.6.3 Design flexural strength of PC members with unbonded prestressing tendons orexternal tendons
The design flexural strength of a PC member with unbonded prestressing tendons orexternal tendons subjected to bending moment and axial force may be calculated on thebasis of the assumptions mentioned in Section 15.6.2, taking into consideration theinfluence of Items (i) and (ii) below:(i) The assumption that strain of unbonded prestressing tendon or an external tendon
is proportional to the distance from the neutral axis of the cross section cannot beapplied.
(ii) In the case of a PC member with external tendons, the effective height of theexternal tendons in the section changes relatively.

[Commentary] Plane conservation cannot be applied to unbonded prestressing tendons and otherunbonded tendons such as external tendons. The amount of increase, therefore, in the tensilestress in such a tendon at the failure state is less than that in a bonded internal tendon. In the caseof an external tendon, the effective height of the external tendon in the free (i.e., not supported bydeviators) portion of the tendon decreases relatively as the deformation of the member increases(see Fig. C15.6.2). Flexural strength tends to be lower than in the case where an unbonded
prestressing tendon, whose effective height does not change. The flexural strength of prestressed279

Standard Specifications for Concrete Structures-2007, Design

concrete members with unbonded prestressing tendons or external tendons should be calculated bya method that appropriately allows for these factors into consideration.
Methods for calculating the flexural strength of members with unbonded prestressing tendons orexternal tendons can be classified into the three types described below. It is preferred to select amethod taking into consideration such factors as the shape of the structure, support conditions, thestate of loads and the nonlinear behavior of the member at the failure state.
Neutralaxis
中立軸

偏心量ep1
Eccentricity

外ケーブル
External
tendon(a)（a）外ケーブルを用いた部材
Member with external tendon
Beamelement
はり部材

偏心量ep1
Eccentricity

Imaginaryelement
仮想部材（b）解析モデル（載荷前）(b) Calculating
model (before loading)Beamelement (deformed)
はり部材（変形後）

ep2＜ep1

偏心量ep2
Eccentricity(c) （c）解析モデル（載荷後）Calculating model (after loading)Fig. C15.6.2

Analysis model and deformation of a member with an external tendon(i) Method of nonlinear analysis considering displacement
In this method, the flexural strength of a member with an unbonded prestressing tendon or an
external tendon is calculated by applying nonlinear analysis that enables the calculation of theflexural strength of a structural system. By taking into consideration the influence of material
nonlinearity and the influence of geometrical nonlinearity, the flexural strength of the member canbe calculated through exact evaluation of the deformation of the concrete member with the increasein loads and the resultant increases or decreases in prestressing force due to changes in the tensionof the unbonded tendon, decreases in the effective height of the external tendon due to changes in
the location of the free portion of the tendon, etc.
In recent years, research on the flexural properties of members with unbonded tendons has madeconsiderable progress, and the flexural strength is evaluated with high accuracy by using nonlinear
analysis. In connection with members with unbonded prestressing tendons, the method of
calculating flexural strength by verifying the compatibility of deformation (the amount ofelongation of a tendon is equal to the total amount of elongation of the concrete at the same location
as the tendon) has been proposed. This method is generally called "rigorous method," and its
application to members with external tendons is currently examined.
According to research results concerning the application of nonlinear finite element analysis,
280

Chapter 15

Prestressed Concrete Structure

external tendons should be modeled directly as chord members (one-dimensional linear elements)
as shown in Fig. C15.6.2. In the case of an unbonded prestressing tendon, multiple deviators(imaginary members) should be used so that the influence of changes of the effective height can beignored. Concrete members need to be modeled appropriately according to their cross sectional
properties, etc. If the deformation of a member occurs only in a two-dimensional analytic space,
the modeling method using planar elements can be used. If flexural deformation is so dominantthat shear deformation can be ignored, the method of modeling the concrete member as a linear
member with axial stiffness and flexural stiffness and using fiber models to which material-specificstress-strain relationship is applied as linear elements can be used (see Fig. C15.6.3). By so doing,
usually, analysis time can be reduced.
A method based on nonlinear analysis can be applied to any type of prestressed concrete
structure, regardless of the type of structure or tendon. If flexural strength needs to be calculated
accurately or if the behavior of a member at the failure state is unknown as when a new type ofstructure with unbonded prestressing tendons or external tendons is constructed, it is desirable thatflexural strength be calculated by using nonlinear analysis.

b(y)1st1番目要素
element

Strain ひずみ分布
distribution
ε’c

A’s
d’s

ds

dps

dp

dc
Ci･dc

中立軸

Neutral axis

Δε’s
Δεci

i番目要素of i
Element
Ap

x

Δεp

Aps

εpe

Δεs
As

Fig. C15.6.3

N番目要素
Element of N

Example of fiber modeling of a concrete member(ii) Method allowing tension increase of tendon caused by displacement
In this method, unbonded prestressing tendons and external tendons are regarded as
tension-resisting members, the amount of increase of the tensile stress, ps, at the failure state isdefined, and the flexural strength of the member is calculated in accordance with the method
described in Section 15.6.2. Experiments and nonlinear analyses are used in combination toconsider such factors as the type of structure, structural conditions and loading conditions, and if theamount of increase of the tensile stress, ps, at a failure state can be appropriately defined inadvance, the flexural strength of the member may be calculated by this method. The differences
between the flexural strength calculation described here and the method described in Section 15.6.2
are explained below (see Fig. C15.6.4).
In this method, the location of the neutral axis is assumed first, and the compressive stressresultant C ' of the concrete, the compressive stress resultant T 'st of reinforcement, the tensile stressresultant Tp of internal tendons and the tensile stress resultant Tst of reinforcement are calculated
from Eqs. (C15.6.1) to (C15.6.4), respectively. In addition, the tensile stress resultant Tps ofunbonded tendons is calculated from Eq. (C15.6.8). Except in the case where the strain of thecross section is completely compressive, the compressive stress resultant C ' of concrete may be
calculated by assuming an equivalent stress block.
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Standard Specifications for Concrete Structures-2007, Design

T ps  A ps   ps  A ps  pse   ps 

(C15.6.8)

where, Aps : cross-sectional area of unbonded tendon

ps : tensile stress of unbonded tendon at failure statepse : tensile stress caused by effective prestressing of unbonded tendon
ps : amount of increase of tensile stress of unbonded tendon at failure state
Eq. (C15.6.5) and Eq. (C15.6.9) can be derived from the equilibrium of cross section. The
location x of the neutral axis can be determined by solving that equation.
(C15.6.9)

N d  C   Tst  T p  T ps  Tst

where, N 'd : design axial compressive force
If the location x of the neutral axis is determined, Tps can be calculated in addition to C ', T 'st, Tp
and Tst. Since the location of action    x of the compressive stress resultant C ' of the concrete
can be calculated from Eq. (C15.6.6), the flexural strength of the cross section can be calculated
from the equilibrium of cross section by using Eq. (C15.6.10).

Strain ひずみ分布
distribution
ε’cu

A’s
d’s

Neutral
axis
中立軸

ds

dps

Δε

x

b(y)

応力分布
Stressdistribution
σc’(y)

’s

T’st

β’x

C’

dN

M

y

dp

Centroid
axis
図心軸

N
Ap

Δεp
Δεps

Aps

Δεs

εpe
εpse

Tp
Tps
Tst

As

Fig. C15.6.4 Method of calculating the flexural strength Mu of member with unbonded
prestressing tendon and external tendon

M u  C d N     x   Tst d N  d s   T p d p  d N   T ps d ps  d N   Tst d s  d N (C15.6.10)

Equation (C15.6.8) was originally proposed as an equation applicable to unbonded prestressing
tendons. When applying the equation to an external tendon, it is necessary to verify that theeffective height of the external tendon does not change relatively at the failure state.
The amount of increase of the tensile stress of an external tendon, ps, at the failure state isdepended on many structural conditions such as the relationship between span length and theeffective height of a tendon, the relationship between span length and the distance between tendon
anchorages, the relationship between span length and deviator spacing, the cross-sectional area ratio
between bonded internal tendons and external tendons, and the amount of tension reinforcement.
It has also been found that the amount of increase of tensile stress in the case where a uniformly
distributed load differs from that in the case where a concentrated load even under identical
282

Chapter 15

Prestressed Concrete Structure

structural conditions. It is thought that load conditions (load types) also affect the amount of
increase of tensile stress. Stresses in external tendons begin to increase significantly after bonded
steel in the concrete has yielded. For this reason, if many internal tendons are used in a PC
member with both internal and external tendons or if many tension reinforcing bars are used in a
PRC member, it is important to determine the amount of increase, ps, of tensile stress in view ofthe possibility of the occurrence of failure before the tensile stress of external tendon increases.
In general, an economical design is made possible by identifying the type of structure, structural
conditions, loading conditions, the amount of increase, ps, of the tensile stress of unbonded
tendons.
(iii) Method ignoring tension increase of tendon caused by displacement
In this method, unbonded prestressing tendons and external tendons are regarded as
tension-resisting members as in the method described in Item (ii), but the amount of increase of thetensile stress of unbonded tendons at the failure state is not taken into account. To be more
specific, by assuming ps = 0 in Eq. (C15.6.8), the flexural strength of a member with unbonded
tendons can be calculated by following the steps similar to the method described in Item (ii). Thismethod is usually the most conservative approach to design.
Another simple method is to reduce by 30% the flexural strength calculated by a method similar
to the method used in cases where bonded tendons are used. This method has been used for longyears in cases where unbonded prestressing tendons are used, and it may be applied to memberswith external tendons. When external tendons are used, it is also possible to regard theprestressing force introduced by external tendons as an external force. In this method, the internal
force caused by the effective prestressing of external tendons is added, as an external force, to theflexural strength calculated by regarding internal tendons and reinforcing bars placed in the member
as tension-resisting members. In general, these methods may be conservative. When using thesemethods, however, it is necessary to take other factors such as economy into consideration.

15.7
15.7.1

Verification Related to Serviceability
General(1) Verification related to serviceability shall be done in accordance with Chapter 10 byclassifying structures either as PC structures or PRC structures.
(2) Appropriate limits shall be set for stress in materials in accordance with theprovisions of this section.

[Commentary] Verification related to the appearance, vibration, displacement and deformation,watertightness, etc., must be done in accordance with Chapter 10. If, however, the requirements
described in Chapter 8 are met, verification related to shear cracking and torsion cracking
associated with appearance may be omitted.

When considering limits of stress in ordinary concrete structures, only concrete stress due tobending and axial force is calculated for concrete. In serviceability-related verification for PC
structures, however, it is necessary to verify that neither shear cracking nor torsion cracking occurs.
This section, therefore, indicates limits for diagonal tensile stress in concrete due to shear force andtorsional moment.

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Standard Specifications for Concrete Structures-2007, Design

15.7.2

Maximum permissible value of stress(1) The maximum permissible value of compressive stress in concrete due to flexure
and axial loads shall be as given in Section 7.3. Also, the maximum permissible value fortensile stresses in prestressing tendon shall be 0.7 f puk , where f puk is the characteristic
value of tensile strength of the prestressing tendon.
(2) Extreme fiber tensile stress in the concrete of a PC structure shall be limited as
specified in Items (i) and (ii) below:(i) The value of flexural strength calculated using Eq. (3.2.4) shall be used as the
maximum permissible value of tensile stress for concrete. However, it shall be ensured
that tensile stresses do not occur at the location of joint in precast concrete members.
(ii) When stress in concrete is tensile, tension reinforcement in excess of the value
obtained from Eq. (15.7.1) shall be provided. Further, the tension reinforcement shall bein the form of deformed bars.

As  Tc /  sl

(15.7.1)

where, As:cross-sectional area of tension reinforcement

Tc:

total tensile force in concrete

 sl

:

maximum permissible value for tensile stresses in tension
reinforcement. A value of 200 N/mm2 may be used for deformed
bars. However, bonded prestressing tendons located in tensile
region of concrete may be considered as tensile reinforcement. In
such cases, a value of 200 N/mm2 may be used for pre-tensioning
tendons and 100 N/mm2 for post- tensioning tendons(3) Diagonal tensile stress in the concrete of a PC structure under a combination of
permanent loads and variable loads shall be limited as specified in Items (i) to (iv) below:(i) 75% of the value of the design tensile strength when either shear or torsion isconsidered.
(ii) 95% of the value of the design tensile strength when both shear and torsion are
considered.
(iii) It may generally be sufficient to examine the diagonal tensile stress at two
locations – one at centroid of the cross section and another at a location where thenormal stress equals zero.
(iv) If the member is directly supported, examination for the diagonal tensile stress is
not considered necessary for sections within a distance equal to half the depth of themember from the front face of support. Sections in that region shall, however, carry thesame amount of shear reinforcement as that used at a distance of half the depth of themember.

[Commentary] (1) The limitation on the tensile stress is not necessary when examinations forcracking in concrete and the fatigue in prestressing steel are carried out. However, when the284Chapter 15

Prestressed Concrete Structuretensile stress exceeds the elastic limit, the situation becomes complicated because the assumptions
made in structural analysis and calculation of stresses do not hold, and, the prestressing force cannot
be dealt with as an external force. Therefore, it shall be ensured that the tensile stress does notexceed the elastic limit. Further, examination for the long-term relaxation of the prestressing steel
shall be carried out under the application of an initial stress equal to 70% of the characteristic valueof its tensile strength. In fact, the maximum permissible value has been determined in a mannerthat both conditions can be satisfied.
(2) (i) Tensile stress in concrete should be limited to the flexural cracking strength, taking into
consideration of the effect of member size, in accordance with Section 5.2.1 (5). However, in thecase of joints in precast concrete members as the longitudinal reinforcing bars are not continuous,
no tensile stress shall be allowed even in the serviceability limit state. Table C15.7.1 shows thevalue of maximum permissible values of tensile stress in concrete in accordance with Section 5.2.1(5).

Table C15.7.1

Limitation of tensile stress of concrete for PC structure (N/mm2)

Cross-sectional height Specified design strength f ' ck ( N / mm 2 )Loading condition
(m)
30
40
50
60
70
80
0.25
2.3
2.7
3.0
3.4
3.7
4.0
0.5
1.7
2.0
2.3
2.6
2.9
3.1
When variable load acts
1.0
1.3
1.6
1.8
2.1
2.3
2.5
2.0
1.1
1.3
1.5
1.7
1.9
2.0
more than 3.0
1.0
1.2
1.3
1.5
1.7
1.8
(ii) Tension reinforcement shall be provided in cases tensile stress exists in concrete, so that thedifference between the stress calculated as an uncracked member and that calculated as a cracked
member could be relatively small.
Alternately, the required amount of tension reinforcement may be calculated neglecting thetensile stress in concrete. However, the method specified in this section may be used because it iseasy to use so long as the tensile stress in concrete does not exceed the design tensile strength, andgiven that it gives a conservative estimate.
The maximum permissible value for tensile stress for prestressing steel should be the stressdifference between prestress induced at prestressing and the yielding stress divided by a safety
factor, however there is no substantial study on how much the safety factor is. In this clause theconstant values are given for the maximum permissible value for simplicity of design. The
maximum permissible value is different for the pre-tensioning and post-tensioning tendon. The
reason is that the bonding ability of tendon in post-tensioning is less than those of pre-tensioning
because tendons in post-tensioning are usually thicker than those used in pre-tensioning.
For PC structure using unbonded tendon or PRC structure, when loads in excess design loads
act and cracking occurs, problems such as a poor distribution of cracks, large crack widths, andoccurrence of secondary forces on account of re-distribution of bending moment, may cause
concern. Since the difficulties encountered could be greater than those in ordinary reinforced
structure, it is advisable to adopt more appropriate load factor.
For concrete members using an external prestressing system, minimum amount of reinforcing bars
should be provided as in the case of reinforced concrete members subjected to bending moment.
In calculating the amount of required tension reinforcement, an increase in variable load may not be285

Standard Specifications for Concrete Structures-2007, Design

considered. Further, external tendons shall not be considered as part of the tensile reinforcement.
(3) (i), (ii) In order to control diagonal cracking in members designed as PC members, themaximum permissible values for the principal tensile stress are determined in a manner that they are
consistent with the conventional allowable principal tensile stresses.
(iii) Diagonal tensile stress in concrete varies with locations in the member cross section. Stresscalculation, therefore, needs to be made only the centroid of the member cross section and at thelocation where normal stress is zero. In cases when the web width on the tension side is smaller
than that at the centroid of the section, the examination should be carried out at a location where themaximum diagonal tensile stress occurs.
(iv) In regions adjacent to the support of a beam, the support reaction causes a large
compressive stress in the web in the vertical direction.
This compressive stress acts
advantageously for the considerations of diagonal tensile stress. Thus, the examination for the
diagonal tensile stress may be omitted for sections within a distance equal to half the depth of themember.
In the case of pre-tensioned members, variation of the prestressing force should be considered in
the design section for shear within the development length. It may be assumed that prestressing
force varies parabolically within the development length, and is zero at the end of the member.
The development length may be assumed as indicated below, provided that the concrete
compressive strength at time of prestressing is not less than 35N/mm2.
- For wire tendons having plain surface or indented wire tendons: 100 times the diameter of thewire tendon- For deformed wire tendons having protruded surface and wire strand: 65 times the diameter ofthe wire tendon or the wire strand

15.8

Verification During Construction

During construction, it shall be ensured that given in (1) to (4) below:(1) In view of safety from the breaking or yielding of tendons during construction, it
shall be verified that the tensile stress in tendons during and immediately after tensioning
be not greater than the values specified in Items (i) and (ii) below, where f puk and f pyk
are characteristics values of tensile strength and yield strength of tendons.
(i) Stress in the prestressing tendon during prestressing does not exceed 0.8 f puk or

0.9 f pyk , whichever smaller.

(ii) Stress in the prestressing tendon immediately after prestressing does not exceed

0.7 f puk or 0.85 f pyk , whichever smaller.
(2) As a general rule, the occurrence of cracking in concrete shall not be permitted, andItems (i) and (ii) below shall be verified.
(i) Tensile stress in concrete does not exceed the value of flexural strength calculatedusing Section 5.2.1(5) taking a value of 1.0 for  c and using the concrete compressive
strength at the time of examination instead of the characteristic compressive strength ofthe concrete.
286

Chapter 15

Prestressed Concrete Structure

Tension reinforcement is provided in concrete in regions where tensile stresses exist,
and the minimum amount of this reinforcement is 3/4 times the value calculated using
Section 15.7.2(2).
(ii) Diagonal tensile stress in concrete due to shear and torsional moment shall not begreater than the design tensile strength of the concrete. The design tensile strength of
concrete may be calculated using the concrete compressive strength developed at thetime of the verification with a value of 1.0 for  c .
(3) The maximum value of flexural and axial compressive stresses due to flexural
moments, axial forces, and prestressing forces immediately after prestressing shall be
0.60 times and 0.50 times, respectively, of the characteristic value of compressive
strength of concrete.
(4) Verification for the safety is carried out in accordance with the provisions describedin Section 15.6 of the Specification.

[Commentary] The words "during construction" should include the periods during prestressing,
immediately after prestressing, and other stages until the structure is actually in-service.

(1) The maximum permissible values for the tensile stress in prestressing steel during
prestressing, Pi , and immediately after prestressing, Pi  Pi  x  , respectively, in Eq. (15.3.1),
should be determined considering the safety for both – failure and yielding, of the tendon.
(2) In principle, occurrence of cracks during construction is not permitted because of thefollowing reasons:i) It difficult to control the crack width during construction.
ii) It difficult to control deflection after the stiffness decreases on account of cracking.
iii) Shrinkage and creep behavior of cracked concrete in the compression region at theserviceability limit state is not adequately understood.
In cases when the above mentioned conditions can be appropriately resolved, cracking during
construction may be permitted. The maximum permissible value for the flexural tensile stressshould be determined on the basis of considerations such as the combination(s) of loads during
construction, magnitude of the flexural tensile stress, and the time when the flexural tensile stress
acts.
When a tensile stress occurs for a short period during construction the amount of tension
reinforcement may be reduced to 3/4 of the value required as per this section. The reduction isallowed on the basis that while the structure is in-service, concrete is usually under compression,and the amount of tension reinforcement required at that state has been independently calculated.
However, the reduction may not be recommended in cases when the tensile stress acts for an
extended period, because the ensuing crack width may grow considerably because of creep ofconcrete.
(3) If the ratio of stress in concrete immediately after prestressing, to the compressive strength is
too high, secondary forces may develop causing non-linearity in the relationship between stress andstrain. Further, the creep coefficient may be different from the value assumed in design. It isbecause of these reasons that a maximum permissible value is imposed in the present section.

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Standard Specifications for Concrete Structures-2007, Design(4) If safety during construction is to be verified, the material factor  c of 1.0 may be used as acharacteristic value of compressive strength of concrete at the time of verification to calculate thedesign compressive strength, etc., of concrete.

15.9

Structural Details

15.9.1 General
If the performance verification of a prestressed concrete structure is made by any ofthe methods described in this chapter, the structural details specified in Chapter 13 andthis section shall be followed.

[Commentary] This section specifies prerequisites for verification methods applicable toprestressed concrete structures such as requirements related to grout for prestressed concrete,requirements related to tendon arrangement such concrete cover over tendons and tendon spacing,and requirements for concrete reinforcement in anchorage zones. Concerning other details common
to reinforced concrete structures, Chapter 13 must be followed.

15.9.2Prestressed concrete grout(1) Prestressed concrete grout shall meet quality requirements so as to fill prestressed
concrete ducts completely and thereby protect the tendons and prevent them fromcorroding and strength requirements so as to make possible the structural integration of
concrete members and tendons.
(2) Prestressed concrete grout shall be grout that has been verified, by the methods
described in the Construction section of this Specification, to meet the quality andstrength requirements. Similarly, it shall be verified that the arrangement, shapes, etc., of
the prestressed concrete grout, sheaths and tendons used are combinations that havebeen verified to ensure complete filling of prestressed concrete ducts with grout.

[Commentary] (1) The purpose of prestressed concrete grout used in conjunction with bonded
internal tendons is to protect tendons from corrosion and structurally integrate concrete memberswith tendons through bonding by filling prestressed concrete ducts. Incomplete prestressed concrete
grouting might cause problems such as the corrosion of prestressing tendons, concentrated cracking
and even a rapid fall in member strength due to the breaking of tendons. Because the degree ofcompleteness of prestressed concrete grouting greatly affects the performance of the prestressed
concrete constructed by using internal tendons, prestressed concrete grouting must be performed
completely so that there is no harmful residual air.

(2) The verification of the completeness of prestressed concrete grouting is usually done at theconstruction planning stage by the method described in the Construction section of thisSpecification. At the design stage, the prestressed concrete grout to be used and the arrangement,
shapes and other details of sheaths and tendons should be selected by referring to relevant
information such as verified and proven examples of successful prestressed concrete grouting
projects.
When selecting prestressed concrete grout, it must be verified that the selected grout meets thefollowing quality and strength requirements:
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Prestressed Concrete Structure(i) The selected prestressed concrete grout has adequate fluidity to fill the entire cross section
uniformly.
(ii) Neither bleeding nor excessive changes in volume do not occur.
(iii) Corrosive substances are not contained in a harmful quantity.
(iv) The grout has adequate bond strength to structurally integrate concrete members andtendons.
It is also necessary to select such details as the diameters of sheaths to be used and the locationsof intermediate vents and indicate them clearly on the design drawings.
(i) Sheath diameters (porosity) and intermediate vent locations should be determined so that
harmful residual air is not left in the ducts.
(ii) Types of structure of inlets and outlets and grout hose diameters that minimize pressure loss
should be selected.
(iii) Anchorage elements that enable complete filling of the space around the prestressing tendon
up to the anchorage end should be used.
(iv) Systems that enable monitoring of grouting and the reinjection of prestressed concrete grout
should be used on an as-needed basis.
The verification method described in the Construction section of this Specification is based on
full-scale experiment results or past construction results. If, therefore, the amount of change in theangle of bend in tendons exceeds the range of full-scale experiment results or past construction data,
it may not be possible to verify the completeness of filling by the verification method described in
the Construction section of this Specification. In such cases, it is important to conduct prestressed
concrete grouting tests, etc., in advance and confirm that complete prestressed concrete grouting ispossible.

15.9.3Cover of prestressing tendon

Cover for a prestressing tendon, sheath or group of sheaths, and anchoring devices
shall not be less than the values given in Section 13.2 of the Specification. However,these values may not be applied to the end regions of a pre-tensioned member provided
the prestressing steel in that region is specially treated for corrosion resistance.

[Commentary] In ordinary post-tensioned members, sheaths are often surrounded by stirrups,
longitudinal reinforcing bars, etc. In such cases, the requirements for tendons and sheaths specified
in Section 13.2 can be met by specifying concrete cover requirements for the reinforcing bars
closest to the concrete surface. If, however, sheaths are not surrounded by stirrups, etc., usually aconcrete cover not smaller than the sheath diameter should be used.

At the ends of pretensioned members, sufficient cover should be provided to ensure that damageon account of chloride induced corrosion does not cause damage in those portions. In cases when
special countermeasures are taken, though the appropriate thickness of the cover may be determined
separately, the efficiency of the countermeasures needs to be confirmed.

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15.9.4

Clear spacing between tendons

Clear spacing between tendons or sheaths shall be determined in view of such factors
as the type of tendon and the diameter of tendons or sheaths so that the space aroundtendons and sheaths can be completely filled with concrete, concrete can be compacted
in reliable way and adequate bonding can be achieved.

[Commentary] In the pretensioning method, it is necessary to secure adequate clear spacing
between prestressing tendons and between prestressing tendons and reinforcing bars. Similarly, inthe post-tensioning method, it is necessary to secure adequate clear spacing between sheaths andbetween sheaths and reinforcing bars. If sheaths are bent, sufficient clear spacing should be secured
so as to prevent the concrete between the sheaths or the sheaths from being damaged because of the
bearing pressure of tendons acting on the inside surfaces of the sheaths.

With respect to details, the Design: Standards, Part 5, of this Specification must be followed.

15.9.5

Arrangements of tendons(1) Prestressing tendons shall be so arranged that the loss in prestress due to friction
is small and that there is no abrupt change in the cross-sectional area of the tendons
throughout the length of the member.
(2) Bonded internal tendons should be placed in a pattern that has been verified, by themethod described in the Construction section of this Specification, to enable complete
prestressed concrete grouting.
(3) Prestressing tendons shall be extended straight for the required length from thebearing face of the anchoring device.
(4) When the tendon profile is curved, except in special cases, the radius shall be sodetermined that the loss in prestress is as small as possible and that the bearing stressacting on the concrete is within acceptable limits.
(5) In region(s) where the member may be subjected to reversal of moments dependingon the combination of loads, tendons should be evenly distributed avoiding
concentration.
(6) At the end support of a girder, some of the prestressing tendons should be provided
along the bottom face and anchored in a region near the bottom face.

[Commentary] (1) Loss in prestress due to friction is proportional to the sum of the angularchanges and the length of the tendon, and therefore, the effect due to such losses could be very large
for a long tendon having a curved profile such as tendons used in a continuous girder. In such cases,
the implementation of measures to make bend angles smaller such as placing prestressing tendonslinearly as much as possible and anchoring prestressing tendons that have many bent sections atintermediate points along a girder in order to minimize friction-induced loss. If, however,prestressing tendons are anchored at intermediate points along a girder, it is necessary to avoid
anchoring many prestressing tendons in the same cross section.

(2) Placement patterns of bonded internal tendons may be determined by the method describedin the Construction section of this Specification.
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Prestressed Concrete Structure(3) In order to prevent non-axial forces from acting in prestressing tendons during tensioning
operation, tendons in a section of a certain length from the bearing surface of the anchorage element
must be placed linearly in parallel with the axis of the anchorage element.
(4) When tension is applied to a prestressing tendon with a curved profile, a bearing force in theradial direction of the curvature acts on the concrete. To avoid excessive bearing stresses in
concrete, the minimum inner radius of prestressing tendon should be approximately 40 times thediameter of the or more tendon when the tendon is in direct contact with the concrete, orapproximately 100 times the diameter of the tendon or more when the tendon is provided in a ductthat is later grouted to develop bond stresses.
The words "special cases" in this clause include cases where a loop-shaped tendon is embedded
and anchored in the concrete, where a loop-shaped tendon is anchored using an anchoring device.
In such cases, examination for safety should be carried out on the basis of experiments.
(5) In regions subjected to reversal of moment depending on loading conditions, tendons shouldbe evenly distributed. Concentration of tendons tends to cause cracks in the concrete due to lackof reinforcing steel in regions near the top and bottom surfaces. Thus, prestressing tendons should
be appropriately distributed in regions near the top and bottom surfaces (see Fig. C15.9.1).

Fig. C15.9.1 Arrangement of prestressing tendons in region
subjected to flexural moment reversal(6) In cases tendons cannot be arranged as described above, additional longitudinal bars (insteadof prestressing tendons) shall be provided as reinforcement.

15.9.6 Anchoring and connection of tendons and reinforcement of concrete in anchorage
zones(1) Anchorage elements and couplers for tendons for a member shall be arranged so
as to ensure that the required prestress can be introduced into the member and shall beadequately protected in order to prevent damage and corrosion during the design service
life of the structure.
(2) Cross-sectional shapes and dimensions shall be determined so that harmful cracks
do not occur in the concrete in the anchorage zones because of the tensioning andanchoring of tendons, and the concrete in the anchorage zones shall be appropriately
protected with reinforcing bars.

[Commentary] (1) In cross sections near anchorage elements, disturbance is caused by the
diffusion of prestressing force and localized stress concentration. The commonly used stress291

Standard Specifications for Concrete Structures-2007, Design

calculation approach for a cross section subjected to eccentric axial force cannot be used.
Anchorage elements, therefore, must be located at distances required for the prestress to act
effectively on the cross section under consideration. If anchorage element is placed at anintermediate location on a member, as a general rule it should be located in the compression zone of
the member. The fatigue strength of anchorage elements is under the influence of stress fluctuations
is usually lower than that of tendons. When placing anchorage elements at intermediate locations ona member, therefore, it is advisable to place anchorage elements at locations that are sufficiently
distant from regions with large fluctuations of stress and locations where stress fluctuations areminimal.
In the post-tensioning method, anchorage elements for a member are in many cases located near
the surface of the member. Because such anchorage elements are vulnerable to external impacts andrainwater, they need to be protected appropriately. In general, it is good practice to install anchorage
elements in recesses formed in members and, after the tensioning is completed, backfill thoserecesses with a backfill material such as concrete or mortar. In such cases, it is important to secure a
concrete cover not smaller than the minimum concrete cover determined in the durability-related
verification and carefully carry out backfilling in order to prevent detachment and chipping overtime. Also, it is desirable that waterproofing measures be taken at backfills. It is also recommended
that if anchorage elements are to be exposed for the purpose of inspection, re-tensioning, etc., in
future, appropriate measures such as using replaceable rust-preventive materials be taken to protect
the anchorage elements. In the pretensioning method, it is necessary to take appropriate rustprevention measures for anchorage end zones in order to protect tendons from corrosion.
Couples, as a general rule, should be placed near the centroid of the cross section or at locations
where the amount of change in bending moment is small. If tendons are to be connected together ina curved section, sections of a certain length that adjoin the coupler must be straight, and thesestraight sections must be aligned with the coupler.
(2) If tendons are tensioned and anchored in the post-tensioning method, the concrete receives aconcentrated load from the anchorage elements. In the pretensioning method, which achieves
anchoring by means of the bonding of concrete and steel, each cross section in the development
length zone receives a concentrated load. Because of these concentrated loads, tensile stress acts on
the concrete near the anchorages. In order to prevent harmful cracks, therefore, it is necessary toreinforce the concrete with reinforcing bars. The concrete near anchorages may be reinforced inaccordance with the Design: Standards, Part 5, of this Specification.
It is a standard requirement that the minimum spacing of anchorage elements, minimum
concrete cover, etc., be determined experimentally. If a long and widely used anchoring method thathas been proved to be sufficiently safe is used, the cross-sectional shapes and dimensions ofanchorage concrete may be determined and anchorage elements placed by using that method.
If unbonded prestressing tendons or external tendons are used, tension fluctuations aretransmitted directly to anchorages. It is therefore necessary to use structures capable of smoothly
diffusing anchorage reaction forces and transmitting them to girders in a reliable way. It is also
necessary to ensure safety from local stresses such as bearing pressure stress, splitting stress andback tensile stress and from bending stress and shear force. When tendons are anchored, usually
many tendons are concentrated in small anchorage zones. It is advisable, therefore, to adequately
reinforce such tendons not only individually but also as groups.

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15.9.7

Prestressed Concrete Structure

Minimum amount of reinforcement(1) Minimum amount of reinforcing steel for prestressed concrete members shall be
0.1% of the gross area of the concrete section. The reinforcing steel mentioned here isdeformed bar and bonded tendon.
(2) For the reinforcing steel meeting the provisions of Section 15.7.2(2), the diameter ofthe bars shall not be less than 9mm, and they shall be arranged in a manner that the
spacing between bars is not more than 300mm.
(3) Across joints in precast members, these provisions of minimum amount ofreinforcement may not be applied.

[Commentary] (1) Cracks due to shrinkage and temperature gradient may occur in concrete inprestressed concrete members even at the stage when the prestress has not been introduced.
Therefore, at any section, a minimum amount of reinforcing steel, equal to 0.1% of the gross area ofthe concrete section, shall be provided to essentially prevent occurrence of such detrimental cracks.

For prestressed concrete members using the post-tensioning or pre-tensioning system, it isrecommended that the amount of total amount of steel, including the bonded tendons should be lessthan 0.15% of the gross area of the concrete section (Section 13.4.1(1)). This provision, however,does not need to be followed in connection with prestressed concrete girders or prestressed concreteslabs constructed by the pretensioning method if it has been verified, for example, through studies
on manufacturing methods, that harmful cracks do not occur in such girders or slabs.
External tendons must not be included when calculating the minimum amount of steel because
external tendons are not bonded to concrete members.
(2) The 'reinforcing steel' referred to in this clause includes deformed reinforcing bars,
pre-tensioning prestressing tendons, or grouted post-tensioning prestressing tendons.
(3) Since the provision for minimum amount of reinforcement is made primarily to control
harmful cracks due to shrinkage or temperature gradient, the provision may not be applied in thecase of joints of precast members.

15.10
15.10.1

Precast Concrete
General(1) Concrete members or products produced in advance at a factory or at a field
production facility, shall be considered as precast concrete.
(2) Precast concrete shall be designed to ensure that it meets the required criteria for
performance and safety as well as economy, when used as a single unit, or as part ofstructure.

[Commentary] (2) Usages of precast concrete can be as a single item, or several members
fabricated together or jointed together with cast-in-place concrete. It is necessary therefore forboth of single item use and the whole assembly of precast concrete to have adequate safety during
construction and service periods; or to possess enough functionality under ordinary usage; and tohave enough during target design life.

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Standard Specifications for Concrete Structures-2007, Design

The Japanese Industrial Standard (JIS) is enacted on many of factory products among precast
concrete. Upon designing factory products, specified values for cracking strength, ultimate
strength, etc. shall be satisfied. The provisions for durability may adopt easier conditions whenfactory products can be replaced easily by new ones. It is also necessary to design structures
taking into account the harmony with surrounding environment. For this purpose, coloring and/or
special surface treatment may be applied to factory products.

15.10.2

Shrinkage and creep of precast concrete

Values adopted for the shrinkage strain and creep coefficient for factory made precast
concrete products should in general be experimentally verified.

[Commentary] Behavior of shrinkage and creep of precast concrete depends on various factors,
such as mix proportion, methods of casting and curing. Their values shall be those confirmed byexperiments.

Influence of accelerated curing is large, and shrinkage and creep become smaller compared withthe cases of otherwise at the same age. It is reported in the case of steam curing that the shrinkage
and creep after the cure decreased by 20 to 40 % compared with those without steam curing. In
the case of autoclave curing, the effect is particularly large making respective values to 1/4 to 1/6.

15.10.3

Relaxation ratio of prestressing steel(1) In the case of precast concrete made by pretensioning, the type of prestressing
steel, the tensile force initially applied to the prestressing steel and the methods ofproduction and curing, shall be taken into consideration when determining the apparent
relaxation ratio of prestressing steel for calculating the loss of prestressing.
(2) In the case of precast concrete made by post-tensioning, values as shown in Table
5.3.1 may be used as the apparent relaxation ratio of prestressing steel for calculating theloss of prestressing.

[Commentary] (1) Relaxation progresses considerably prior to transfer of prestress forpre-tensioning system. Particularly under high temperature such as during steam curing, there istendency of increase in amount of relaxation and there even are reports that the values at 65˚C are
three times of that at the normal temperature. On the other hand the relaxation is small after
returning to the normal temperature and there are reports that no difference between the two cases
id found in the long run. Therefore, the apparent relaxation ratio should be determined, as a rule,taking into account the difference, such as by type of prestressing steel; period until the prestressing
and method of concrete curing.

Further, low relaxation prestressing steel has especially smaller amount of increase under higher
temperature than other types of prestressing steel.
After applying prestress, the apparent relaxation ratio of prestressing steel as shown in Table
5.3.1 which is for the case of post-tensioning system, may be adopted. When steam curing isapplied as stated above, there is a tendency of relaxation being reduced after prestressing and thevalues shown in Table 5.3.1 may be altered after confirming through experiments.
(2) For post-tensioning system, high temperature curing is not applied after prestressing and294

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Prestressed Concrete Structure

there is no difference from ordinary prestressed concrete.
Section 5.3.7 shall be adopted.

15.10.4

Therefore the values provided in

Loads

Precast concrete shall be designed considering not only ordinary design loads but
also loads that may act during storage, transportation, fabrication, jointing and others.

[Commentary] Upon designing of precast concrete, loads for design of ordinary structures
including those which may apply during construction and design life, shall be considered. Apartfrom these, loads during storage, transportation, fabrication, joints and others shall also be
considered in order to avoid occurrence of critical cracks and to ensure safety. Reinforcing shallbe necessary in some cases.

15.10.5

Unit weight

In general, the unit weight of precast concrete should be determined using
experiments.

[Commentary] Unit weight of precast concrete is affected by various reasons, such as
aggregates; mix proportions, amount of steel and method of casts. Therefore, the value confirmedby experiments is generally adopted. In case without experiments, the design values of unit
weight of precast concrete to be used in designs may adopt those shown in Table C15.10.1.

Table C15.10.1

Unit weights of factory productsCompaction method

Unit weight (kN/m3)

Vibrating compaction

25

Centrifugal compaction

26

Pressurized compaction

15.10.6

Connection(1) In cases when precast concrete is used in a part or the whole of a structure, thestructural analysis shall be carried out, determining the load transfer capacity ofconnections with the consideration of the connection method.
(2) It shall be confirmed that the connection secure the required strength and the
durability based on the connection method.
(3) Connections should, in principle, be provided at locations where the effect ofloading is small[Commentary] (1) The method stated below is usually adopted as the connection method of
precast concrete.
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Standard Specifications for Concrete Structures-2007, Designi) The method to lap and anchor the reinforcement, furthermore to grout concrete or mortarii) The method to connect by prestressing forceiii) The method to connect steel products projected from precast concrete by tightening the bolt
or weldingi) is the method that transforms a part of normal concrete of single cast and cast-in-situ into
precast concrete. A large gap is required to secure the desired development length ofreinforcement. However, the connection can secure the same level of stiffnesses and durability asin precast concrete.
ii) is connection method usually used in precast concrete, the connection shall be designed
based on Section 15.10.7.
iii) is the connection method adopted for the shield segment and others. The advantage is not
to require the form and curing, because of no casting concrete or mortar in the connection.
However, it is necessary to arrange in highly accurate position and dimensions at the manufacturing,assembling, and connecting, and to note sufficiently partial reduction of stiffnesses, durability andfire resistance.
(2) When the connection is special structure, it shall be confirmed by the experiment for thisstructure to suit the purpose.

15.10.7

Joining by prestressing force(1) In cases when independently fabricated precast elements are joined byprestressing, the location and details of these joints shall be fully examined, and it shallbe ensured that the structure or member has the required strength.
(2) Joint structures, etc., shall be as specified in Items (i) to (iv) below.
(i) The angle between the face of the joint and the resultant compression force acting
on the joint should, in general, be 90°. This angle shall not be smaller than 45 degrees.
(ii) Any special measures to be taken for preparation of the surface of the joint, should
be clearly specified on the drawings.
(iii) Use of multiple keys shall be made to ensure better contact. Appropriate
reinforcement shall be provided at the ends of a member near joints or in regions adjacent
to keys, as these locations are potential weak-spots.
(iv) Examination shall be carried out for the water-tightness of the joint.
(v) Tendons across joints of precast members generally are arranged in regions
without tension reinforcement so that when internal cable is used, the tendons should bebonded by grouting and some of these are arranged near the tension edge. In cases when
only unbonded tendons or external cable are provided, care should be taken in choosing
the method of calculation of failure strength and other details.
(3) Verification related to safety shall ascertain that Items (i) and (ii) below are met.
(i) Design shear capacity of the joint shall exceed the actual shear force. The design296Chapter 15

Prestressed Concrete Structure

shear capacity, Vcwd , of the joint may be calculated according to Section 9.2.2.5
considering the shear capacity of joint key.
(ii) key shall be safe against the actual bearing stress.

[Commentary] (1) When independently fabricated precast elements are joined by prestressing,
the structural characteristics of the joint depend on several factors such as location of the joint,
properties of the materials used for the joint, level of prestress. Therefore, depending upon therequired condition of the joint, care should be taken in choosing the structural type and materials of
joint.

(2) (i) When the angle between the face of the joint and the direction of resultant force acting on
the joint is not equal to 90°, shear force acts along the joint. In such cases, unless effective
countermeasures are taken, the precast elements may move relative to each other along the face ofthe joint. When that angle is between 70° and 55°, appropriate measures such as chipping should
be taken. When that angle is between 55° and 45°, a joint key shall be provided on the face of thejoint.
(ii) Widely used methods of joining precast concrete members include the method of directly
joining members by use of adhesive and the method of joining members by using cast-in-placemortar or concrete. It is necessary to indicate on the design drawings joint details including themethods of treatment of the faces in contact with the joints of precast concrete members describedin the preceding section.
When mortar is used in the joint(s), cracking often occurs in the joint mortar. Further, sincemortar tends to have relatively large shrinkage and creep, the width of the joint should be as small
as possible. From the viewpoint of workability, the width between 10mm and 60mm may be used.
In cases when the mortar is applied on the joint face a width between 10mm and 20mm is
recommended, in which the joint should be fastened using prestressing before the mortar hardens.
A width between 30mm and 60mm is recommended in cases when the joint is fastened byprestressing after the strength of the cast-in-situ mortar reaches the required value.
When concrete is used in the joint, the width of the joint should be small so that the amount of
in-situ concrete used can be kept small. In such cases, the joint width may be kept at a level that ishigher than that determined on the basis of considerations such as reinforcement layout and castingof concrete. When the reinforcing bars are used as tension reinforcement, the joint width should
be determined so as to provide the required lap splice length specified in Section 13.7.
Further, in the early stages after concrete casting, more cracks often occur in the joint region
than in other portions. When the examination for the serviceability limit state is carried out forstructures, where cracking is considered detrimental, conditions a) or b) below should preferably besatisfied.
a) When mortar or adhesives are used for the joint, adequate compressive stress should remain
in concrete around the joint at the serviceability limit state.
b) In cases when concrete is used for jointing and tension reinforcement is provided to control
crack width in the concrete in the region of the joint, the tensile stress in concrete due to bending
and axial forces for evaluation of the serviceability shall not exceed the flexural strength of concrete.
In cases when effective tensile reinforcement is not provided, provisions of a) above should be
adhered to.
(iii) When adhesives are used at the joint, the opposite faces should be firmly in contact witheach other. For this reason, appropriate methods such as match-casting method are used to297

Standard Specifications for Concrete Structures-2007, Design

manufacture precast members.
preferably provided as a guide.

To facilitate re-construction the desired shape, a joint key is

Joint key is provided to not only serve as a guide for re-construction, but also to increase theshear capacity. Especially, in case that segments are erected one by one such as cantilever erection
method, the axial force at joint is comparatively small. Therefore, joint keys shall bear almost
shear force. It should be noted that the shape of the concrete shear key is decided to ensure shear
failure but bearing failure. The shape given in Fig. C15.10.1 may be used as a reference indeciding the shape of the shear key. In case a steel key is used, the details should be decided withconsideration to the mode of failure.

thFig. C15.10.1

t : height of concrete shear key
h :length of concrete shear key
t h  1/2
t  30mm

Shape of concrete shear key(iv) Joints often lack watertightness so that evaluation for watertightness should be taken
according to Section 10.6. For joints in structures where presence of water is considereddetrimental, appropriate steps to ensure waterproofing should be taken.
(v) Cracks tend to concentrate near the joint of precast members in cases tensile reinforcement
is not provided. However, the width of cracks near the joint does not become too large provided
the tendons are bonded and some of tendons are provided around the tension edge. If the lattertendons are not provided, the crack-width may become large, resulting in a reduction in the ultimate
strength. Experimental studies have shown that the reduction in ultimate strength can becontrolled to a large extent by ensuring that compressive failure of concrete does not occur.
However, as it is not clear how much reinforcement is necessary, a careful consideration of all
aspects should be taken.
(3) (i) As tensile stress does not occur at joints for serviceability verification, friction resistanceby prestressing force can be expected. Therefore, verification for shear force may not be generally
necessary.
Shear forces for safety verification at joints may be taken into account in the following manner:
Design strength in shear Vcwd may be calculated by Eq. (C15.10.1) by setting βM=0 in
Eq.(9.2.21).
Vcwd  Vcwd , c  ( c  Acc  Vk ) /  b(C15.10.1)

 c    f ' cd b  nd 1b(C15.10.2)

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 nd  (1 / 2) P'c / Acc(C15.10.3)

where,  nd : average compressive stress which acts to shear plain verticallyPc : axial force which acts in compression zone of the member cross section
Acc : area of shear plane in compression zoneb

: coefficient that indicates plane configuration (0−1), which is 1/2 in case of jointof precast member by adhesive agent: average friction coefficient of solid contact, which may be 0.45

Vk

: shear capacity by shear key
for multiple key or corrugated key,
Vk  0.1Ak  f ' cd , Ak : area of compressive side of shear key b : generally it may be 1.3
Area of shear plane Acc should be the area indicated by Fig. C15.10.2, for shear force istransmitted through only web part.

45°45°

σ'nd

45°45°σ'nd45°(i) case that both side is compression(ii) case that upper side is compression

σ'nd

45°

(iii) case that lower side is compression
Fig. C15.10.2

How to estimate the compressive area at shear plain

In cases when a steel shear key is used, Vk may be calculated by Eq. (C15.10.4).
Vks  N  Ak  f vk

where, Vks
N(C15.10.4): shear force that steel shear key can carry: number of steel shear key

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Standard Specifications for Concrete Structures-2007, Design

Ak: area of steel shear key (Fig. C15.10.3)

f vk: limit value of shear stress that shear key can carryf vk may be 240 N/mm2 at ultimate limit state when its material is FCD450.

Fig. C15.10.3

Bearing part of steel shear key(ii) Bearing stresses acting at the shear key may be calculated as follows:i) in the case of using steel shear key

 a  (Vk / N ) /( B  ( L / 3))
where,  a(C15.10.5): bearing stress that acts to single steel shear key at execution or ultimate limit
state

Vk

: shear force at execution or ultimate limit stateN: number of steel shear key

B: outer diameter of steel shear key

L: embedded depth of steel shear keyii) in the case of using concrete shear key (Fig. C15.10.4)

Vk/Nt/sinθ
θ

(Vk/N)sinθ
tFig. C15.10.4 Calculation method of bearing stress of concrete shear key
300

Chapter 15

Prestressed Concrete Structure a  (Vk / N )  sin  /( B  t / sin  )  (Vk / N )  sin 2  /( B  t )where, σa(C15.10.6): bearing stress that acts to single concrete shear key at execution or ultimate
limit stateVk: shear force at execution or ultimate limit stateN: number of concrete shear key

B: width of shear keyt: height of shear key

θ: angle between shear key and vertical line

Bearing strength of shear key is calculated according to Section 5.2.1(4).

15.10.8

Concrete cover(1) Concrete cover for precast concrete shall not be less than the diameter ofreinforcing bars.
(2) Minimum concrete cover for mass-produced factory products shall be as shown in
Table 15.10.1.
Table 15.10.1

Minimum concrete cover (mm)

20
15

10
10

12
9

8
8

(3) Minimum concrete cover for precast concrete exposed to the effect of chloride shallconform to the provisions of Chapter 8, or appropriate alternative measures shall betaken.

[Commentary] (1) and (2) The provisions are ruled taking into account; i)the Japanese Industrial
Standard (JIS) is applied to many of mass-produced factory products among precast concrete, andii) for precast reinforced concrete and precast prestressed concrete, when compared with theordinary reinforced concrete and prestressed concrete structures, the water to cement ratio is smaller,
more compaction is conducted, dimensions of formworks are more accurate and better quality
control is maintained for reinforcement distribution, sizes of members are smaller making
occurrence of cracks less likely, and replacing is easier. However, the values ruled here areminimum ones and it is necessary to deeply consider the type of precast product, method of curing;301

Standard Specifications for Concrete Structures-2007, Designimportance as a structure; condition on service environment; design life; and others, when
determining the minimum concrete cover. Also, when the thickness of factory products isparticularly thin to apply the values shown in Table 15.10.1, and it is clear that it will not affectpractically durability, then the concrete cover may be reduced slightly from the ones shown in Table
15.10.1. The minimum concrete cover, even in this case, shall be not less than the diameter ofreinforcing steels.
When centrifugal compacting is applied, the compacting around reinforcement is better done
than vibrating compaction and since it has been confirmed by past experiments, that a centrifugallycompacted concrete product has better durability, concrete cover may be reduced compared withvibrating compaction. Also pressurized compacting may follow the case of centrifugal
compacting.
When artificial lightweight aggregates are used, it is preferable to add 5 mm to the values shownin Table 15.10.1.
It is necessary to determine the concrete cover to secure enough durability for comparatively
large-scale precast products such as girder of bridges, box culverts and segments, since they are ofgreat importance and their surrounding environments of use very much. This is also necessary
since JIS is not applied on large-scale precast products. In those cases, concrete cover shallpreferably be conformed the provisions of Section 13.2, with taking into consideration, particularly,
the importance, surrounding environments, designed life and others.
(3) When precast concrete is used in sea water or in atmosphere above the sea level as well as
when anti-freezing or deicing agents are used, it is necessary to make the concrete cover larger thanthe values shown in Table 15.10.1 since chloride will seep in from the surface and accelerate
corrosion of reinforcement. Further, it is necessary to make the concrete cover, as a rule, not lessthan the maximum size of coarse aggregates. Instead of making concrete cover, as a rule, not lessthan the maximum size of coarse aggregates. Instead of making concrete cover larger,
reinforcement with anti-corrosion treatment or painting on surface of the concrete may be applied
however ample examinations must be made on applications.

15.10.9

Clear distance between reinforcing bars

(1) Clear distance between reinforcing bars shall not be less than the diameter ofreinforcing bars and not less than 5/4 the maximum size of coarse aggregate.
(2) In cases when precast concrete is made using the pretension method, the clear
distance between prestressing tendons shall not be less than 5/4 the maximum size ofcoarse aggregate. However, in cases when adequate bond between concrete andprestressing tendons is needed at the end of a member, it shall not be less than 3 times
the diameter of prestressing tendons.
(3) Clear distance between sheaths shall not be less than 5/4 the maximum size ofcoarse aggregate.

[Commentary] (1) to (3) As precast concrete are made under sufficient production control, thespacing between reinforcing bars may be smaller than that for ordinary concrete structures. When
reinforcing bars, prestressing steels or sheaths are bundled together and production control is
identical with cast-in-place concrete, the provisions of Section 13.3 and 15.9.4 shall be applied.
However, the minimum clear distance between the bundled steel materials determined by the
maximum size of coarse aggregate may still be 5/4 the maximum size of coarse aggregate.
302

Chapter 16

Composite Steel and Concrete Structure

CHAPTER 16 COMPOSITE STEEL AND CONCRETESTRUCTURE
16.1

General(1) This chapter lays down specifications for design of structural members made using
a combination of concrete and structural steel. Provisions are given for design of suchmembers, including the limit states defined for checking durability, safety, and seismic
performance procedure for examination of such limit states and structural details that are
prerequisite for the examination.
(2) The provisions given here apply to following types of composite (i) steel reinforced
members, (ii) concrete-filled steel columns, and (iii) steel-concrete sandwich members.

[Commentary] (1) The provisions of this chapter apply to members in which steel and concrete aremechanically composed to resist stress resultant. Such composite members include those where
the structural steel is embedded inside concrete and those where the steel reinforcement is placedoutside concrete.
Reinforced and prestressed concrete members made using conventional steel reinforcement are
not considered ‘composite members’ as far as the provisions in this chapter are concerned. Apartfrom the three types mentioned in this chapter, several types of composite member have been
proposed to date, and it can be expected that newer proposals will continue to be made in the futurealso.
Of the many possible types of composite members, the provisions in this chapter, in principle,
cover only those general types that have been used in earlier construction, and for those, for which
the methods of checking performance and methods of design are largely established. The designof other composite members, including detailing, may be carried out using the publication'Guidelines for Performance Verification of Steel-Concrete Hybrid Structures (Draft)' of the Japan
Society of Civil Engineers, the provisions of this chapter as a reference, and on the basis ofappropriate experimental or analytical results. For parts relating to steel structures may be made to
publications such as the ‘Standard Specification for Steel and Composite Structures’ of the Japan
Society of Civil Engineers.
(2) The provisions of this chapter may be used for the design of the following types ofcomposite members:
1) Composite beams: reinforced concrete slabs placed upon steel beams and interconnected withshear connectors.
2) Steel reinforced concrete members: members including reinforced concrete beams andcolumns that contain rolled steel sections, steel plates or built up sections such as I-section, in theirsections.
3) Concrete-filled steel columns: column members consisting of steel tubes filled with concrete4) Composite walls: wall members consisting of laterally continuous rows of steel columns
covered by concrete or wall members consisting of laterally continuous rows of steel columns filled
by concrete.

303

Standard Specifications for Concrete Structures-2007, Design5) Composite slabs: slabs made of a combination of steel plates and plates and conventional
reinforced concrete slabs interconnected with shear connectors.
6) Steel-concrete sandwich members: slab or wall members consisting of a concrete infill
between two steel plates.
Representative examples of composite structural members are shown in Fig. C16.1.1.
Characteristics of composite members covered by this chapter are as follows:(i) The structural steel reinforced concrete members are members that consist of rolled
H-sections or Warren truss members incorporated into conventional reinforced concrete, and inwhich both combine to resist external forces. Such members can be categorized superimposedtype structures, which utilize the steel section with full web or reinforced concrete type structures
where a combination of conventional steel reinforcement and structural steel is used, reinforcement
depending on the arrangement of the structural steel and its bond with the concrete. In principle,
conventional steel reinforcement, as main and shear reinforcement is arranged around the structuralsteel sections. If such reinforcement is not provided, adequate measures should be taken to protect
the concrete against delamination and, if necessary, distribution of crack should be examined.
(ii) Concrete-filled steel columns are structural forms consisting of circular or rectangular steel
tubes with concrete infill.
(iii) Sandwich members are structural forms consisting of two steel plates interconnected bysteel and with the space between them filled with concrete.
Figure C16.1.2 shows some of the structural forms described above. The concrete should beplaced within the spaces between steel plates or inside tubes in a manner that no voids are left.
For the design and construction of sandwich members, reference may also be made to "TheSpecification for Design and Execution of Steel-Concrete Sandwich Structures (Draft)" publishedby the Japan Society of Civil Engineers.

Expansive concrete
T-section steel with protrusions

Distribution reinforcement
Main reinforcement

Steel plate

Shear reinforcements
Composite slab
(stud dowels)
RC deck
Steel reinforcements

Beam
CornerMain girder

ColumnLongitudinal rib
Deck plateTransverse rib
Steel-concrete composite slab

Composite column

Fig. C16.1.1 Composite members

304

Concrete infill

Chapter 16

Composite Steel and Concrete Structure

Chord

Diagonal
Full web type (cross section)

Warren truss

Warren truss (cross section)
Steel reinforced concrete

Steel plate

Steel plate

Steel plate for shear reinforcement

Direction ofmembera is

Steel plate
Stiffener

Concrete

16.2

Steel plate for shear reinforcement

Steel-concrete sandwich structure

Concrete-filled columns ( cross sections)Fig .C16.1.2

Stiffener

Concrete

Composite members covered

General requirements for composite structures

Composite members defined in this chapter shall satisfy the following requirements:(1) There is a perfect bond between the concrete and structural steel, and the bondremains throughout the period when the structure is in service.
(2) Structural steel embedded in concrete does not buckle.
(3) The durability of composite members should be comparable to that of conventional
reinforced concrete members. In cases when structural steel is placed outside theconcrete in the composite members, the steel should be provided with an appropriate
anti-corrosion coating, etc. depending upon the environment to which the structure or
member is exposed.
(4) For structural steel arranged outside the concrete, appropriate fire-resistant coveretc. should be provided if the structure or member is likely to be exposed to very hightemperatures such as in the event of fire.

[Commentary] (1) When considering the ultimate limit state of conventional reinforced concrete,a perfect bond (i.e. the average strain is the same in both materials at a given point) between thesteel reinforcement and the concrete may be assumed. For composite members, however, theultimate strength may be estimated either with the assumption that the steel and concrete have aperfect bond and their strains are continuous, or even without making that assumption.
(2) All steel embedded in concrete should be embedded in a manner that they do not buckle.
When the steel plates (or sections) lie on the outside, enhancement of local buckling strength and/or
the post buckling strength may be expected by means such as providing shear connectors or
stiffeners.

305

Standard Specifications for Concrete Structures-2007, Design(3) When structural steel is embedded in concrete, the provision of sufficient concrete cover
should be ensured, along with appropriate means to disperse cracks and restrict the width of cracks,
in a manner similar to the measures taken in the case of conventional reinforced concrete. In
contrast, when such structural steel lies outside, the steel surface shall be painted or treated toensure adequate durability depending on the specific environmental conditions. In cases where there
is direct contact with seawater, the provision of heavy-duty corrosion protective coating or cathodic
protection may be specially considered. When the structural steel lies on the outside of concrete,
and it can be ensured that the enclosed concrete is completely sealed, the provision for restricting
crack width does not apply from the point of view of durability.

16.3
16.3.1

Design Method
Selection of steel

In addition to steel generally used, steel developed especially for composite structures
may be also used as the steel in plates and bar reinforcement.

[Comments] To have an adequately proportioned cross-section in the composite structure at boththe safety and serviceability limit state, steels which have similar mechanical properties, such as
yield strength and yield strain, should be used in the main elements of the composite member.
Steel plates with protrusions or perforations may be used to augment the bond between the steel andconcrete, or to disperse cracking. The provision of the present specification does not apply whenmaterials such as carbon fibers or high strength steel with a yield stress in excess of 700-800 N/mm2
are used.

16.3.2

Verification method of performance(1) The structural performance shall be verified depending upon the type of thecomposite member.
(2) It shall be ensured that composite members meet the performance requirements
both during erection and while in service.
(3) Durability of composite members may be verified according to Chapter 8 of thisSpecification. In cases the steel is provided with an appropriate anti-corrosion coating,etc. depending upon the environment to which the structure or member is exposed,
examination for steel according to Chapter 8 need not to be carried out.

[Comments] (1) and (2) There are many different types of composite members, and it is difficult
to lay down a single procedure to examine the limit states to cover all of the members. Therefore,
the Specification allows and prescribes the use of separate methods for the examination depending
upon the type of the member. Efficiency of erection can be enhanced and steel can be more
efficiently used if steel is used as formwork or supports during erection, and then remains inposition as part of a composite member after completion. It is necessary to examine theperformance during the construction work and in service separately as (a) the loads acting during
the construction and in service, and, (b) the required performance of the members, in these stages,
can be different.
(3) Durability of steel-concrete composite member is necessary to be verified appropriately forthe steel arrangement. If steel is embedded in concrete, an adequate concrete cover must be
306Chapter 16

Composite Steel and Concrete Structure

provided. Measures must also be taken to distribute cracks, and crack width must be verified inaccordance with Chapter 8 as in the case of reinforced concrete members. If steel is placed outside
the concrete, it is necessary to take measures to meet durability requirements such as coating thesteel surface. If the structure is contact with seawater, the use of heavy-duty coating or cathodic
protection should be considered on an as-needed basis. In cases where steel is placed outside theconcrete, if the concrete is completely closed, it is not necessary to follow the rules applicable toreinforced concrete members with respect to crack width limits from the viewpoint of durability.
When steel is arranged in steel-concrete composite member, verification needs to be carried out
according to Chapter 8 as in the case of reinforced concrete.

16.3.3

Shear connector

Adequate shear connectors shall be provided in the form of stud dowels, or steel
shapes, etc.

[Commentary] Use of appropriate shear connector is required when shear forces need to betransmitted between structural steel plates and concrete. Though stud dowels are frequently used
as shear connectors, similar role can also be expected using structural steel or reinforcing bars otherthan those shown in Fig. 11.3.1. Several types of shear connectors have been developed for bridge
decks. In principle, the amount and layout of shear connectors should be decided to ensure thatshear forces are adequately transmitted and no buckling of the structural steel plates occurs. Layoutof the shear connector should be such that Eq.(C 11.3.1) is satisfied.

iHd

nsc

V
i 1

where,  i

scdi

:

 1 .0(C.16.3.1)

structure factor

H d : design shear force acting per unit width between steel and concrete over aparticular segment
Vscdi :

design shear transfer capacity of each individual shear connectorn sc

Number of shear connector within the area of calculating H d:Ease of welding the shear connector and the thickness of the steel plates involved should be
kept in mind when designing the shear connectors in composite members. Diaphragms or steel
plates with protrusions, etc. may also be used as shear connectors though their actual shear strength
should be determined through appropriate experiments, etc.

16.3.4

Examination of limit states during erection

Appropriate examination shall be carried out at the design stage to ensure theadequate strength of the structural steel and to ensure that the criteria for limits states forstrength, deformation and buckling of the structural steel are satisfied. All the above
criteria shall be met at both stages – before and after the steel and concrete isinterconnected and for all the structural steel involved, including plates or built-up
section, or rolled sections.

307

Standard Specifications for Concrete Structures-2007, Design[Commentary] Steel is sometimes used as formwork for placing concrete or as a support during
erection. The limit states during construction should be examined for both the stage before
placing concrete and the stage when concrete is in fresh state after being placed. Stress having asimilar distribution to fluid pressure is transferred from fresh concrete to the steel plates. In thecase of high-flowable concrete, the distribution is rather close to that of hydrostatic pressure. It
should be ensured that under the action of such distributed loads, the steel does not deform
excessively and that the stresses generated are within acceptable limits. Thus, the properties ofconcrete used, rate of placing, atmospheric and concrete temperatures, and placement height should
be taken into consideration when planning the construction work.
The stress induced in the steel plates during erection should in principle be superimposed when
examining steel plate buckling. However it does not need to be superimposed in examination ofultimate limit state.

16.4

Examination of completed structures containing steel sections used during erection

The effect of structural steel to be used solely for the purpose of erection on theoverall stiffness and the failure mode of the member after completion shall beappropriately considered.

[Commentary] Structural steel sections, plates and built-up sections to be used solely for the
purpose of erection are sometimes left in a member after the structure is completed. Since thepresence of such steel is not accounted for at the time of design, the actual capacity of the member
is larger than the estimation. However, this may also make a change in the overall stiffness andfailure mode of the member, and these should be appropriately considered.

16.5

Structural Performance of Joints and Corners(1) Joints of members and corners of frames shall be designed to appropriatelytransmit bending and torsional moments, and axial and shear forces, to adjacentmembers (beams, columns, etc.).
(2) Connection bases shall be designed to appropriately transmit all forces in thecolumns to the foundation(s).

[Commentary] (1) The actual distribution of stresses at the joints between members and in thecorners of frames is complicated due to abrupt change of cross sections. Steel should be provided
and arranged at the corners to appropriately transmit forces. If necessary, haunches should be used
to provide for the corner. Figure C16.5.1 shows an example of the corner of a sandwich member.
ShearplatesSteel plates

reinforcing

CornerExample of corner in sandwich member

Fig. C16.5.1

Corner structure
308

steel

Chapter 16

Composite Steel and Concrete Structure

Column bases should be designed to ensure appropriate transmission of forces from the column
to the footing, and prevent the column itself from being pulled out. The capacity for transmitting
forces can be checked using appropriate tests, non-linear analysis or equations, of which accuracy
and applicability is already confirmed, or using the Part 6 of the Standard methods in thisspecification.

16.6

Effect of Shrinkage and Creep of In-Filled Concrete

The effect of drying shrinkage of concrete used to fill structural steel may, in principle,
be neglected. The effect of creep should appropriately be examined. If the structural
system changes from that at the erection stage to that after completion, staticallyindeterminate forces produced by the creep of concrete shall be accounted for.

[Commentary] In sandwich members and concrete-filled columns, the concrete infill is locatedin an airtight environment and therefore the drying shrinkage may be considered to be small.
Consequently, drying shrinkage may be neglected. In cases where creep, drying shrinkage, or
autogenous shrinkage is expected to pose a difficulty, their effects should be appropriately
examined.

16.7

Steel Reinforced Concrete Members

16. 7. 1

Classification of structural types

Provisions of this section shall be applicable to the following steel reinforced concrete
members:(i) Superimposed-type, which is characterized by presence of steel sections with full
web or similar.
(ii) Reinforced concrete type, which is characterized by presence of rolled steel used
as together with conventional reinforcing bars.
(iii) Erection type, in which structural steel rolled sections, steel plates or built-up
sections are used solely for the purpose of erection, and their presence may be neglectedin the structural analysis.

[Commentary] Since it is difficult to provide definite specifications for design of various types ofstructural steel reinforced concrete, they have been classified into three types as above consideringexperiences in the past. Appropriate provisions have been made separately for each type. In caseof (iii), when steel plates or built-up sections are not taken into account in structural analysis, thedesign may be carried out in the same manner as for conventional reinforced concrete structures.

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Standard Specifications for Concrete Structures-2007, Design

16.7.2
16.7.2.1

Examination of safety
Examination of limit state of failure of cross section(1) Capacity of a superimposed-type composite member in flexure and under the actionof flexure and axial forces shall be taken as the sum of the individual capacities of theconventional reinforced concrete components and that of the rolled steel sections, steel
plates and/or built-up sections, computed separately. Similarly, the capacity of areinforced concrete type composite member shall be computed in a manner similar toconventional reinforced concrete members, accounting for the presence of rolled steel
sections, steel plates and/or built-up sections as equivalent reinforcing bars.
(2) Capacity of a superimposed-type composite member in shear shall be taken as thesum of the individual capacities of the conventional reinforced concrete component andthat of the rolled steel sections, steel plates and/or built-up sections, computed
separately. The shear capacity of a reinforced concrete type composite member shall becomputed in a manner similar to conventional reinforced concrete members, accounting
for the presence of rolled steel sections, steel plates and/or built-up sections asequivalent reinforcing bars.

[Commentary] (1) When moments are dominant in a superimposed type composite member
having a symmetrical cross section, it may be assumed that moments are carried only by theconventional reinforced concrete together with rolled steel sections, steel plates and/or built-up
sections, whereas the axial compressive forces are carried only by the conventional reinforced
concrete. When axial compressive forces are dominant, it may be assumed that the axial
compressive forces are carried by conventional reinforced concrete together with rolled steel
sections, steel plates and/or built-up sections, whereas the moments are carried by rolled steel
sections, steel plates and/or built-up sections alone.
(2) Shear capacity of rolled steel sections, steel plates and/or built-up sections, in a composite
member can be computed using one of the following equations (refer to Fig. C16.7.1.):
Full-web girder type:
Vsy = fvydzwtw/γb(C16.7.1)

where, Vsy:

shear capacity provided by web of steel shapes, plates or fabrications

fvyd

:

design yield shear strength of steel shapes, plates or fabricationszw:

web height of steel shapes, plates or fabrications

tw:web thickness of steel shapes, plates or fabrications

Warren truss type:
Vsy = fwsdAswzssinθ/γb(C16.7.2)

Vsy:

shear capacity provided by Warren truss

fwsd

:

design yield strength of the diagonals of steel shapes, plates or fabrications

Asw:

area of the diagonals of steel shapes, plates or fabrications

:angle between the axis of the diagonal and that of the chord
310

Chapter 16

zs:Composite Steel and Concrete Structure

lever arm of steel shapes, plates or fabrications

zs

tw

zw

弦Chord材θ斜Diagonal
材

Warrentruss
ワーレン形

充腹形（断面図）
Full web girder(cross-section)

Fig. C16.7.1

16.7.2.2

Structure of steel shape plates and/or built-up section

Examination of limit state of fatigue failure

In cases where examination for fatigue limit state is required, the examination shall be
performed separately for both rolled steel sections, steel plates and/or built-up sections
and for conventional reinforcing bars.

[Commentary] Presence of welds or forming holes in the rolled steel sections, steel plates and/or
built-up sections, generally reduces the fatigue strength. If the steel is in wet condition the fatigue
strength may be further reduced. Examination for the fatigue limit state should also account forsuch reduction in the fatigue strength of steel.

16.7.3

Examination of serviceability(1) When examining the serviceability limit state in terms of crack width, it should be,
as a rule, carried out in the same way as for conventional reinforced concrete, accounting
for the presence of rolled steel sections, steel plates and/or built-up sections asequivalent reinforcing bars.
(2) Examination of displacement and deformation may be carried out as forconventional reinforced concrete members.

[Commentary] Since the bond strength of the rolled steel sections, steel plates and/or built-up
sections with the surrounding concrete is likely to be smaller than that of deformed reinforcing bars,
there could be a tendency for the crack width to become larger as the ratio of the area of rolled steel
sections, steel plates and/or built-up sections to the gross cross-sectional area of the section
increases. Methods of dispersing cracks including welding studs to the steel or using steel plateswith protrusions should be used depending upon the requirements. The permissible tensilestresses in steel has been imposed primarily because it is not appropriate to apply methods of crack
width computation normally used for conventional reinforced concrete directly in the case ofstructural steel reinforced concrete. In general, tensile stresses in steel should not exceed the values
given in Table C16.7.1.

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Standard Specifications for Concrete Structures-2007, Design

Table C16.7.1

Upper limit of tensile stress in steel

Ass / As

Upper limit oftensile stress (N/mm2)

Not more than
30%
50%
70%

180
160
140

Ass : cross sectional area of tension steel shapes, plates or fabrications
As : total cross sectional area of tension reinforcing bars and tension steel shapes, plates orfabrications

16.7.4Structural details(1) Maximum and minimum amounts of steeli) For structural steel reinforced concrete members, the maximum area of thelongitudinal steel including rolled steel sections, steel plates and/or built-up sections, andconventional reinforcement shall not exceed 8 % of the area of a concrete section. The
minimum area shall not be less than a half of the minimum amount specified in Chapter
13. The minimum amount as tension reinforcement shall be provided in accordance with
Chapter 13.
ii) The minimum shear reinforcement shall be in accordance with Chapter 13, and shallbe provided in the forms of stirrups, ties, or hoop reinforcements enclosing all
longitudinal steel. The area of stirrups, ties, and hoop reinforcement shall be not lessthan half the minimum value specified in Chapter 13.
(2) CoverConcrete cover for structural steel in steel reinforced concrete should generally be
100mm. The cover for conventional reinforcing bars shall be conformed to that ofconventional reinforced concrete.
(3) Connection of steel and end treatment
Structural steel such as rolled steel sections, steel plates and/or built-up sections shallbe connected at sections where the capacity of the cross section has an enough margin
for stress resultant. Connections of steel shapes, plates or fabrications shall be
designed to possess at least 75 % of the strength of material. Care shall be taken that thecross section having such connections does not become the critical section.
Tension and compression steel in the free end of a cantilever and similar situations
shall be sufficiently anchored.
(4) Spacing of reinforcing bars and steel
The conventional reinforcing bars and the rolled steel sections, steel plates and/or

312

Chapter 16

Composite Steel and Concrete Structure

built-up sections shall placed in a manner that the clear distance between the bars, etc.
for the concrete to pass is neither less than 40 mm nor less than 4/3 the maximum size ofcoarse aggregate.
(5) Splices and anchorages of reinforcing barsi) Splices for the conventional reinforcing bars and connections of rolled steel
sections, steel plates and/or built-up sections shall not be located at the same crosssection.
ii) Provisions for anchorages and splices of conventional reinforcing bars shall be inaccordance with Chapter 13 of this Specification.

[Commentary] (1) Presence of excess amounts of steel affects the ease of placement of concrete,
which in turn affects the quality of concrete. Splitting cracks may occur in such cases. The
maximum amount of steel in a given member is specified assuming that construction is carried out
in accordance with the minimum specified standards and that the constructability of concrete used
meets the requirements of the Standards Specifications for Concrete Structures “Materials andConstruction”. Provision for a minimum area of conventional reinforcing bars along the axis of
the member has been made to prevent excessive cracking or spalling of concrete.
(2) A concrete cover of 100mm has been specified for rolled steel sections, steel plates and/or
built-up section, taking into consideration various factors including workmanship, and also toprevent spalling of concrete. However, it is desirable to provide additional cover when using wide
steel sections. Concrete cover for rolled steel sections, steel plates and/or built-up section should
be taken as the clear distance between the surface of the rolled steel sections, steel plates and/or
built-up section and the surface of concrete.
(3) In members such as cantilevers, simply supported beam, or, at the head of a column etc., theends of structural steel such as rolled steel sections, steel plates and/or built-up section should beappropriately anchored in a manner similar to conventional reinforcing bars. However, since thebond strength between structural steel and surrounding concrete could be smaller than that inconventional reinforced concrete, use of special measures such as connecting tension andcompression steel members in a composite section using other members is recommended. The
members used for interconnecting should have stiffness comparable to that of the tension andcompression members connected. However, in such cases, it is desirable that loading tests be
carried out to check the shapes and dimensions of interconnected members.

16.8

Concrete Filled Steel Columns

16.8.1
16.8.1.1

Examination of safety
Examination of limit state of failure of cross section(1) For flexure and axial forces, the ultimate capacity shall be computed as for aconventional reinforced concrete member, accounting for steel as equivalent reinforcing
bars.
(2) Shear capacity shall be computed assuming that only the steel tubes carry shear.

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16.8.1.2

Examination of limit state of fatigue failure

Examination of the fatigue limit state for the steel tubes shall be performed according
to Chapter 9 of this Specification.

16.8.2

Examination of serviceability(1) In general, examination for the crack width need not be carried out.
(2) Examination for displacement and deformation shall be carried out in a manner
similar to that for conventional reinforced concrete members.

[Commentary] (1) In concrete filled steel columns, steel tube is arranged all around the concrete
and as long as it can be ensured that this steel is sound, and the watertightness and airtightness aremaintained, it may be assumed that any occurrence of cracking in the concrete will not have a large
effect on performance of the member, such as its durability and/or the appearance. Thus, it isimportant to ensure that the steel tube does not lose its function of completely protecting thein-filled concrete on account of its interaction with the environment by corrosion. Any holes madein the steel to facilitate erection should be appropriately sealed.

16.8.3

Examination for placing concrete

When concrete is placed into steel tube, deformation and stresses on the surrounding
steel due to lateral pressure induced by the concrete shall be appropriately examined[Commentary] The lateral pressure of the concrete before it hardens acting on the steel tube is
estimated taking into account various factors including the rate and height of concrete placement,
air and concrete temperatures, etc and then the stress and deformation of the steel tube arecalculated. If any construction of structure is to be carried out above the column, sufficient timeshould be taken to allow the concrete to cure. When using concrete having standard workability asprescribed in Specifications ”Materials and Construction”, concrete should be placed using tremies
or pipes ensuring that any segregation does not occur. The concrete should be appropriately
compacted by vibrator, etc and placed gradually steadily starting from the bottom of the column.
High-flowable concrete may be used in cases it is difficult to compact the concrete sufficiently.

16.8.4Structural details(1) Maximum and minimum amounts of steel
For concrete filled steel columns, the maximum and minimum amounts of rolled steel
sections, steel plates and/or built-up section shall be such that the proportion of axial
forces to be borne by the structural steel is between 20% and 80% of the total axial
compression forces borne by composite member. The minimum thickness of steel plateshould, in principle, be 8 mm.
(2) Manholes and openings
All manholes and openings shall be sealed by welding with steel plates after
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Composite Steel and Concrete Structurecompletion of concrete placing.
(3) Treatment of inside of steel tubes
The steel surface of steel tube in contact with concrete, shall be unpainted, and any oil,grease, loose rust or mill scale shall be removed before the concrete is cast.
(4) Vents
Appropriate air vents shall be provided, especially in corners, etc., to prevent air fromgetting trapped and enable concrete to fill all space.

16.9

Sandwich Members

16.9.1
16.9.1.1

Examination of safety
Examination of limit state of failure of cross section(1) For flexural and axial forces, the ultimate capacity shall be computed as for aconventional reinforced concrete member, accounting for tension steel plates as
equivalent reinforcing bars.
(2) Shear capacity shall be computed on the basis of shear resisting mechanisms
accounting for the orientation and intervals of shear reinforcing steel plates.

[Commentary] The provisions for sandwich members assume that concrete fills all space
between the steel plates in the sandwich member.
(1) Stiffeners of tension steel plates, and shear reinforcing steel plates oriented along themember's axis may be considered as tension reinforcing steel of the sandwich member. Local
buckling of compression steel plates and shear reinforcing steel plates oriented along the member
axis should be appropriately accounted for when the ultimate capacity in compression is calculated.
(2) Steel-concrete sandwich members resist shear forces by means of a truss-like mechanism.
Since the layout and shape of tension reinforcing structural steel and shear reinforcing structuralsteel in sandwich members are different from conventional reinforced concrete the computation of
the shear capacity should take this difference into account. In the computation of shear capacity,
both cases – failure of concrete compression diagonals, and, yielding of shear reinforcement steel
plates, should be examined. Care should be taken as different methods are required to be used
depending upon the relative orientation (refer to Fig. C16.9.1) of the shear reinforcing structuralsteel, i.e. when the shear reinforcing steel is oriented only in the axial direction, when it is oriented
perpendicular to the axial direction, and cases where it is oriented in both directions. Examination
for the ultimate capacity of the welded point should be carried out, since sandwich members tends
to have many welding.

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Concrete

Steel plate

Axial orientationof memberConcrete

Steel plate

Axial orientationof member

Steel plate for shear reinforcement
Steel plate for shear reinforcement oriented in axial direction

Steel plate for shear reinforcement
Steel plate for shear reinforcement oriented perpendicular to axial direction
Steel plate

Axial orientationof memberConcrete

Steel plate for shear reinforcement

Mix of steel plate for shear reinforcement oriented in axial direction and steel plate for shear
reinforcement oriented perpendicular to axial direction

Fig. C16.9.1

Shear reinforcement concepts

As far as the torsional capacity of sandwich members is concerned, no clearly establishedmethods are yet available, and therefore the capacity may be estimated using only the torsional
moment capacity provided by the structural steel. However, the torsional moment capacity can be
estimated based on the experimental results of loading test.

16.9.1.2

Examination of limit state of fatigue failure

Examination for the fatigue limit state, if required, shall be carried out in accordancewith Chapter 9 of the Specification.

[Commentary] Examination should account for a possible reduction in the fatigue strength of thesteel by welds or forming holes in rolled steel section, steel plates or built-up sections. Further
reduction in the fatigue strength on account of dampness should also be accounted for.

16.9.2(1)

Examination of serviceability
In general, examination for the crack width need not be carried out.

(2) Examination for displacement and deformation shall be carried out in a manner
similar to that for conventional reinforced concrete members.

[Commentary] In steel-concrete sandwich members, structural steel is arranged all around theconcrete. As long as it can be ensured that this steel is sound, and the water-tightness andair-tightness are maintained, it may be assumed that any occurrence of cracking in the concrete will
not have a large effect of the member. Thus, it is important to ensure that the surrounding
structural steel does not lose its function of completely protecting the in-filled concrete on accountof its interaction with the environment by corrosion. Special attention should be paid to ensurethat there are no holes that are harmful to durability at locations where the steel plates are welded.
Holes made the steel to facilitate erection purposes should also be sealed. Where shear connectors
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Composite Steel and Concrete Structure

are provided, the occurrence of cracking is more concentrated than in conventional reinforced
concrete member, and the load at which crack occurs is smaller. This must be taken into accountwhen computing the bending moment that produces cracking.

16.9.3Structural details(1) Minimum plate thickness
The minimum structural steel plate thickness used in sandwich members should be 8mm.
(2) Vents
In order to prevent air becoming entrapped during concrete placement, air vents must
be provided at appropriate locations. The location and the size of the holes should be
decided in a manner that their presence does not weaken the structure. When rolled
steel sections are used for shear reinforcement, appropriate gaps or holes should be
provided, in the sections to facilitate placement and compaction of concrete.
(3) Openings in steel plates
Openings in the structural steel plates shall be as small as possible. Appropriate
reinforcement shall be provided around the openings to ensure adequate strength of thestructural steel plates. Openings made in the plates to facilitate erection should besealed using additional steel plates and welding appropriately.

[Commentary] (1) A minimum plate thickness has been set at 8 mm to take into accountweldability, etc. If there are no problems for fabrication or design, steel plates of 6 mm thickness
may be used.
(2) It should be ensured that concrete passes through the steel plates without obstruction. In
cases when a vibrator or similar equipment cannot be used, concrete having high-flowability should
be used, though it should be ensured that no segregation occurs. Use of self-compacting concreteis also recommended317

Standard Methods

Part 1

PART 1

Structural Analysis of Members

STRUCTURAL ANALYSIS OF MEMBERS

CHAPTER 1

GENERAL

1.1 Scope(1) This Specification for Design provides a method of performance verification using
the linear analysis method specified in Chapter 7 of "Design: General Requirements."
When making structural analysis by nonlinear analysis, this Specification may beconsulted.
(2) For reinforcing bar arrangement where members or structures are designed inaccordance with this Specification, it should in principle adhered to the relevant
stipulations in "Design: Standard Methods Part 5."[Commentary] (1) This Specification presents a simple structural analysis method based on thelinear analysis method for the performance verification of members or structures, and describes
verification methods and structural details for individual members or structures. When structural
analysis is carried out using nonlinear analysis, this Specification may be consulted. The general
requirement for modeling and structural analysis should be referred to Chapter 7 "Design: General
Requirements.
(2) The design methods for members and structures specified in this Specification are based on
the assumption that the requirements specified in "Design: Standard Methods Part 5" should besatisfied. Where using the design methods specified in this Specification, not only the details of
ordinary reinforcing bar arrangement specified in "Design: Standard Methods Part 5" but also thedetails of reinforcing bar arrangement for related members should be observed.

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Standard Specifications for Concrete Structures-2007, Design

CHAPTER 2 BEAMS
2.1

General(1) Member forces in beams shall be computed by linear analysis taking into accountstructural systems, loading conditions, and so forth.
(2) Where member forces are obtained by linear analysis, flexural, shear and torsional
stiffnesses of members may generally be computed using gross concrete section.

[Commentary] (1) Generally beams are classified by the shape of their cross sections, e.g.
rectangular, T- or I- shaped, or box- beams, or by their support conditions, e.g. simply supported,
continuous, fixed or cantilever beams. These beams are usually built separately and connected toeach other with cross beams.
Structural analysis of beams means computation of member forces such as moments andshearing forces in a beam, by replacing the actual loads and structures with appropriate structuralmodels. Member forces can be obtained by selecting a structural analysis method that suits
loading conditions, structural systems, span-width ratio, flexural and torsional stiffnesses of beams
and slabs, and the required accuracy of design computations. Structural analysis is determinedcorresponding to the selected analysis method.
(2) Member forces may be computed by linear analysis using gross concrete section, since itdoes not significantly affect the distribution of member forces in the whole structure provided thereinforcement in the sections is within a normal range. Even in a statically indeterminate structure
where the member forces are dependent on member stiffnesses, the presence of steel or the decreaseof stiffness due to cracking is only relative and thus, has little influence on the distribution of themember forces.
In a structure made up of different kinds of members, such as reinforced concrete columns androlled steel beams, the effect of steel stiffness shall be accounted for in the analysis. For the
structural analysis of statically indeterminate structures, the effect of deformations due to thechanges of temperature, shrinkage or creep shall be taken into account in accordance with theprovisions in Sections 5.2 and 5.3.

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2.2

Structural Analysis of Members

Span Length(1) The distance between centers of supports shall be taken as the span length indesign of simply supported beams. In case of wide supports, the sum of the clear span
and the depth of member at midspan shall be taken as the span length.
(2) For beams built monolithically with rigid walls or beams, the clear span may betaken as the span length.
(3) For continuous beams, the center-to-center distance of supports shall be taken as
the span length.

[Commentary] (1), (2) and (3) The provisions in this section are made to ensure that conservative
estimates are used for span lengths in the design of simply supported, fixed and continuous beams.
Span lengths to be used for simply supported, fixed and continuous beams are shown in Fig.
C2.1.1 (a),(b) and (c), respectively.

ｈh

h

ｈ

l or (l’+h) ｈ
Whichever is smaller(a) Simply supported beams

l or (l’+h)ｈWhichever is smaller(b) Fixed beams

Fig. C2.1.1

2.3(c) Continuous beams

Span lengths of beam

Effective Compression Flange Widths of T- Beam

(1) Effective compression flange widths of T- beams for flexure may be determined inaccordance with Eq. (2.3.1) or (2.3.2).
(i) For beams with slabs on both sides of the web (see Fig.2.3.1(a)),

lbe  bw  2(bs  )8(2.3.1)

where, be shall not exceed the distance between the centers of slabs on both sides.
(ii) For beams with a slab on one side of the web only (see Fig.2.3.1(b)),

be  bl  bs l8

(2.3.2)

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Standard Specifications for Concrete Structures-2007, Design

where, be shall not exceed the sum of bl and 1/2 the clear span length of the slab. In
the above computations, l shall be taken as the span length for a simply supported beam,
the distance between points of inflection for a continuous beam, or twice the clear span
length for a cantilever beam. The value of bs shall not be greater than the depth of
haunches.
bebeFig. 2.3.1

Effective compression flange widths T-beams(2) Effective compression flange widths for axial loads may be taken as overall widthsof slabs.
(3) Effective compression flange widths of T-beams used for computation of theindeterminate forces may be taken as overall widths of slabs.

[Commentary] (1) When beams having compression flanges such as T- beams or box- beams are
subjected to loads, the distribution of longitudinal stresses in the flanges may be taken as shown in
Fig. C2.3.1. For the sake of design simplicity, the stress is computed assuming that it is uniformly
distributed over a flange width of be , which is called the effective compression flange width.
Though the effective widths should, in principle, be determined taken into consideration loading
conditions, dimensions of beams, span to flange-width ratio and support conditions, the method
becomes practically inconvenient. For simplicity, this section stipulates λ shown in Fig. C2.3.1,
called the effective width on one side, to be equal to l/8, based on the past research results relating
to effective flange widths for loads similar to uniformly distributed loads. For a continuous beam,
l in the equation for be may be taken as shown in Fig. C2.3.2. When the flange width isespecially large, horizontal shear at the intersection of the flange and the web shall be examined forsafety.

Fig. C2.3.1

Effective widthFig. C2.3.2
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Values of l for continuous beam

Part 1

Structural Analysis of Members(2) On the basis of past research, this section permits considering the overall flange width as theeffective width for axial loads. In the case of prestressing forces in a prestressed concrete member,the forces should be broken down into axial forces and moments due to eccentric loading, and theeffective width for each used respectively.
(3) When deformation due to shrinkage or creep of concrete is restrained in a staticallyindeterminate structure, indeterminate forces are produced due to the restraint. For computation ofsuch forces, this section permits overall widths to be taken as effective widths in the case of T andbox type beams as past research and experience has shown adequate safety.

2.4

Isolated Beam

Isolated beams, unless analysis for lateral stability is carried out, shall comply with thefollowing requirements (i) to (iv).
(i) Isolated rectangular beams shall be laterally supported at spacing not exceeding 15
times the width of beam.
(ii) Isolated beams shall be laterally supported at spacing not exceeding 25 times thewidth of web.
(iii) Isolated beams shall have a flange thickness not less than 1/2 the width of web.
(iv) Effective compression flange widths of isolated beams shall not exceed 4 times thewidth of web.

[Commentary] In the design of isolated beams, it is required to take into account stress due tolateral loads which may occur other than due to ordinary vertical loads. When using isolated
beams with narrow width, total stability of the member shall be checked. Lateral buckling of
concrete in compression may occur, if lateral spacing of isolated beams is excessively large.
Provisions (i) to (iv) are so specified as to ensure safety, unless specific analysis is conducted.

2.5

Continuous BeamAs for continuous beams, the negative moments at intermediate supports, may be
reduced in accordance with Eq. (2.5.1) (see Fig. 2.5.1).

M d  M od  rv 2 / 8（2.5.1）providing, M d  0.9M od
where,

Md : reduced design moment at intermediate support
M od : design moment at intermediate support calculated as support

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Standard Specifications for Concrete Structures-2007, Designr  Rod / v
Rod:design support reaction force at intermediate supportv : hypothetical distribution width of support reaction force along
centroidal axis of member

centroidal axis of member

Fig. 2.5.1

Design flexural moment at intermediate support[Commentary] This section permits the reduction of the moment as specified, since it is assured
by finite element analysis and other methods that the distribution of negative moment over the
support of continuous beams is graded due to the effect of the width of bearing, depth of beam, andexistence of cross beams.

2.6Structural Details(1) Thickness of the flange in T-beams and the top and the bottom slabs in box beams
shall not be less than 80 mm.
(2) Thickness of webs in T-beams and box- beams shall not be less than 100 mm.

[Commentary] For important structures such as bridges, it is recommended that a slab thickness
be not less than 100 mm, and a web thickness not less than 150 mm.

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2.7

Structural Analysis of Members

Deep beam(1) In cases when the span length to overall depth ratio of beams is less than the value
indicated below, and a detailed examination of the beams is not carried out, the beams
shall be designed as a deep beam in accordance with provisions of this section.
(i) simply supported beaml / h  2.0(ii) continuous beam with two spansl / h  2.5(iii) continuous beam with three or more spansl / h  3.0

where,

l : span of beamh : height of beam(2) In the examination for flexure, axial tension reinforcement may be computed inaccordance with Section of 9.2.1 of "Design: General Requirement" using the maximum
flexural moment obtained by the ordinary beam theory. Reinforcement located within adistance of 0.2 h from the extreme fiber in tension zone of a cross-section shall beconsidered as axial tension reinforcement and shall be anchored in accordance with
Section 7.2 of "Design: Standard Part 5".
(3) Shear should, in general, be checked at the ultimate limit state of failure at the crosssection, where the design shear capacity Vdd may be computed using Section 9.2.2.2 of"Design: General Requirement".

[Commentary] (1) When the depth of beam is large in comparison with the span length and thus
the stress distributions of the beams are different from ordinary beams, such beams are called deep
beams. Scope for beams to be treated as deep beams has been defined referring to current codes ofvarious countries and results of past researches. Provision shows only a guideline, and need not beapplied if a more detailed examination is carried out.
(2) Behaviors of deep beams are similar to those of tied arches in a way that axial tension
reinforcement in deep beams operates in the same manner as tension tie members in tied arches
after the formation of diagonal cracks. Therefore, failure of a deep beam occurs, either whenreinforcement as tension tie members in tied arches yields (flexure failure), or when concrete asarch rib reaches compression failure (shear failure). Provision has been made from the fact thatfor the yielding of reinforcement the computation in accordance with Section 7.2 of "Design: Standard
Part 5" based on moment obtained by ordinary beam theory also gives reasonable value.
Because axial tension reinforcement is considered to be tension tie members in tied arches, allamount of reinforcement required for maximum moment should extend beyond the support andshould never be anchored in the spans.

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Standard Specifications for Concrete Structures-2007, Design

2.8

Corbel(1) A cantilever beam shall be considered a corbel and treated in accordance with thepresent section in cases when the ratio of the distance between the loaded point and thecolumn face to the overall depth is less than 1.0 (see Fig.2.8.1), unless specific analysis iscarried out.

Fig. 2.8.1

CorbelFig. 2.8.2

Analytical model for corbel(2) Corbels may be analyzed as a truss system comprising of a horizontal tension
member and a diagonal compression member as shown in Fig. 2.8.2.
(3) In the examination for flexure, axial tension reinforcement shall be provided to resist
the horizontal tensile forces calculated in Clause (2).
In cases when the axial tension reinforcement is arranged in two or more layers, thereinforcing bars shall be placed within a distance of d 4 from the upper surface ofcorbels (see Fig. 2.8.3), where d is the effective depth of corbel at the column face.
(4) In general, the check for shear should be carried out at the ultimate limit state of
failure at the cross section, and the design shear capacity, Vdd , may be calculated using
Section of 9.2.2 of "Design: General Requirement". In this equation, av and d shall betaken as the distance between the loaded point and the column face, and the effective
depth of corbel at the column face, respectively.
(5) Effective depth of the corbel at the loaded point shall not be less than 1/2 theeffective depth at the column face (see Fig. 2.8.3).

Fig. 2.8.3 Effective depth at the loading point
and primary tension reinforcement in corbel
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Part 1

Structural Analysis of Members[Commentary] (1) Corbels can be considered the same as deep beams, since corbels have thesimilar distribution of stresses and the resisting mechanism to those in deep beams. But,
considering particular characteristics and detailing in corbels, the provision specifically applied tocorbels have been made separately. Geometrically corbels are defined as cantilever beams having
small ratio of overhanging length from the column face to the overall depth of beam, and theprovision stipulates the value of such ratio as not exceeding 1.0 for the purpose of design.
(2) From past experimental results and researches by finite element analyses, it has been
permitted to assume the resisting mechanism by means of truss analogy as shown in this section.
(4) Failure of corbels is defined as, yielding of axial tension reinforcement, or the compression
failure of the web concrete acting as the diagonal in compression of a truss. As the compression
failure of the web concrete of corbels is similar to that in deep beams, the equation applied to deep
beams also applies to the calculation of the shear capacity of corbels.
(5) (i) When the effective depth of the corbel at the loaded point is insufficient, failure as shownin Fig. C2.8.1 occurs and there is no formation of the resisting mechanism of the truss system.
Therefore, the minimum effective depth at the loaded point is stipulated to prevent this kind of
failures.

Fig. C2.8.1 Example of failures due to insufficient effective depth at the loading point

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Standard Specifications for Concrete Structures-2007, Design

CHAPTER3
3.1

COLUMNS

GeneralDesign of columns shall be carried out on the basis of the axial force, moment, shear
force and so forth as calculated from structural analysis, taking into consideration the
shape and rigidity of members, relative stiffness ratio of adjoining members, occurrence ofconstruction joints, loading conditions, and so forth.

[Commentary] Column is a member mainly subject to axial compression force, but it is generally
subject also to moment, shear force and so forth simultaneously with the axial compressive force
according to the relative stiffness ratio to the members to be adjoined, the construction of joints,
loading conditions, and so forth. This provision prescribes the column as a member mainly
governed by the axial compressive force. And when the column is greatly affected also by
moment or shear force, it shall be examined as a beam in accordance with Chapter2.

3.2

Slenderness ratio(1) Slenderness ratio shall be taken as the ratio of the effective length to the radius of
gyration of columns.
(2) Effective length of columns shall be determined according to the degree of fixity atboth ends.
(i) For columns laterally supported at both ends, the length of axis line of structures
shall be taken as the effective length of columns.
(ii) For columns with one end fixed and the other end free, the effective length shall betaken as 2 times the length of axis line of the structure.
(3) Gross cross-section of concrete may be used for calculating the radius of gyration.

[Commentary] When lateral displacements of both ends of a column cannot occur, the effective
length of the column shall be determined according to the degree of fixation against rotation at bothends. When both ends of column are laterally confined by beams or the like in a multistory rigid
frame structure or others, both ends of column may be considered as hinges and the length of axis
may be used as the effective length of column for the purpose of simplifying calculations. A
column with one end fixed and the other end free indicates the deformation equal to that of acolumn with the length of 2 times longer and both ends hinged. Thus, the effective length ofcolumn with one end fixed and the other end free shall be 2 times the length of the column.

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3.3

Structural Analysis of Members

Short Column

A column with slenderness ratio not exceeding 35 may be designed as a short column
and the effect of lateral displacement may be neglected.

3.4Long Column

A column with slenderness ratio exceeding 35 shall be designed as a long column,
considering the effect of lateral displacement. Secondary moments due to lateraldisplacement, shall be calculated considering factors such as slenderness ratio, shape ofsection, type of load, restraining condition at column ends, characteristics of material,amount and arrangement of reinforcement, eccentricity due to construction error,
shrinkage and creep, and so on.

[Commentary] It is necessary to design a long column based on a rational analysis of structure
containing the effect of lateral displacement. The relation between stress and strain of concrete isnonlinear, so that the relation between the moment that act on each section and the deformation is
nonlinear. For this reason, in general, the deformation curve of column is supposed, the methodthat makes repeatedly calculation until the deformation curve due to internal force suits the
supposed deformation curve is adopted. The advantage of this method is to be accurate and tohave a generality to be effective for various boundary conditions.
The long column composed by reinforced concrete is also designed by the method that theeffect of secondary moment is approximately considered except general preceding method. When
slenderness ratio is roughly no greater than 100, it can be designed by approximate formulae
admitted in general.

3.5

Tied reinforced Column

The minimum lateral dimension of tied reinforced columns shall not be less than
200mm.

[Commentary] Tied reinforced column is a reinforced concrete column having longitudinal
reinforcement hooped by lateral ties.
The limit for the minimum lateral dimension of a column has been provided herein because theprincipal columns are greatly related to the capacity of structures, and the capacity of the column isgreatly affected by defects of concrete induced by various causes created during and after
construction, especially when the minimum lateral dimension of the column is small.

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3.6

Spiral reinforced Column(1) Characteristic compressive strength of concrete used for spiral reinforced columns
shall not be less than 20 N/mm2.
(2) Diameter of the effective cross section, which refers to diameter of the circle drawn
using the centerline of the spiral, of spiral reinforced columns shall not be less than 200
mm.

[Commentary] Spiral reinforced column is a reinforced concrete column having longitudinal
reinforcement entwined by spiral bars. Column with longitudinal reinforcement bars hooped bycircular ties instead of spirals may be treated as spiral reinforced column, if reinforcement iscompletely anchored.
(1) Spiral reinforced column can enhance the compressive strength of concrete by confining thelateral strain of concrete by its spirals and thus is used when it is necessary to support a large loadwith a column having a relatively small cross section. In this case, concrete with strength as large
as possible is used and further reinforced with spirals. Therefore, spiral reinforced column using asmall strength concrete is unable to fully achieve its features. Because of this, the minimum strengthof concrete has been set forth.
(2) This provision has been prescribed for the same reason as the case of tied columns set forthin Section 3.5. Diameter of effective cross section is considered because concrete located inside
the spirals works effectively against failure load of spiral reinforced column.

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Structural Analysis of Members

CHAPTER4
4.1

RIGID FRAMES

General(1) A structure made of beams and columns or slabs and walls held together
monolithically shall be analyzed as a rigid frame.
(2) Rigid frames shall be designed considering the relative stiffness of the connected
members, the loading conditions, degree of fixity of the support, and so forth. The effect of
the ground shall also be appropriately examined depending upon the condition.

[Commentary] (1) Besides ordinary beam and slab type rigid frames, flat slab, gantry
constructions, culverts and so forth should also be analyzed as rigid frames.

4.2 Structural Analysis(1) The axis line of a rigid frame shall coincide with the centroids of cross sections ofrespective members. The influence on centroidal lines due to presence of haunches may
be neglected unless they are especially large.
(2) Rigid frame structural analysis shall be carried out considering the presence of rigid
areas at the connections and at haunches.
(3) Rigid frame structural analysis may, in general, be carried out considering only
flexural deformations. However, in cases the ratio of the thickness and the length of themember is not less than 0.3, the analysis shall be carried out taking into considerations
shear deformations of the members.
(4) The moment considered for examination of cross-sections at the ends of members
shall be in accordance with Fig.12.3.1. However, as far as a haunch is concerned, only the
portion where the slope is gentler than 1:3, shall be considered effective, in thedetermination of the cross section.
(5) The shear forces for examining cross sections at the ends of members shall be theshear force at the upper and lower faces of the beam in the case of column analysis. And, it
shall be the shear force at the position, which is at a distance of 1/2 the depth of the crosssection at the front face of column from the front face of column in the case of beam
analysis. However, as for haunch, only the portion, which has a slope gentler than 1:3,
shall be considered as effective in calculation of cross section.

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Standard Specifications for Concrete Structures-2007, Design

Fig. 4.2.1

Moment for check of sections at the end of member[Commentary] (1) When the haunch is especially large, a polygonal line shall be considered asaxis, and the change of cross section shall be taken into consideration.
(2) Structural analysis of a rigid frame shall be made, as a rule, taking into considerations therigid zones by estimating the effects of connection parts of members and haunches. Rigid zones
shall be generally determined by the methods from i) to iii) stated below.
i) When there is no haunch, the rigid zone shall be the inner portion starting from the crosssection which is distant at 1/4 the depth of member inside from the ends of members (see Fig.
C12.3.1(a)).
ii) When a member has a haunch sloped not less than 30 degrees from its axis, the rigid zone
shall be the inner starting from the cross section whose depth is 1.5 times the depth of the member.
However, when the slope of haunch is not less than 60 degrees, the rigid zone shall be the inner
portion starting from the cross section which is distant at 1/4 the depth of member inside from thestarting point of haunch (see Fig. C4.2.1(b)).

Fig. C4.2.1

Rigid areaiii) When two or more points are determined by i) and ii) above mentioned because of thedifference between right and left haunches, the point that creates a larger rigid area shall beselected.
(3) In the rigid frame, only the flexural deformation may be generally considered in the
structural analysis of a rigid frame. However, when the height of member is large compared with
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the length of member, then the shear deformation of member shall not be neglected in comparison
with flexural deformation, and so, in this case, shear deformation shall preferably be taken into
considerations in the structural analysis. Generally speaking, a structural analysis shall be madeconsidering shear deformation when the ratio of height to length (the length of axis) of member is
not less than 0.3.
(4) When a structural analysis has been made considering rigid areas, then the moment to be
used for checking the section at the end of member shall be as shown in Fig. 4.2.1(a). When an
analysis has been made neglecting the rigid areas, then it shall be as shown in Fig. 4.2.1(b).

4.3Structural details
In principle, haunches should be provided at the corners of rigid frames.

[Commentary] It is generally possible to cope with large moment and shear force at the corners
relatively easy by increasing the height of cross sections through providing haunches at the corners,
and the haunches are effective to smoothly transfer stresses at the corners. Because of this, it has
been prescribed as a rule to provide haunches at corners. However, haunches sometimes cannot beprovided because of structural reasons or other reasons related to appearance. In this case, it ispreferable to provide large chamfers.

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Standard Specifications for Concrete Structures-2007, Design

CHAPTER5
5.1

ARCHES

General(1) In principle, axis of an arch should coincide with the thrust line of the loads.

(2) The shape of the cross-section of an arch rib shall be determined taking the
span-to-rise ratio, axis of the arch, strength of concrete, and method of construction into
consideration.
(3) The strength of the foundation of an arch rib shall be high enough to resist thereactions at the end of the arch rib.

[Commentary] (1) The thrust line of arch due to loads is the line which connects acting points ofresultants in the section of arch rib. As for the shape of arch axis, normally used is quadratic
parabola, hyperbolic (exponential) curve or quadratic curve. Circle, two-centered circle ormulti-centered circle is often used as the shape of arch axis where the span is small, only because
the forms and the temporary supports can be simplified.
(2) Sectional shape and dimensions of arch rib are determined by referring to actual examples ofstructures built in the past or by assuming them with approximate formulas and making repeatedcalculations.
Construction method sometimes becomes an important factor for determining thecross-sectional shape of arch rib, so the adequate constructing conditions must be comprehended
during design stage.

5.2

Structural Analysis(1) The line connecting the centroids of cross-sections of the arch rib shall be taken as
the axis of the arch.
(2) Effects of shrinkage and temperature change of concrete shall be taken into
consideration in calculating member forces.
(3) Effects of changes in the cross-section of the arch rib shall be taken into
consideration in calculating statically indeterminate forces.
(4) The effect of settlement or displacement in a foundation, whenever required, shall beappropriately taken into consideration.
(5) In cases when the slenderness ratio of arch rib is not less than 35, the effect of
movement of arch axis should be taken into consideration in principle in calculating

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member forces.
(6) Safety of the arch-rib against in-plane and out-of-plane buckling shall be confirmed.
(7) Examination of the arch-rib in the out-of-plane direction may be carried out inaccordance with Section 12.2, assuming that the arch rib is a straight column subjected toan axial force equal to the horizontal reaction acting at the end of arch rib. In this case,the length of the column should be taken as equal to span of the arch, in principle.

[Commentary] Structural analysis of arch can be made in various ways including the method inwhich the member forces are calculated by the frame structural analysis theory approximating thearch rib member to a polygonal line and combining it monolithically with members such as verticalmembers. Therefore, a linear analysis shall be applied as a rule from the viewpoint of practicality,
when calculating member forces to be used in the examination of each critical state.
(2) This has been especially prescribed because in an arch the effects of temperature change andshrinkage of concrete are significant compared with those of beams.
(4) Foundation at the end of arch is desired to be sufficiently strong. But when there is thepossibility of the foundation displacement, the effect of displacement of foundation shall be taken
into consideration during design stage.
(5) When designing an arch rib, small displacement theory may be employed in calculating
member forces that arch span is small or the slenderness ratio is not greater than 35. However, thisdeformation shall be taken into consideration as a rule, because the deformation in arch cannot be
neglected in such cases that arch span is large or its slenderness ratio is not less than 35.
The slenderness ratio of arch member shall be calculated by Eq. (C5.2.1) using the equivalent
length of member (le) of arch member calculated by using δ given in Table C5.2.1.

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Standard Specifications for Concrete Structures-2007, Design

Table C5.2.1

  le 

Values of δ

A1/ 4  cos 1/ 4
Im

where, le    ll

(C12.4.1)：slenderness ratio：equivalent length of member

A1/ 4：cross-sectional area of arch rib at 1/4 point of

1/ 4：slope angle of arch axis at 1/4 point of l：average moment of inertia of arch rib section (m4)Imlll (m2)：span length considering the degree of fixation of foundation (m)(6) The arch rib is a member that subject to large axial compressive force due to horizontal
reaction. Not only examination for stress and sectional strength of arch rib, but also safety against
buckling of in and out-of-plane direction of arch rib shall be confirmed. Structural analysis forbuckling of out-of-plane direction shall be made in accordance with (7).

336Part 1

5.3

Structural Analysis of Members

Structural Details

In cases when an arch rib has a box type cross section, diaphragms shall be provided
at the connections with support columns (see Fig.12.4.1).

Fig. 12.4.1

Diaphragm of box-section arch rib

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Standard Specifications for Concrete Structures-2007, Design

CHAPTER 6
6.1

DESIGN OF PLANAR MEMBERS

Scope and Definitions

Provisions of Section 12.5 shall apply to design of planar members, such as slabs,
footings, shells and walls, whose width in directions perpendicular to the principal axis of
the member is much larger than its height or thickness.

[Commentary] Slabs including flat slabs may be taken to be thin, plane-sided members that resist
moments and shear due to transverse loads. Footings used in foundations of structures are muchthicker than ordinary slabs, and have a different purpose compared to that of a slab. Shells are
three dimensional spatial structures made up of one or more curved or folded plates. Walls are
consisting of vertical plane.

6.2

Structural analysis of planar Members

The structural analysis shall be carried out in accordance with the provisions of
Chapter 7 of "Design: General Requirement", considering the effect of (i) transverse load,(ii) in-plane load, or, (iii) a combination of transverse and in-plane loads.

6.3
6.3.1

Design of Slab
Structural analysis(1) Flexural moment, shear force, torsional moment and support reaction in slabs
should, in principle, be computed using thin-plate theory taking into account the supportconditions, geometry and loading conditions. However, generally accepted approximate
methods may also be used.
(2) Examination of the ultimate limit state of failure at the cross section for slabs may be
carried out using a method based on plastic analysis, provided the method has been
confirmed to be safe.
(3) In cases the support condition for slabs are likely to change during construction orwhile the structure is in-service, the slabs and their supports shall be appropriately
designed for satisfactory performance under those changes.
(4) The center-to-center distance between supports shall be taken as the span length forthe purpose of analysis. In case of slabs with long supports the sum of the clear span andthe slab thickness at midspan shall be taken as the span length. For slabs built
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Structural Analysis of Members

monolithically with rigid walls or beams, the clear span may be taken as the span length.
(5) Loads acting on slabs shall be taken as distributed over areas of the slab in a shapesimilar to the loaded area, at a distance of half the slab thickness from the periphery of theloaded area. In cases when the slabs are overlaid with concrete or asphalt-concrete, thefull thickness of the overlayer shall be added to the above distance. In cases of overlays
with soft material, 3/4 of the thickness of the overlay shall be considered as the distribution
thickness.

[Commentary] (1) In principle, the thin-plate theory may be adopted for structural analysis ofslabs since the theory of bending of slabs with small deflections is generally applicable. For thisanalysis, the span length and the distribution width of concentrated load shall be in accordance with(4) and (5) respectively.
Reinforced concrete slabs are generally built monolithically and the properties of the section perunit length in two orthogonal directions are similar. When applying the thin-plate theory linear
elastic analysis for isotropic slabs may be used on the assumptions that flexural stiffness in two
orthogonal directions is equal and remains unchanged after cracking. In cases when a slab is built
integrally with beams and the distances between beams in the two orthogonal directions are notequal, the flexural stiffness in the two orthogonal directions may be significantly different, it isrecommended that such effects should be accounted for in the analysis.
Member forces in slabs, such as flexural moment and shear force, may be calculated using
methods of numerical analysis such as the finite element method, on the basis of the thin-plate
theory making appropriate assumptions such that the actual configuration, etc. are represented in theboundary conditions. Such calculations, however, tend to be complicated, and establishedmethods may be used for approximate analysis. Available charts and tables may also be used.
For slabs having a complex shape, member forces may be evaluated using experimental results
obtained from testing of scale models.
(2) For slabs under serviceability limit state, the deformation remains sufficiently elastic.
Therefore, linear analysis should be used considering the simplicity of design. For slabs underultimate limit state of failure at the cross section, the redistribution of moments become moresignificant and the member forces calculated by linear analysis tend to differ from the actual values.
In such cases, plastic or nonlinear analysis in accordance with the provisions of Chapter 7 of"Design: General Requirement" may be carried out, provided it could be assured that plastic hinges
can freely rotate.
In a continuous slab, or in other similar cases, flexural moment calculated at supports using
linear analysis may be increased or decreased in accordance with Section 7.3.2.1 of "Design:
General Requirement". For practical purposes, for the plastic analysis in slabs, yield-line theory
and strip method may be used. In both methods, the effect of torsional moments can be eliminatedand there are fewer limitations in the analysis compared to linear analysis. On the other hand, itshould be borne in mind that the principle of superposition cannot be used in this case and theanalysis may be complicated depending on load conditions. Due consideration should be given to
the above features when using plastic analysis.
(3) For instance, the support conditions for precast concrete slabs at the time of lifting during
construction may be different from when they are in-service after installation. Further, a change inthe support condition may occur when slabs deteriorated after being in service for a long time arerepaired or strengthened.
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Standard Specifications for Concrete Structures-2007, Design

In cases when a deteriorated beam–slab system is replaced by a new slab, it is not necessary thatthe new or repaired slabs are supported in a manner similar to that prior to deterioration. In suchcases, in addition to the slabs, possible changes in the support conditions for the beams and/orcolumns shall also be considered.
(4) The provisions in this Section for the spans to be used in design of simply supported orcontinuous slabs and slab monolithic with walls, etc. are based on considerations that have beenfound to be empirically safe.
The span of a slab may be taken as the smaller of the following two distances:(i) the distance between the centers of supports.
(ii) the sum of the clear span and the thickness of the slab at midspan.
For slabs built to be monolithic with beams or walls which may be considered as fixed, the span
may be taken as the clear span between faces of the walls or beams. In cases when the slab is
supported on bearings, the span shall be taken as the distance center-to-center of the bearings. In
cases when the length of bearing is small, the effects due to bearing stress shall be examined.
(5) A concentrated load with rectangular contact area (measuring t1  t2 ,) acting directly on thesurface of the slab, may be resolved into an equivalent rectangular uniform load acting over an areaof [( t1  t ) x ( t 2 ,  t )], where t is the thickness of the slab. The dimensions ( t1  t ) and ( t 2 ,  t )may be taken to be the ‘distribution widths’ at a distance of 1/2 the slab thickness (from the edge ofthe concentrated load), assuming a load distribution at 45. When an overlay, having a thickness‘ s ’, is present over the slab surface, the distribution width shall be taken as ( t1  2s  t ) and( t 2 ,  2 s  t ), respectively. In cases of overlays with soft material, the distribution width shall betaken as ( t1  1.5s  t ) and ( t2  1.5s  t ) (see Fig. C12.5.1).

s :thickness of overlay

t1, t2 :contact length of loadt : thickness of slab
Equation shown in bracket isapplicable to overlays with
soft material.

Fig. C6.3.1

Distribution width of concentrated load

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6.3.2

Structural Analysis of Members

Examination for applied member forces(1) Examination for flexural moment
Examination for moments in slabs may be carried out as in the case for a beam, in
accordance with the relevant requirements. In cases when the direction of principal
moment does not coincide with the direction of reinforcement, sufficient flexural strength
shall be provided in all directions.
(2) Examination for shear
Calculation of shear capacity of slabs should be carried out in accordance with thefollowings:(i) The shear capacity may be calculated in accordance with the provisions for linear
members assuming that a slab near a support acts as a wide beam and resists shear at thecross section in one direction.
(ii) For circular slabs subjected to uniform loading, the extra shear resistance due tocircumferential reinforcement may be included.
(iii) Examination for punching shear around a concentrated load or near a supportshould be carried out assuming that the surface resisting shear is conical or pyramidal inshape.
(3) Examination for torsional moments
Torsional moments in slabs should be considered as equivalent shear forces at the endof the slab and as equivalent bending moments at other position of the slabs.

[Commentary] (1) Examination for flexure in slabs shall, in general, be carried out at each point
for two orthogonal directions considering the slab to be a beam with unit width and accounting forthe moment distribution in slabs. Even in a wide slab, where moments in one direction may be
dominant, moments also arise in the transverse direction, and therefore, appropriate distribution
reinforcement should also be provided in the transverse direction.
Reinforcing bars are, in general, provided in the two orthogonal directions of a slab. In mostcases, reinforcing bars are provided in the direction of the principal moment at the point where themaximum moment occurs. In regions of the slab away from the area of the maximum moment andin the neighborhood of the edges of the slab, it could be subjected to unsymmetrical loads. Further,near openings the direction of principal moment differs significantly from the direction ofreinforcing bars because of presence of torsional moment.
Slabs with two-way flexural and torsional moments may be designed as plates subjected tomembrane forces in accordance with the provisions of Section 9.2.2.4 of "Design: General
Requirement", using the method specified in 6.5(2) of the Specification, which resolves these
moments into membrane effects.
When using plastic analysis for the examination of the ultimate limit state, adequate
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Standard Specifications for Concrete Structures-2007, Design

serviceability shall be ensured. Therefore, the degree of moment redistribution shall be limited as
far as the result of linear analysis is applicable. Further, when assuming formation of plastic
hinges, it shall be ensured that adequate plastic deformation can be guaranteed.
(2) As provided above, when designing a slab section, examination should be carried out for
moments and shear forces assuming the slab to act as a beam. Further, in slabs subjected to aconcentrated load, the examination for punching shear should be carried out.
However, available researches have shown that slabs such as an underground LNG tank, whose
width is larger than their thickness, have greater shear resistance than that of ordinary slender beams.
For example, experiments have shown that shear resistance of circular slabs is larger than that ofordinary beams because of the restraint to radial expansion provided by the reinforcing bars
arranged in the circumferential direction. Experiments have also shown that the shear strength ofsimply supported and uniformly loaded circular slabs, whose diameter is larger than ten times theeffective depth, may be computed in accordance with the provisions of Section 9.2.2.4(commentary) of "Design: General Requirement", which has been derived from Eq.(6.3.3) andmodified to account for the resistant due to circumferential reinforcements, which results in radial
compressive forces.
(3) Torsional moments at other positions than the end of the slab are the elements of main
bending moments and should be examined as described in (1) above.

6.3.3
6.3.3.1

Examination for slabs having different shapes
One-way slab

(1) For simply supported one-way slab subject to a concentrated load, the maximum
moment per unit width may be computed as in the case of a beam with an effective width
given in Eqs. (6.3.1) and (6.3.2).
(i)when c  1.2x1  x l  (see Fig. 6.3.1(b)),

be    2.4 x1  x l (6.3.1)(ii)when c  1.2x1  x l  (see Fig. 6.3.2)),be  c    2.4 x1  x l 
where(6.3.2)c : minimum distance between edge of the load and free edge of slab
x : minimum distance between the concentrated load and supportl : span lengthu,ν: distribution width of concentrated load342

Part 1

Structural Analysis of Members

Fig. 6.3.1 Effective width of one-way slab
(2) When the design of slabs in shear is based on the method applied for beams, theeffective width shall be taken in accordance with the provisions of 1).

[Commentary] (1) The method given in this section gives the approximate moment in a slab
supported along two parallel sides perpendicular to the span direction due to a concentrated load.
Here, the moment per unit width may be computed as in the case of a beam using the effective
width (measured parallel to the edge of support) as given here (see Fig. 6.3.1).
In cases multiple concentrated loads act on a slab in a manner that their effective widths overlap,
the effect of all the loads shall be adequately accounted for in the design of each region. However,in an application where the requirement of the reinforcement varies for different regions, thefollowing simplification may be made.
In cases when the variation in the requirement for the different regions is not significant, thereinforcement per unit width, Asd , may be distributed as shown in Fig.C.12.5.2 in accordance withthe theory of plasticity, except in the case of skewed slabs for which a separate treatment may berequired.

As1 , As 2 , As 5 : amount of reinforcement per unit width for each region
l1 , l 2 ,l5 : effective width for each load
Fig.C.6.3.2 Example of reinforcement provided in slabs
subject to multiple concentrated loads

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Standard Specifications for Concrete Structures-2007, Design

For continuous slabs, the following approximate method may be adopted.
(a) The maximum moment per unit width at midspan, Mc, shall be calculated as follows.

M c  Kmc
where, mc =midspan moment in a continuous slab calculated as a continuous beam
total width of slab

K =moment per unit width of simply supported slab with effective width
moment per unit width of simply supported beam

The span used in the calculation of K shall be taken as follows.
end span

0.8l1 , where l1 is the length of end spancenter span

0.6l2 , where l2 is the length of center span(b) The maximum moment per unit width at support, M e , shall be calculated as follows.
M e  K 'me

where, me =moment at support in a continuous slab calculated as a continuous beam
total width of slab

To calculate the support moment at the first intermediate support, the coefficient K ' should betaken as the average of K at the end span and at the first intermediate span. Also, for the second
intermediate support, average value of K at the first and second intermediate spans should be
used.
In cases when a one-way slab is fixed at opposite ends, and is subject to the action of aconcentrated load, the effective width shall be computed using Eq. (C6.3.1) and (C6.3.2) for
positive moment at center span and negative moment at fixed end, respectively.

be  v  x(1  x / l )(C6.3.1)be  v  0.5x(2  x / l )(C6.3.2)

344

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6.3.3.2

Structural Analysis of Members

Two-way slab

(1) In cases of two-way slabs, with the ratio of shorter to longer span not exceeding 0. 4,
subject to uniformly distributed loads, member forces may be computed as in the case of
one-way slab on the assumption that the loads are carried only along the shorter span.
(2) For two-way slabs other than in 1), member forces in slabs shall be computed using
the thin-plate theory or other approximate methods.

[Commentary] (1) When two-way slabs with a ratio of shorter span to longer span l x l y , notgreater than 0.4 are subjected to uniformly distributed loads, the magnitude of moment in x
direction is nearly equal to that calculated as a one-way slab in the short span direction. In thiscase, the moment may be computed as a beam with unit width of slab spanning in short span
direction. It is necessary to provide distribution reinforcement for the moment in y direction
accordingly.

6.3.3.3

Cantilever slab

(1) For a cantilever slab subject to a partially distributed load, the maximum moment perunit width of the slab may be computed using the effective width, be , as defined below.
For load applied in the center (Fig.6.3.2(a))

be  v  2x

(6.3.3)For load applied at the edge

be  v  x(6.3.4)

where, x ：distance between support and loadv ：distributed width of load

Fig. 6.3.2

Effective width of cantilever slab345

Standard Specifications for Concrete Structures-2007, Design(2) For a cantilever slab subject to uniformly distributed load, the maximum moment in
the direction of the span may be computed as in the case of a beam, in accordance with therelevant requirements assuming the cantilever slab to act as a cantilever beam.

[Commentary] (1) When a wide cantilever slab is subject to a concentrated load P
perpendicular to the slab surface at a distance x from the fixed end as shown in Fig. C6.3.3(a), theinfluence lines for moment M on the edge of support are given in Fig. C6.3.3(b). This Section is so
specified that the effective width for the approximate calculation leads to a satisfactory margin ofsafety.

Fixed
end

Fig. C6.3.3

Influence lines for moment at point A on fixed end

Hooks shall be provided for primary reinforcement in a cantilever slab.
Where the thickness of slab is not enough to anchor a reinforcing bar shall be bent down at thefree end and extended along the bottom of slab. (Fig. C6.3.4)

Fig. C6.3.4

Development of primary reinforcement in cantilever slab
subject to large concentrated load at free end

346Part 1

6.3.3.4

Structural Analysis of Members

Skewed slab

(1) For skewed slabs, member forces shall be computed taking into account the degreeof the skew angle and the width of slab.
(2) For simply-supported skewed slab with the skew angle not less than 45, member
forces may be computed using the following simplified methods (i) and (ii) (see Fig. 12.5.4).
(i) For b / l i  0.75
Positive moment shall be evaluated as in the case of a one-way slab using the skewed
span length, l i .
(ii) For b / li＞0.75
Positive moment shall be evaluated as in the case of a one-way slab using the straightspan length, l n .

Fig. 6.3.3

Skewed slab

[Commentary] (1) For the calculation of the member forces in skewed slab, the methods shallconsider the degree of the skew angle and the width of slab. For skewed slabs with skew angle
less than 45˚ analysis by such as finite element method or grid theory shall be employed.
(2) When the value b / li of skewed slab is small, it is pointed out that the simplified
calculation method specified in this Section leads to a rather conservative estimate of design
moment assuming the skewed length as the span length. This method, however, allows the use of
the skewed span length for safe estimations.

6.3.3.5 Flat slab
(1) General
Provisions of this Section shall apply to the flat slab constructions, where the slab is
supported directly or through drop panels by the columns. The following definitions oftechnical terms in flat slab construction have been used.
Column line: Line connecting the centers of columns

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Standard Specifications for Concrete Structures-2007, Design

Column strip: A strip having a width of 0.25l x or 0.25l y on either side of column line
Middle strip: A strip having a width of 0.5l x or 0.5l y , sandwiched between column
stripswhere l x : length of span measured between center to center of supports in a directionof the column lines

l y : length of span perpendicular to the direction of l x(2) Structural analysis(a) Member forces of flat slab may be calculated as substituted rigid frames which canapproximate the behavior of the portions of flat slab as divided by the center lines between
adjacent column lines or by the center lines of middle strips. In this case, examination
shall be carried out for each of the two orthogonal directions in the plane of slab.
(b) The following approximate method may be adopted for the analysis of flat slabs
reinforced in two directions. In this case, however, the structural details as given in
Section 6.3.4 of "Design: Standards Part 5"shall be satisfied.
(i) For vertical loads, calculations shall be carried out in accordance with a) to c) below.
a) Slabs in flat slab construction shall be considered as made up of two groups oforthogonally intersecting beams divided by column lines in two orthogonal
directions – x and y . A rigid frame made up of these beams and columns shallbe considered in each direction, and calculations shall be carried out by applying
complete loads in worst conditions to the frame. In the x direction of the rigid
frame, the span and width of the beam shall be taken as l x , and l y respectively.
The depth of the beam shall be taken to be t , which is the thickness of the slab. It is
the same for the y direction (see Fig. 12.5. 7). In the case of multistory rigid
frames, only the flexural resistance of columns directly connected to slabs being
considered may be taken into account.

Fig. 6.3.4

Frames of flat slab

Fig. 6.3.5

Distribution of momentb) Slabs shall be divided into a middle strip ABDC having width of l/2 and the column
strips ABFE and CDHG each having width of l/4. 45 % of positive or negative span
moment calculated as rigid frame shall be uniformly distributed to the middle strip,
348

Part 1

Structural Analysis of Members

and the remaining 55 % uniformly to the column strips on both sides. 25 % ofnegative support moment shall be uniformly distributed to the middle strip, and theremaining 75 % uniformly to the column strips on both sides (see Fig. 6.3.5). In casewhen the edges of the flat slab are supported throughout their length, 3/4 of the
moment of the ordinary middle strip may be used for the portion with the width of
3l/4 from the supporting edge.
c) Columns shall be considered as vertical members of a rigid frame.
(ii) For horizontal loads, calculations shall be carried out assuming the rigid frame asconsidered above. However, the width, b, of the beam in the rigid frame shall be given by
Eq.(6.3.5)b  (l  c ) / 2(6.3.5)where, l : span length in each direction

c : with of the column head (diameter in the case of circular column)
Moment of beam obtained shall be distributed in the proportion of 0.7 and 0.3 to thecolumn and the middle strip, respectively.
(3) Design for the connections between slab and columns(a) Connections between the slab and columns shall be checked against punching
shear.
(b) In cases when moments are transferred between the slab and column at theirconnection, in addition to punching shear, the bending and torsional moments, and shear
force acting at the face of the connection shall be accurately determined. The dimensions
and materials of the connection shall be so determined to safety the limit state
requirements against the above forces.
(4) Structural details(a) Thickness of slab should, in general, not be less than 150mm. However, thiscondition may not apply to cases when the load is small, e.g. in the case of roof slabs.
Ratio of effective depth of slab to the larger span should, in general, not be less than
1/32. Even in cases when the applied loads are small, e.g. in roof slabs, the ratio should
not be less than 1/40.
(b) Width of column shall be larger than 1/20 of the distance between the centers ofcolumns in the same direction as that of the width, 1/15 of the height of story and 300mm,
whichever is the largest (see Fig. 6.3.6).
(c) Dimensions of column head shall conform to Fig. 6.3.6. When calculating thestresses in the column head, only the portion above the 45 line from the horizontal line
shall be considered effective.

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Standard Specifications for Concrete Structures-2007, Design

Fig. 6.3.6

Flat slab system[Commentary] (1) When designing flat slab as a rigid frame, the rigidity of column and slab may
be determined based on the rigidity of actual cross sections.
Moment of slab may be obtained by properly distributing the moment of beam, calculated fromthe substituted rigid frame, to column strips and middle strip. Moment may be uniformly
distributed within column strips and middle strip.
(2) For the practical application the simplification has been made in the distribution method of
moment specified here, based on the results from the theoretical calculation.
Edges of flat slab supported throughout their full length means that flat slab is supported bywalls or beams. In this case, the moment acting on slab strip adjoined to and in parallel to the
supporting edge is smaller than that of other ordinary slab strips. Therefore, 3/4 of the moment ofordinary middle strips may be taken into account for this portion.
(4) The provisions for the dimensions of each portion specified here have been prescribed taking
into considerations not only the requirements as flat slabs but also the conditions for approximate
analyses of them. The method specified in Fig.12.5.9 is applicable to not only y direction but also
x direction.

6.3.4

Structural details

Minimum thickness of slabs shall be 80mm.

[Commentary] This Section specifies the minimum thickness of 80mm for the normal in-situ
concrete slab because in a thin slab the defects due to inadequate workmanship may affect thestrength of the slab. Nevertheless, in determining the slab thickness, due consideration shall begiven to control the deformation of slab to be sufficiently small, not to damage the serviceability
and appearance of structure and not to give adverse effect on the overlayers.
In a thin slab, it is generally difficult to arrange shear reinforcement effectively.
350

For slab with

Part 1

Structural Analysis of Members

the thickness not less than 200 mm, however, shear reinforcement may be provided to resist shear
force.

6.4

Design of footing

6.4.1

GeneralProvisions of this Section shall apply to design of isolated footings, wall footings andcombined footings, which are used as foundations of structures.
The following
definitions of technical terms related to footings have been used.
Isolated footing: A footing that distributes forces transmitted through a single column
or a pedestal and is not combined with other footings
Wall footing: A footing that distributes forces transmitted through a wall
Combined footing: A footing that distributes forces transmitted through more thansingle column or pedestal, or, that connecting isolated footings with members.

6.4.2

Structural analysis(1) Footings shall be designed taking into account not only the forces transmitted
through columns, walls, etc. but also loads due to self-weight and soil surcharge (oroverburden). The reaction from the ground for spread foundations, the pile reaction forpile foundations and buoyancy shall also be considered.
(2) In principle, footings should have sufficient thickness so as to behave as a rigid
body.

[Commentary] (1) Footings shall be designed by taking into account the loads fromsuperstructure, self weight of footing, surcharges due to soils, subgrade reaction, pile reaction,buoyancy and so on. The effect of the surcharge may be unsafe or safe depending on the locationof the design cross section. Therefore, footings shall be designed by the possible loading
conditions on safety side.
(2) The existing design has been formulated on an assumption that a footing is connected rigidly
with foundations and columns or walls. This implies that footing shall have enough rigidity
compared with foundations or columns and walls. Therefore, a footing should have enough depth
to be handled as a rigid body. The decision whether a footing can be treated as a rigid body or not
may be evaluated by its relative rigidity to soil or foundation. A footing may not need to be a rigid
body, if it is analyzed precisely.
The required depth to handle a footing as a rigid body may be obtained in the following way.

351

Standard Specifications for Concrete Structures-2007, Design(a) In case of isolated footing and combined footing, average depth of a footing shall not be lessthan about one fifth of the long side of the footing.
(b) In case of wall footing, average depth of a footing shall not be less than about one fifth of
the remaining width of footing after deducting the thickness of wall.
When it may be on the unsafe side to handle the footing of pile foundation as a rigid body, thefooting shall be analyzed by taking into consideration its elastic behavior.

6.4.3

Examination for flexural moment(1) Computation of design flexural moment and critical cross section(i) Isolated footing and wall footinga) Design flexural moment in a footing shall be computed assuming it to be a cantilever.
The critical cross section shall be taken as the vertical plane at the face of rectangularcolumn or wall or at a location one tenth of the diameter inside of the circular column.
b) Flexural moment at the critical cross section shall be computed as the moment
generated by all forces acting over the entire area of footing at the face of column or wall.
(ii) Combined footinga) The cantilever portion of a combined footing shall be treated in a manner similar toisolated footings. The portions between columns in a combined footing shall be treatedas a rigid monolithic frame.
(2) Effective width at critical cross section
Effective width at the critical cross-section of footing for flexural moment shall beobtained using Eq. (6.4.1)
For spread foundation: be  b0  2d  B(12.5.8)

In the case of pile foundations, it shall be appropriately determined considering the pilearrangement and configuration of the footing.
where, be : effective width
B : total width of footing

b0 : width of column or pedestald : effective depth of member for flexure

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Part 1

Structural Analysis of Members(3) Design capacity of member at critical cross section
The design capacity of the member at the critical cross-section shall be calculated inaccordance with the method described in Chapter 9 of "Design: General Requirement".

[Commentary] (1) Flexural moment of isolated footing and wall footing may be computed byconsidering the critical cross section as a support of cantilever.
When the cross section of a column is neither square nor rectangular, it shall be substituted bysquare or rectangular having the same area and center as the original one for determining the criticalcross section. For circular column, the critical cross section may be determined to be the verticalplane at one tenth of diameter inside of it (see Fig. C6.4.1(b)).

CriticalColumnColumnFig. C6.4.1

Critical cross section for flexural moment

Flexural moment at the critical cross section AB as shown in Fig. C6.4.1 shall be computed as
the flexural moment by all the forces acting on the entire area of ABCD.
In a footing with two-way reinforcement arrangement, although the forces acting over corners
are counted twice for the cross sections at right angle to each other, they shall not be reduced.
The footing in between columns should be, as a rule, designed as a monolithic rigid frame
consisting of column, beam, footing and foundation structure.
(2) Effective width of footing for flexural moment is determined by assuming 45 degree
distribution of forces from the edge of columns or walls.
This effective width shall be replaced by Eq. (C6.4.1) when the tensile pile reaction makes theupper axial reinforcement.

be  b0  d  B(C6.4.1)

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Standard Specifications for Concrete Structures-2007, Design

6.4.4

Examination for shear(1) Critical cross section and effective width(i) Near the columns or walls, the critical cross section shall be at section A-A which ish 2 away from face of column or wall (see Fig. 6.4.1)

Critical crossCriticalsection for shear

Fig. 6.4.1

Critical cross section of footing for shear adjacent to column or wall(ii) In cases when a pile foundation has a single row of piles on one side and the
distance between the center of piles and the face of column or wall is less than twice theheight of the footing at the face of column or wall, the critical cross section shall be taken
as the section B-B, which is at a distance a 2 from the face of column or wall (seeFig.6.4.2).

where, a : distance between center of piles and face of column or wall ( a ≦ 2h )be : effective widthFig.6.4.2

Critical cross section for shear and effective width of pile foundation
with single row of pile on one side(iii) Effective width be of footing shall be the entire width of the footing at the criticalcross section. However, for wall footings of pile foundations with a single row of piles on
one side, the effective width, be, per pile shall not exceed two times the distance between
the center of pile(s) and the face of wall.
354

Part 1

Structural Analysis of Members(2) Design shear capacity at critical cross section
Design shear capacity at critical cross section shall be computed in accordance withthe provisions of Section 9.2.2.4 of "Design: General Requirement."[Commentary] (2) Based on experiments, the effective width for shear design is provided in an
ordinary footing, where the ratio of distance between the face of column or wall and the center ofpile to the effective depth of member at the critical cross section is, in many cases, less than 2.0.
However, when the width of column is relatively small compared with the width of footing, theeffective width should be determined in a different way.
In general, the behavior of footing is similar to that of deep beams and it may be sometimes
difficult to arrange vertical stirrups because of spatial restriction. Attention should be paid toarrangement of vertical stirrups because they may in some case initiate diagonal cracking.
In case where the ratio of the distance a between the center of ground reaction and overburden
load and the face of column or wall to effective depth d is less than 2.0(a/d < 2.0) in spreadfoundations where footing is directly supported, verification may be made using design
compressive shear capacity of deep beam Vdd as the design limit value. In the case where a/d ≥ 2.0,
verification should be made using design shear capacity Vyd of linear member as the design limit
value. As the effective width of wall footing for shear force, total width of wall footing may be
used. However, where the width of column is relatively small compared with the width of footing,the effective width should be determined in a different way. The case where the footing is notdirectly supported referred to the case where the top face of footing is subjected to tensile stress (seeFig. C6.4.2).
In the case where a pile foundation has several rows of piles, verification for shear force shall be
carried out at each pile head. In general, A-A cross section h1/2 away from the outside of the rowof piles may be used as the critical cross section (see Fig. C6.4.3).
In the case where a pile foundation has a single row of piles on one side and the distance
between the center of pile and the face of column or wall is less than twice the height of the footing
at the face of column or wall, the design punching shear capacity should be calculated for each pileand the combined total of shear capacity should be used as the design limit value. As the punching
shear capacity per pile, the design compressive shear capacity Vfdd calculated using Eq. (C6.4.2)
may be used (see Fig. C6.4.4). The distance to the edge of the footing, however, should exceed
be/2. If the effective width exceeds the total width of the footing, the width of the footing should be
used as the effective width. In the case where multiple piles have overlapping effective widths, theeffective width should not exceed 1/2 of the distance to the adjacent pile.

Vfdd＝（βd＋βw）βp･βa･ffdd･be･d1/γb(C6.4.2)

where, Vfdd: Design compressive shear capacity (N)ffdd＝0.19

f 'cd（N/mm2）βd＝ 4 1000 / d 1

where d > 1.5,βd is taken as 1.5

1  100 pv
2

where  p> 1.5,βp is taken as 1.5

βp ＝

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Standard Specifications for Concrete Structures-2007, Design

βa＝5/[1＋{1.1(a1－R/2)/d1}2]
βw＝4.2{ 3 100 p w ･{1.1(a1＋R/2)/d1－0.75}/

f 'cd }

where  w< 0，βp is taken as 0

be : Effective width （＝0.8 a1+R） (mm)d1 : Effective height at the face of the column or the wall (mm)a1 : Distance from the face of the column or wall to the center of the pile
R : Pile diameter (mm)pv : Ratio of tension reinforcement pv＝As/(be･d1)
As : Cross sectional area of tension reinforcement (mm2)pw : Ratio of shear reinforcement pw＝Aw/(b1･s1)
where p w< 0.002，pw is taken as 0.002

A1 : Cross sectional area per vertical stirrup (mm2)b1 : Spacing of vertical stirrups perpendicular to the member axis (mm)s1

: Spacing of vertical stirrups in the direction of the member axis (mm)f'cd : Design compressive strength of concrete (N/mm2)

b: Member factor, for which 1.2 may generally be taken

Overburden Load

Ground Reaction

Fig. C6.4.3 Critical cross section for shear force near pile head
Cross section for verification

Fig. C6.4.2 Case where the footing is not directly supported

356

Part 1

Structural Analysis of Members
部材軸方向
Directionof the member axis

杭Pile

Bridge Pier

s1

s1

b1a
b1b

Pile diameter R

be averagebb11:: bMay
1a とb1value of b1a and b1b(a)Effective width be
Fig. C6.4.4

6.4.5(b) Spacing of stirrup

Verification of punching shear of pile

Examination for punching shear(1) Examination for punching shear shall be carried out in accordance with theprovisions for planer members. However, for pile foundations with a single row of piles
on one side, the examination of punching shear may not be necessary in cases when the
distance between the center of the piles and the face of the column or wall is less than
twice of the effective depth of footing at the face of column or wall.
(2) When the distance between centers of piles is small, examination for punching shear
shall be carried out by calculating the resistant length as a pile group.

[Commentary] In footings free edge is sometimes very close to piles. This is quite different
from the case of punching shear for ordinary slabs because of small resistant area. Therefore
punching shear of footings shall be examined. However, for pile foundation with single row ofpiles on one side, when the ratio of distance between the face of column or wall and the center ofpile to the effective depth of member at critical cross section is less than 2.0, the relevant
experiments show that the shear failure plane of footing passes the equally divided plane between
the outer edge of pile and the face of column or wall and the failure mode is similar to that ofpunching shear. However, the examination for punching shear may be eliminated, because
experiments show that the calculated shear capacity for beam with the effective depth specified
12.5.7.3(2) well describes the failure loads.
Depending on pile arrangements, due attention should be paid to cases which require
examination for punching shear by column in isolated footing.

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Standard Specifications for Concrete Structures-2007, Design

6.4.6

Examination for pull-out shear(1) In cases when a footing is supported by piles and pullout forces act throughanchors, the examination for pull-out shear shall be carried out in a manner similar to thatfor punching shear.
(2) When the distance between centers of piles is small, the critical cross section shallbe determined by taking into consideration the angle of diagonal crack.
(3) When shear reinforcement is provided, its effect may be appropriately considered in
the computation of the pull-out shear capacity.

[Commentary] (1) When the design for pull-out shear is conducted in accordance with the casefor punching shear, the peripheral length u of loading face shall be computed in accordance withthe provisions of Section 9.2.2.3 of "Design: General Requirement".
(2) When the distance l between the edge of loading face and the center of the piles is lessthan the effective depth d , the critical cross section shall be, in general, at 1/2 of distance between
the edge of loading face and the center of the piles.
(3) When pull - out force is applied to footing, the mechanism of failure is clearly similar to thecase of punching shear. Some experimental results with shear reinforcements show them to be
similar to the cases of directly transmitted shear. However, there are not many experimental datafor cases with shear reinforcement and formula has not yet been established to-date. Therefore,
when the effect of shear reinforcement is confirmed by an experiment or other method, pull-out
shear strength may include this effect.

358

Part 1

6.5

Structural Analysis of Members

Design of Shell and Wall

(1) In general, structural analysis of shells and walls shall be carried out in accordancewith i) to iii).
i) In shell design the selection of curve shapes shall consider the mechanicalcharacteristics of the shells. However, analysis or structural models may be simplified as
far as the three-dimensional elastic behavior of shell structure can be properly
approximated.
ii) Shear walls subject to in–plane horizontal loads may be designed as frame
structures consisting of columns, beams and walls as a web.
iii) In general, linear analysis may be used to evaluate member forces.
(2) When shells are subject to flexural and torsional moments and axial forces due totransverse and in-plane loads, they may be examined as planar members subject toin-plane loads or beams subject to flexural moment and axial force by resolving moments
into in-plane loads (axial forces) in accordance with Section 6.3.6 and 6.2 respectively.
(3) The examination for shells in shear shall be similar to that of beams.
(4) In general, structural details of shells and walls shall be determined in accordancewith i) to iii)
i) End members supporting shell should have larger rigidity than that of the shell, andalso the plane subject to concentrated loads should have supporting members.
ii) The effective width of shells acting together with supporting or end members shall betaken in accordance with the provisions of Section 2.3
iii) Thickness of a shear wall shall not be less than 100mm, nor less than 1/25 of thelength of unsupported side of wall, and also not less than 1/30 of the shorter side in the c.

[Commentary] (1) i) Shells treated in this Section shall resist member forces due to both in-plane
and transverse loads and shall have a structural shape to which the theory of shell can be applied.
The folded plate forms a curve if it is divided into small elements. In such a case it may beconsidered as a shell.
The design of large shell structures shall include the effects of reduction in rigidity due to cracks
and of the progress of deformation due to creep as well as buckling.
In the analysis of shell structures, member forces and displacement shall be calculated in such amanner that the force equilibrium as well as the compatibility are satisfied even after deformation.
However, only limited cases can evaluate solutions strictly satisfying these conditions theoretically.
In practice the simplification may be allowed as far as the behavior of shell structure can beproperly approximated. For instance, membrane theory may be applied to the ordinary portion of
the shells, while local bending effect should be taken into account in the vicinity of boundary.

359

Standard Specifications for Concrete Structures-2007, Design(1) ii) Wall is a vertical plate with horizontal length not less than 4 times its thickness and it isused as members from (a) to (d) as explained below according to stress conditions (loading
conditions).
(a) Walls subject to vertical loads:
columns.

These members have properties similar to those ofWalls subject to vertical loads may be designed as columns with a rectangular cross section asshown in Fig. C12.5.10 in accordance with Section 12.2.
(b) Walls subject to loads normal to the plane: These members have properties similar to thoseof slabs, such as retaining walls. Since the placing direction of concrete is different from that ofslabs, their structural details governed by construction methods and so forth are different from thoseof slabs.

where,

d : wall thickness
u : distribution width of applied load

Fig. C12.5.10

Walls subject to vertical loads(c) Walls subject to bending in plane: When walls not uniformly supported at bottom but fixed
only at both ends, are loaded at its span, they are subject to bending in plane. These walls have theproperties similar to those of beams, such as deep beams.
(d) Shear walls: These walls support loads mainly through the shear resistance of walls, suchas earthquake resisting walls. This Section specifies the design of the shear wall as shown in Fig.
C12.5.11.
If shear cracks and so forth occur in the wall, the reduction in rigidity shall be examined. In
addition, the calculation of deflection or other deformations shall consider not only effects ofmoment but also shear force.

360

Part 1

Structural Analysis of Members

Fig. C12.5.11

Shear wall(2) When shells are subject to membrane forces ( N x , N y , N xy ),flexural moments ( M x , M y )torsional moment( M xy ) and out-plane shear ( V x , V y )as shown in Fig. C.6.5.3, they may bemodeled as comprising three layers, two outer layers and one central zone (Fig.C.6.5.4). Fig.C6.5.5
illustrates that flexural and torsional moments may be resolved into statically equivalent membrane
forces. It also shows the lever arm z (distance between centroid of compression force and that oftensile reinforcements) taken as the distance between the upper and lower reinforcements. This
simplification is, in general, conservative in resolving moments into membrane forces. Shells
subject to combined loadings can then be replaced as for planar members subject to in-plane loads
only and the ultimate limit state of failure at cross section for them is verified according to Section
9.2.2.4 of "Design: General Requirement". This design method is applicable to cases when N1 is
tension in principal membrane forces ( N1 ≧ N 2 )and reinforcements should be less than 50% ofbalanced ratio at any section of shells.
When orthogonally reinforced concrete plates are subject to axial forces and in-plane shear,these membrane forces are resolved into one set of principal forces N1 and N 2 at angle  to
the reinforcement direction as shown in Fig. C.9.2.15 of "Design: General Requirement". As far
as neither the yielding of reinforcement nor compression failure of concrete of shells occurs, so
called “Seismic Performance 1” specified in the Chapter 11 of "Design: General Requirement" issatisfied. Shells subject to membrane forces shall follow Section 9.2.2.4 of "Design: General
Requirement" in calculation of design membrane forces and capacity respectively.
Upper layer
Reinforcement
Central zone

Lower layer
Fig. C12.5.12 Applied forces
and moments in shells

Fig. C12.5.13 Upper and lower
layer model of shells

361

Standard Specifications for Concrete Structures-2007, Design

Fig. C12.5.14

Moments resolved into equivalent membrane forces(4) i) Shells are thin in comparison with other types of concrete structures. Therefore, if shells
such as domes are subject to concentrated loads, they should be supported by more rigid members,in order to prevent excessive deformation and to assure smooth flow of stresses.
(4) ii) When the end member or supporting member carry flexural stresses, shells on one side orboth sides of them may also resist the flexural stresses. The effective width of shell utilized in
calculations is specified here. This width may be the same as the effective width of slab as T-beamflange.
(4) iii) The minimum wall thickness is specified. Construction work may be difficult and therigidity against flexural buckling or others may decrease, if the wall thickness is small comparedwith the dimensions of the plan. Generally, the thickness should not be less than 150mm.

362

Part 2

PART 2

Seismic Design

SEISMIC DESIGNCHAPTER 1
1.1

GENERAL

Scope

This Specification for Design presents a method for satisfying Chapter 11 of "Design:
General Requirements." This Specification is applicable to the seismic design ofreinforced concrete structures that satisfy the following conditions.
(i) Structures in which the first mode of vibration is predominant(ii) Structures with limited major plasticity areas[Commentary] “Design: General Requirements” describes a flow from setting waveforms oftime history accelerations on the surface of the engineering bedrock to calculating the response by
conducting coupled time history response analysis using an analysis model incorporating thestructure and the soil, or conducting time history response analysis in which the time history
acceleration at a designated depth obtained by response analysis of soils is input to an analysis
model of a structure on land, and checking by comparing the response value of the member with thelimit.
In this Specification, the results of implementation of the above verification flow using themodels of soil and structure that have already been developed are presented as spectra at thedesignated seismic coefficient at the yield point. Then, the Specification describes a design
method based on the seismic coefficient method using the designated seismic coefficient at the yield
point, and a design method using nonlinear spectra, as seismic design methods for the soil andstructure similar to their models.
This Specification describes a design method that meets the requirements for seismic
performance verification described in “Design: General Requirements” in a limited scope of
application. This Specification is applicable to structures in which the first mode of vibration is
predominant and with limited major plasticity areas. For the structures to which this Specification
is inapplicable, the seismic performance verification should be made in accordance with “Design:
General Requirements.”
Even beyond the scope of application, the design method described in this Specification may be
used for designing the cross section or making assumptions for reinforcement arrangement for
performance check stipulated in “Design: General Requirements.”

1.2

Seismic Performance That Should Be Made Available

This Specification stipulates that the following seismic performance should be madeavailable.
(i) Seismic performance 1 should be made available against level 1 ground motions.
(ii) Seismic performance 2 should be made available against level 2 ground motions.
363

Standard Specifications for Concrete Structures-2007, Design[Commentary] For the design methods described in this Specification, the relationship between
the design ground motion and seismic performance has been specified as described above. In
cases where other type of relationship between the design ground motion and seismic performance
than that specified here is specified, check should be made in accordance with “Design: General
Requirements.” In this Specification, the limit seismic performance is defined as described below.
Seismic performance 1: Yield strength and yield displacement of the member
Seismic performance 2: Shear carrying capacity and ultimate displacement of the member

364

Part 2

CHAPTER 2
2.1

Seismic Design

DESIGN BY SEISMIC COEFFICIENT METHOD

GeneralThis chapter is applicable to seismic design using the seismic coefficient method.

[Commentary] This chapter describes a standard seismic design using the seismic coefficientmethod using the required yield point seismic coefficient spectra. A flowchart of the seismic
design method using the required yield point seismic coefficient spectra is shown in Fig. C2.1.1.

START
Assumption for the size of a frame or a member
Judgment of the soil typeCalculation of the equivalent natural period
Calculation of the design horizontal seismic coefficient
Calculation of the cross-sectional force at thedesign horizontal seismic coefficient(Linear analysis)(Required yield point seismic coefficient)(Linear analysis)

Assumption of the amount of longitudinal reinforcement

Safety verification for the
flexural capacity γi・Md／Myd

No

Yes
Calculation of the shear force, Vmu when themember reaches its flexural capacity
Assumption of the amount of transverse reinforcement

Safety verification for the shear
capacity γi・Vmu／Vyd≦1.0

No

Yes
Assumption of the amount of transverse reinforcement

Check of the amount oftransverse reinforcement within
the plastic hinge

No

Yes
END

Fig. C2.1.1

Flow of seismic design using the required yield point seismic coefficient spectrum

365

Standard Specifications for Concrete Structures-2007, Design

2.2
2.2.1

Loads
General(1) Seismic effects on structures should be considered under permanent, variable andaccidental loads. For permanent and variable loads used for seismic performanceverification, refer to "Design: General Requirements."(2) As seismic effects, inertia forces of the mass of the structure and of the imposed
mass should be considered.
(3) The inertia forces generated by an earthquake may be obtained by multiplying themass of the structure and the imposed mass by the design horizontal seismic coefficient.
(4) Seismic ground motions in two orthogonal horizontal directions should generally
be considered independently.
(5) The design horizontal seismic coefficient should be determined based on therequired yield point seismic coefficient spectra according to the soil type and theequivalent natural period of the structure.
(6) The required yield point seismic coefficient spectra should be developed
considering the vibration characteristics of the surface soil at the construction site, andthe equivalent natural period and deformability of the structure.

[Commentary] (6) Numerous structures are modeled while fixing the flexural-shear capacity
ratio (Vyd/Vmn) and other parameters, and the deformability of the structure is verified based on the
response obtained by the time history response analysis under level 2 ground motions. Based on
the results of the verification, the designated seismic coefficient at the yield point should bedetermined so as to meet the seismic performance requirements and the requirements against
level-1 ground motions. A schematic diagram of the required yield point seismic coefficient
spectrum is given in Fig. C2.2.1.

Response under level 2 ground motion
1.0○OK ×NG

Designated yield point spectrum

× ○

× × ○
○

0.5

0.1

○
○ ○
○
× ×

× ×○
× ○

0.1

0.5

1.0

Level 1 ground motion

5.0

Fig. C2.2.1 Schematic diagram of the required yield point seismic coefficient spectrum

Examples of the required yield point seismic coefficient spectrum are shown in Fig. C2.2.2.
These are obtained for the structure on soils except liquefied or irregular grounds in which theflexural-shear capacity ratio (Vyd/Vmn) of the member at the plastic hinge set as 2.0 where thecolumn in a structure was damaged mainly. The seismic ground motions shown in Figs. C6.4.2 to366

Part 2

Seismic Design

C6.4.4 of “Design: General Requirements” were used in the calculation. Rigid-frame viaducts andbridge piers with a firmly fixed spread foundation or pile foundation with underground beams were
examined. The equivalent natural period of the study structure Teq ranged from 0.5 sec to 2.0 sec.

Required yield point seismic coefficient, Khy

1.0

0
.
2

0.1

Equivalent natural period, Teq (sec)Natural period of subsurface ground (0.250.5sec, normal ground）

0.5≦Teq≦2.0 K hy=0.43
1.0

3
4
.
0

3
4
.
0

0.1

1.0

0
.
2

0.1

)
c
e
s
(

q
e
T
期
5 周
.
0
有
固
価
等

Required yield point seismic coefficient, Khy

2
4
.
0

Equivalent natural period, Teq (sec)

0.1

)
c
e
s
(

)
c
e
s
(

1.0

8 q
e
.
0 T
期
5 周
.
0
有
固
価
等

0
.
2

9

0.1

1.0

2
4
.
0

9
3
.
0

9
3
.
0

0.1

-1.087

0.5≦Teq＜0.8 K hy=0.330Teq
0.8≦Teq≦2.0 K hy=0.42
7
.
0

1.0

Natural period of subsurface ground (0.25sec, rock)

y
h
K
度
震
伏
降
要
所

y
h
K
度
震
伏
降
要
所

8
.
0

y
h
K
度
震
伏
降
要
所

-1.222

0.5≦Teq＜0.9 K hy=0.343Teq
0.9≦Teq≦2.0 K hy=0.39

. q
0
e
T
期
周
5
.
0
有
固
価
等

Required yield point seismic coefficient, Khy

In cases where spiral reinforcing bars are arranged inside the longitudinal reinforcing bars in the
cross section at the member that became plastic, the required yield point seismic coefficient
spectrum should be developed in accordance with the provisions in this section.

Equivalent natural period, Teq (sec)Natural period of subsurface ground (0.5sec, soft ground）

Fig. C2.2.2 Examples of required yield point seismic coefficient spectrum

2.2.2

Calculation of equivalent natural period

Equivalent natural period should be calculated using the stiffness of the structure
obtained by a static linear analysis for the structure considering the nonlinear
characteristics of the member and the soil.

[Commentary]
Teq  2.0

Equivalent natural period may be calculated using equation (Eq. C2.2.1).

W
K（C2.2.1）

where, Teq : Equivalent natural period of the structure (sec)
W : Equivalent weight of the structure (kN)
Bridge pier: W = Wu + 0.3Wp
Rigid-frame viaduct: W = Wu + 0.4Wp
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Standard Specifications for Concrete Structures-2007, Design

Wu : Weight of the superstructure. Self weight in the portion subjected to main
vibration and an imposed weight may generally be specified. (kN)
Wp : Weight of the portion of the structure above the soil surface considered in theseismic design except Wu (kN)K : Secant stiffness at the yield point of the structure. K P(kN/m)
δP : Unit lateral force (kN)

 : Lateral displacement for the lateral force P (m).

2.3
2.3.1

Calculation of Response Value
GeneralWhen calculating the response value by the seismic coefficient method using therequired yield point seismic coefficient spectrum, the design cross-sectional force may be
calculated from static linear analysis using structural analysis models for structuralmembers and soil which are modeled by linear elements and a spring, respectively.

[Commentary] This section presents a general method for calculating response values by theseismic coefficient method using the required yield point seismic coefficient spectrum. The
method presented in this section should be adopted in the case where it can be assumed that only
the inertia force of a structure causes seismic effects on the structure. Therefore, in cases where noeffects of soil displacement due to an earthquake can be ignored, the verification using the response
displacement method in which the soil displacement is subjected to the structure is additionallyrequired.

2.3.2

Modeling of structure(1) In cases where the structure is of a continuous shape, the entire system of thecontinuous structure should be modeled. In cases where individual structures havenearly the similar natural period, mode of failure and horizontal load carrying capacity, thestructures may be modeled separately by dividing the system according to the design
vibration unit.
(2) The structure and soil should be integrally combined into a model. In cases where
the plasticity of the foundation or soil has small effects, however, the foundation may bereplaced with a spring for modeling.
(3) For the stiffness of members and soil, the stiffness of the gross cross section may
be reduced considering the nonlinear characteristics at the yielding of the structure
according to the study items.

[Commentary] “Design: General Requirements” stipulate that response values should be
calculated using an analysis model that takes the nonlinear characteristics of materials into
consideration. The objective is to trace the process in which members become plastic based on thetime history. The structural analysis described in this section is aimed at calculating the368Part 2

Seismic Design

displacement and cross section force at the yield point of the structure. Members are assumed tobehave beyond the yield point like the members of the structure used as a model when developing
the required yield point seismic coefficient spectrum on condition that adequate transverse
reinforcement is arranged. Based on this assumption, linear analysis is applied for structural
analysis. Herein, the members suffer the reduction of stiffness due to the effects of cracking at theyield point. The stiffness of members should therefore be evaluated properly. When using therequired yield point seismic coefficient spectra shown in Fig. C2.2.2, the stiffness reduction
coefficient may be specified as shown below for members. For bridge piers or viaducts, stiffness
is reduced only for members in which major nonlinear characteristics are considered. For othermembers, the stiffness of the gross cross section is considered.
Bridge piers:

0.3

Rigid-frame structures: 0.5

2.3.3

Calculation of design response value

For the design cross-sectional force for structures, the cross-sectional force obtained
from the static linear analysis under the inertia equivalent to the design lateral seismic
coefficient should be adopted.

[Commentary] For the design cross-sectional force for structures, the cross-sectional force thatcan be obtained in structural analysis in which the inertia obtained based on the design lateralseismic coefficient is applied should be used. The cross-sectional force obtained here satisfies theyield strength of the structure and serves as a goal when designing members for which plasticizationis considered. As for members in which no plasticization is considered, the nonlinearity of theentire structure for which the required yield point seismic coefficient was assumed should beensured. In addition, the cross-sectional force which is properly incremented according to theyield strength or flexural strength of the member that becomes plastic should be used for design inaccordance with Section 2.4.

2.4
2.4.1

Seismic Performance Verification
GeneralThe design cross-sectional force of each member should be used as the response
value in the seismic performance verification.

[Commentary] In the verification of seismic performance of structures by the seismic coefficientmethod, the yield strength of structures and the shear carrying capacity of members should bechecked using the design cross-sectional force, and the deformability of the members should beensured.

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Standard Specifications for Concrete Structures-2007, Design

2.4.2

Examination for bending moment(1) Safety of the member in which plasticization is allowed against bending moment
should be verified whether or not the design flexural yield capacity, Myd satisfies theconditions expressed by equation (2.4.1) against the design bending moment at thedesign horizontal seismic coefficient, d.
γi  M d / M yd  1.0

where,(2.4.1)

Md : Design bending moment
Myd : Design flexural yield capacity
i : Structural factor, which may be set at 1.0.

(2) Safety of the member for which plasticization is not allowed against the design
bending moment should be verified using equation (2.4.1) where the design bending
moment at an actual yield point seismic coefficient and the restorability of the members inwhich plasticization is allowed is considered.

[Commentary] (2) In order to prevent the occurrence of multiple plastic hinges, as a prerequisite
for applying the required yield point seismic coefficient spectrum, this provision shall be used forthe member for which no plasticization is allowed. In this provision, the cross-sectional force ofthe member at the actual yielding shall be used for simplicity. The seismic coefficient at the yield
point of the member in which plasticization is allowed cannot be fully identical to the design
horizontal seismic coefficient because of the arrangement of reinforcement but exceeds the design
horizontal seismic coefficient. In this Specification, the horizontal seismic coefficient when themember in which plasticization is allowed actually yields is referred to as the actual yield point
seismic coefficient.
This Specification assumes that if the variance between the design horizontal seismic coefficientand the actual yield point seismic coefficient is small in design, the cross-sectional force is nearly
proportional to the seismic coefficient, and stipulates that the actual yield point seismic coefficient
may be calculated using equation (C2.4.1).
The actual yield capacity of the member in which plasticization is allowed should be calculatedusing the actual yield strength of the reinforcement considering all the longitudinal reinforcement
arranged in the cross section as followed in Section 2.4.3 (1).
(Actual yield point seismic coefficient) = (Actual yield capacity of the member for whichplasticization is allowed)/(Cross-sectional force at the design horizontal seismic coefficient) (Design horizontal seismic coefficient)(C2.4.1)

2.4.3

Examination for shear force(1) Safety of the member in which plasticization is allowed against shear forces shouldbe verified whether or not the design shear carrying capacity, Vyd satisfies the condition
expressed by Eq. (2.4.2) against the shear forces in each cross section of the member
when the flexural capacity, Mu in the member is reached.
γi  Vmu / V yd  1.0

where,(2.4.2)

Vmu : Shear force in each cross section of the member when the flexural
370

Part 2

Seismic Design

capacity in the member is reached. Vmu = Mu / La
Mu

: Flexural capacity which is calculated considering all the longitudinal
reinforcement arranged in the cross section. As the nominal value ofthe tensile yield strength of steel, a material modification factor  of
1.2 multiplied by the JIS requirement for lower limit of tensile yieldstrength may be used.

La: Shear span. A half of the member length for rigid-frame viaducts. As
for bridge piers, the height from the bottom of the column to the pointin the superstructure that is subjected to the inertia.

Vyd: Design shear carrying capacity which is calculated in accordance with
"Design: General Requirements."(2) Safety of the member in which plasticization is not allowed against shear forces
should be verified whether or not the design shear carrying capacity, Vyd satisfies thecondition expressed by Eq. (2.4.3) against the design shear force calculated considering
the actual yield strength of reinforcement and the effect of structural characteristics of themember in which plasticization is allowed.
γi  Vd / V yd  1.0

where,(2.4.3)

Vd : Design shear force that is calculated considering the actual yield strengthof reinforcement and the effects of structural characteristics.
Vyd : Design shear carrying capacity.

i : Structural factor which may be set at 1.0.

[Commentary] (1) The member in which plasticization is allowed responds as the deformation
progresses after yielding through the displacement at the maximum flexural capacity, andeventually the ultimate displacement is reached. Therefore, as the design shear force that isassumed the maximum shear acting on the member, the shear forces in each cross section of themember when the flexural capacity in the member is reached is used for the verification. Herein,since the calculating the maximum shear acting on the member is required, the actual yield strengthof reinforcement to calculate the flexural yield capacity should be used. According a provenprocedure, the JIS requirement for lower limit tensile yield strength multiplied by a material
modification factor of 1.2 as long as JIS-conforming reinforcement is used as the actual yieldstrength of reinforcement.
(2) Since both the difference of the actual yield strength to the nominal strength ofreinforcement and the structural characteristics affect on the design shear force, a rate of theincreases in the design shear force at the design horizontal seismic coefficient should be determinedby a preliminary examination with detailed information. The rate of the increase in the design
shear force should generally be set as around 1.5 for a RC beam in single-layer rigid-frame
structures and as around 2 for piles. For the piles with the reduction of the axial force, the design
shear carrying capacity should be calculated considering with the twice of the reduction of the axial
force.

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Standard Specifications for Concrete Structures-2007, Design

2.4.4

Examination for the amount of hoops in portion that becomes plastic

The amount of hoops should be determined so that the prerequisites for developing
the required yield point seismic coefficient spectrum should be satisfied.

[Commentary] In order to provide the member that becomes plastic with the deformability that isassumed when developing the designated seismic coefficient spectrum at the yield point, hoops
should be arranged in the area where members become plastic if the designated seismic coefficient
spectrum at the yield point shown in Fig. C2.2.2 is used.
Vyd / Vmu  2.0

where,(C2.4.4)

Vmu : Shear force in each member cross section of the member when the flexural capacity
in the member is reached. Vmu = Mu / La
Mu : Flexural capacity which is calculated considering all the longitudinal reinforcement
arranged in the cross section. As the nominal value of the tensile yield strength ofsteel, a material modification factor  of 1.2 multiplied by the JIS requirement forlower limit of tensile yield strength may be used.
La : Shear span. A half of the member length for rigid-frame viaducts. As for bridgepiers, the height from the bottom of the column to the point in the superstructure thatis subjected to the inertia.
Vyd : Design shear capacity which is calculated in accordance with “Design: General
Requirements.” For column members, the design shear carrying capacity should be
calculated with the consideration of the axial force at the design horizontal seismic
coefficient.

372

Part 2

CHAPTER 3
3.1

Seismic Design

DESIGN USING NONLINEAR SPECTRA

ScopeThis chapter describes provisions for seismic design using nonlinear spectra.

[Commentary] This chapter presents a standard method of seismic design using nonlinear spectra.
A flowchart of steps of the seismic design method using nonlinear spectra is shown in Fig. C3.1.1.

START

Assumption for the size of a structure and a member

Assumption of the amount of reinforcement

Static nonlinear analysis

Calculation of the equivalent natural period

Judgment of the soil typeCalculation of the plastic response ratio(Nonlinear Spectra)

Calculation of maximum response values of themember (Curvature, shear force)

Judgment of the failure mode of the member

Verification for the curvature andshear force

END

Fig. C3.1.1

Steps of the seismic design method using nonlinear spectra373

Standard Specifications for Concrete Structures-2007, Design

3.2

Loads

(1) Seismic effects on structures should be considered under permanent, variable andaccidental loads. For permanent and variable loads used for seismic performanceverification, refer to "Design: General Requirements."(2) Seismic ground motions in two orthogonal horizontal directions should generally
be considered independently.
(3) As seismic effects, inertia forces of the mass of the structure and of the imposed
mass should be considered.

[Commentary] (1) Used as the design loads for the seismic performance verification arepermanent, variable and accidental loads. The variable loads should be treated as subordinate
variable loads and combined with the seismic effects as the accidental loads. The live loads
among the variable loads may be given an appropriate value in the range from zero to the expectedvalue of the maximum during the design service life. The value should be set properly considering
the fact that the response value depends on the change in stiffness of the structure due to the thermal
effect or other factors and also considering the relationship between the seismic effects and theinterval of recurrence.
(2) The linear spectra shown in this Specification are for the seismic response of structures ofwhich two-dimensional models can be developed. The seismic effects should therefore beconsidered independently in two orthogonal horizontal directions.
(3) Earthquakes have such effects as inertia, soil displacement, earth pressure and hydrodynamic
pressures during an earthquake, and lateral flow due to soil liquefaction. This Specification
presents seismic design methods in cases where only the inertia is taken into consideration. Other
seismic effects should be taken into consideration separately, if any.

3.3
3.3.1

Calculation of Response Values
GeneralWhen calculating response values using nonlinear spectra, the response values ofstructure may be calculated from the load-displacement curves obtained by static
nonlinear analysis using structural analysis models for members and soil which aremodeled by linear elements and a spring, respectively[Commentary] This section shows a general method for calculating response values using
nonlinear spectra in cases where only the inertia of the structure can be assumed to be the effect ofan earthquake. Therefore, in cases where no effects of soil displacement due to an earthquake canbe ignored, the verification using the response displacement method in which the soil displacement
is subjected to the structure is additionally required. Since the yield strength of reinforcement isgenerally higher than that of the JIS requirement for lower limit, higher shear force acts on the
structure than when the nominal strength is used in the calculation. Response values for theseismic performance verification should therefore be calculated both in cases where the JIS
requirement for lower limit of tensile yield strength and the actual yield strength are used for the
calculation.
In cases where actual yield strength is unknown, the lower limit strength of JIS requirement374

Part 2

Seismic Design

multiplied by a material modification factor of 1.2 may be used.

3.3.2

Modeling of structure(1) Structures should be divided into units that vibrate independently for modelingpurposes. If structures continuously in place have nearly the same period, failure modeand lateral load carrying capacity, they may be divided into independently vibrating units
and modeled individually.
(2) The structure and soil should be considered as one unit, and be modeled using
linear elements and a spring, respectively. If the plasticization of the foundation or soil
has small effects, the foundation may be replaced with a support spring when developinga model.
(3) For members and the soil, nonlinear effects should be taken into consideration.
For considering the effects of nonlinearity of members, the methods shown in "Design:
General Requirements" Section 7.2.2.2 may be used. The effects of the nonlinearity ofthe soil should be taken into consideration using an appropriate method.

[Commentary] (1) Nonlinear spectra are generally developed focusing on the dynamic responseof a single structure. Structures should be divided into independently vibrating units to meet theprerequisites. Bridge piers or viaducts that are located continuously may be divided into
appropriate design independent vibrating units in the longitudinal and transverse directions if thestructures have nearly the same period, failure mode and lateral load carrying capacity. In cases
where dividing into the independent vibrating units is difficult, the verification should be made inaccordance with “Design: General Requirements”.
(2) Superstructure and foundation behave as one unit during an earthquake. Superstructure andfoundation may therefore be treated as one unit and may be modeled using linear elements and aspring, respectively. In cases where the soil or foundation has small effect on superstructure, thesuperstructure and foundation may be modeled separately. The effects of the foundation may bemodeled using the support spring of the superstructure in view of the interaction.

3.3.3

Calculation of equivalent natural period

The equivalent natural period should be calculated using the secant stiffness joining
the origin to the yield point of the entire structure on the load-displacement curve that is
obtained in the static nonlinear analysis of the structure considering the nonlinearity ofthe member and soil.

[Commentary] The equivalent natural period should be calculated by the following equation
using the yield stiffness joining the origin to the yield point of the entire structure on theload-displacement curve that is obtained in the static nonlinear analysis of the structure.
Teq  2.0

WK

where,

Teq : Equivalent natural period of the structure (sec)(C3.3.1)

W : Equivalent weight of the structure (kN)375

Standard Specifications for Concrete Structures-2007, Design

Bridge piers: W = Wu + 0.3Wp
Wu : Weight of the superstructure supported by the bridge pier (kN). The
weight of the beam or an imposed weight may generally be used.
Wp : Weight of the portion of bridge pier above soil surface considered in
the seismic design (kN)
Rigid-frame viaducts: W = Wu + 0.4Wp
Wu : Weight of the superstructure of the rigid-frame structure (kN). The
weights of the upper layer beam, deck slab, and an imposed weight
may generally be specified.
Wp : Weight of the portion of the viaduct above soil surface and below thebottom surface of the upper layer beam considered in the seismic
design (e.g. underground beams, middle-layer beams and columns)(kN).
K : Secant stiffness at the yield point of the structure. (kN/m)K

R
δ

(C3.3.2)

R : Lateral load when the yield point is reached for the entire structure (kN).

 : Lateral displacement when the yield point is reached for the entire structure (m)3.3.4

Calculation of design response values(1) The required yield point seismic coefficient spectra that are developed for theplasticization condition of the structure, according to the type of design seismic groundmotion, structural type, material properties and soil type should be used for calculating
the design response value using nonlinear spectra.
(2) When calculating the design response value of the structure using nonlinear
spectra, the response ductility factor should be calculated from the required yield point
seismic coefficient spectrum using the equivalent natural period and yield seismic
coefficient that can be obtained in static nonlinear analysis while regarding the inertia as
an incremental load.
(3) The maximum response displacement of the structure should be calculated using
the response ductility factor. In addition, the angle of rotation of each member and the
response value for the cross sectional force at the maximum response displacement of
the structure should be calculated.

[Commentary] Shown below is a general procedure for calculating the response ductility factorof the structure using the required yield point seismic coefficient spectra.
(i) Obtain the yield point seismic coefficient, Khy in static nonlinear analysis of the entire
structural system.
Defined as the yield point seismic coefficient for the structure, Khy is the seismic coefficientwhen the structural member initially yields.
376

Part 2

Seismic Design(ii) Obtain the equivalent natural period, Teq in accordance with Eq. C3.3.3 Calculation ofEquivalent Natural Period.
Natural period Teq should be calculated by equation (Eq. C3.3.3) using the lateraldisplacement δy / Khy at the yield point seismic coefficient of the structure.
Teq = 2.0×（δy / Khy）1/2(C3.3.3)(iii) Obtain the intersection of (i) and (ii) above using the designated seismic coefficient
spectrum at the yield point and identify the response ductility factor.
The response ductility factor μr identified should be used to calculate the maximum response
displacement δr of the structure by equation (C3.3.4).
δr = δy×μr(C3.3.4)(iv) Calculate the angle of rotation and shear of each member at the maximum response
displacement of the structure.
An example is shown in Fig. C3.3.1.

Required yield point seismic coefficient

The designated seismic coefficient spectrum at the yield point can also be used to estimate thestrength that should be provided to the structure (designated seismic coefficient at the yield point) incases where equivalent natural period Teq and design ductility factor  r are known. The intersectionof curves of equivalent natural period and ductility factor represented by the value along thehorizontal axis indicates the designated seismic coefficient at the yield point.

Fig. C3.3.1

3.4

Resp. duct.
factor μr=3.0

Khy = 0.6

Teq = 1.0 sec

Equivalent natural period (sec)Method for obtaining the response ductility factor, μr from equivalent natural
period, Teq and seismic coefficient at the yield point, Khy

Seismic Performance Verification(1) Seismic performance should be verified regarding the failure mode of the member
using the angle of rotation and shear of each element as response values.
(2) The failure mode of the member should be checked as shown below.

Vmu / Vyd≦

1.0 : Flexural failure mode

Vmu / Vyd＞

1.0 : Shear failure mode

where,

Vmu : Shear force when flexural strength develops in the member. Vmu = Mu / La

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Standard Specifications for Concrete Structures-2007, Design

Mu: Flexural load carrying capacity of the member. Calculated considering
all the longitudinal reinforcement arranged in the cross section. As thestrength of steel, the characteristic value multiplied by the material
modification factor m should be used.

La: Shear span.

Vyd: Design shear carrying capacity of the member.

(3) The seismic performance of the structure should be verified that each element andmember satisfy equation (3.4.1).

γi・Sd / Rd
where,

Sd≦

1.0(3.4.1): Design response value.
Angle of rotation and shear force of each element at the maximum
response displacement obtained from the nonlinear spectra.

Rd: Design limit value.
Design shear carrying capacity and ultimate angle of rotation or
ultimate displacement of the member.
Herein, the design shear carrying capacity of the member should bespecified for the minimum cross-sectional area of shear reinforcementat out of the plastic hinge.

γi: Structural factor which may be set at 1.0.

[Commentary] (1) Members should be verified according to the failure mode of the members
because the response of and the damage in the members vary according to the failure mode.
For the member to which the flexural failure mode is considered to be applicable, the angle ofrotation of the member in the form of a plastic hinge should be verified. As for the member towhich the shear failure mode is considered to be applicable, shear carrying capacity should beverified. When checking either of the parameters, limit values should be specified. Here, themember to which the shear failure mode is considered to be applicable rapidly loses its horizontal
resistance when flexural yielding occurs. The verification should therefore be made to determine
whether flexural yielding occurs or not.
(2) The failure mode of a RC member should be identified by comparing the shear carrying
capacity of the member with the maximum shear occurring in the member when the flexural
capacity is reached. Then, the maximum shear occurring in the member should be obtained from
actual flexural capacity. For calculating the flexural capacity, the material strength should be used
where all the longitudinal reinforcing bars are considered and the actual yield strength of the tensile
steel is taken into consideration. In cases where SD295, SD345 or SD390 reinforcing bars areused as tensile reinforcement, a material modification factor m of 1.2 multiplied by the lower limit
strength of the JIS requirement may be used as the nominal value of tensile yield strength.
In simple structures, Vmu can be obtained direct from the design flexural capacity by properly
assuming the shear span. In cases where assuming the shear span is difficult such as in pile
members or statically indeterminate structures, no shear failure occurring due to a shear at the point
where the load carrying capacity of the structure reaches the maximum seismic coefficient may be
378

Part 2

Seismic Design

determined as a failure mode using equation (Eq. C3.4.1). Then, if equation (Eq. C3.4.1) issatisfied, the verification may be made as a member to which flexural failure is applicable.
γi・Vd / Vyd＞1.0(C3.4.1)

where, Vyd : Design shear
Vd: Design shear carrying capacity.
i: Structural factor which may be set at 1.0.

The design shear carrying capacity should be calculated using the minimum cross-sectional areaof shear reinforcement in the member. In calculation, the effects of a shear span to depth ratio
should be considered in accordance with “Design: General Requirements.”(3) When specifying the limit of the angle of rotation of the member in accordance with Section
7.2.2.2 of “Design: General Requirements,” the limit may be specified using equation (Eq. C3.4.2).
As the longitudinal reinforcement used for calculating the limit of the angle of rotation, the hoop
located in the plastic hinge zone or closed stirrup should be used. In the plastic hinge zone,
adequate reinforcement should be arranged so as to meet the requirements specified in this section
and based on the Explanation in Section 2.4.4.
θn=θm+η{1－(Mn / Mm)}

(C3.4.2)

where, θn : Ultimate angle of rotation. Specified in compliance with Section 7.2.2.2 of “Design:
General Requirements.”η: Factor to consider the softening gradient of the member which may generally be set
at 1.0.

θm: Angle of rotation at the maximum strength. Specified in accordance with Section
7.2.2.2 of “Design: General Requirements.”

Mn : Bending moment at the ultimate angle of rotation.
specified.

Yield bending moment may be

Mm : Bending moment at the maximum load carrying capacity.

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Standard Specifications for Concrete Structures-2007, Design

PART 3 DURABILITY DESIGNCHAPTER 1
1.1

GENERAL

Scope

This Specification presents a method for ordinary concrete structures built underordinary conditions to meet the provisions in Chapter 8 of "Design: General
Requirements."[Commentary] Structures should meet the designated performance requirements throughout theirdesign service life. Chapter 8 of "Design: General Requirements" describes the methods forverifying that no problems occur throughout the design service life due to the deterioration ofmaterials in the structure subjected to chloride intrusion, carbonation, frost action or chemical
intrusion. Structures are checked for expected deterioration phenomena. The structures built underordinary environment with few effects of chloride intrusion may actually pass various durability
checks described in Chapter 8 of "Design: General Requirements" easily if highly durable concretewith a water-cement ratio below a certain level is used, a certain concrete cover depth is provided
and the crack width is held to a certain level. For such structures, therefore, design work may be
simplified by selecting the concrete cover and water-cement ratio that pass the check forcarbonation. Chapter 2 of this Specification presents the minimum concrete cover and water-cement
ratio of concrete that should be provided by concrete structures constructed under a generalenvironment for the beam, column and slab. A general environment here refers to an environment
free from the fear of chloride intrusion, frost action or chemical intrusion. Selecting concrete cover
and water-cement ratio in the specified range and achieving the limit crack width shown in
Section 8.3.2 of Chapter 8 of "Design: General Requirements" enable the elimination of durability
check described in Chapter 8 of "Design: General Requirements".
If a structure is away from the seacoast by at least 1.0 km, it is generally free from the effects offlying salt. Even if the structure is away from the seacoast by a larger margin, it may sometimes be
subjected to the effects of flying salt depending on the surrounding topography and meteorologicalconditions including monsoon or oceanographic conditions. Decision should therefore be made forindividual structures.
For structures vulnerable to chloride intrusion due to flying salt ,or special structures or
structures requiring a high level of durability although not under the effects of flying salt, durability
check should be made as stipulated in Chapter 8 of "Design: General Requirements".
When conducting durability check using the method described in Chapter 8 of "Design: General
Requirements", if the range of combinations of specifications for passing the durability test is
known easily, it will contribute to efficient design work. Chapter 3 of this Specification presents
nomograms and mathematical tables that facilitate the identification of the range of parameters forconcrete that passes durability tests for chloride intrusion, carbonation, frost action or chemical
intrusion such as the material, mix proportions and concrete cover.

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Part 3 Durability Design

CHAPTER 2

CONCRETE COVER OF STRUCTURES UNDER ORDINARY ENVIRONMENTS(1) If an ordinary structure constructed under a general environment meets therequirements for the water-cement ratio of concrete and the concrete cover shown in
Table 2.1 and the crack width is below the limit shown in Section 8.3.2 of Chapter 8 of"Design: General Requirements", the structure may be assumed to pass the check forcarbonation specified in Chapter 8 of "Design: General Requirements."

Table 2.1 Minimum concrete cover and maximum water-cement ratioof structures meeting standard durability requirements*
Maximum value of
W/C**

Minimum concrete
cover c (mm)Construction error ∆ce(mm)Column

50

45

±15

Beam

50

40

±10

Slab

50

35

±5

Bridge Pier

55

55

±15

* A design service life of 100 years is assumed.
** Ordinary Portland cement is used.

(2) When the durability check specified in Chapter 8 of "Design: General
Requirements" is eliminated by adopting the water-cement ratio and concrete covershown in Table 2.1, the values of the parameters should be presented in the design
drawings.

[Commentary] (1) In concrete structures constructed under a general environment with little
chloride intrusion, the corrosion of reinforcing bars can be prevented by giving concrete cover so as
to provide adequate durability against deterioration factors such as carbonation expected under an
ordinary environment. The concrete cover is generally provided by the design engineer
considering concrete quality, environmental conditions of the structure, construction error andimportance of the structure with a view to passing durability check. Shown here are standard
combinations of concrete quality and concrete cover for which durability check may be eliminatedwithout causing any problem under a general environment. Table 2.1 lists the standard values forthe maximum water-cement ratio, minimum concrete cover and construction error for concrete
using ordinary Portland cement, for respective members. If the requirements listed in the table aresatisfied and the crack width is below the limit under a general environment shown in Section 8.3.2
of Chapter 8 of "Design: General Requirements", the structure may be assumed to pass the checkfor carbonation described in Chapter 8 of "Design: General Requirements. Table 2.1 assumes nocases where either inspection or repair is difficult for the completed structure, where the structure isconstructed under severe conditions or where precast members are used even under a generalenvironment. In these cases, it should be verified that durability requirements are met based on the
results of durability check described in Chapter 8 of "Design: General Requirements."

381

Standard Specifications for Concrete Structures-2007, Design(2) As stipulated in Chapter 4 of "Design: General Requirements," the design drawings should
carry all the characteristic values specified in design and be handed to construction engineers. The
characteristic values for concrete concerning durability check include the coefficient of rate ofcarbonation, chloride ion diffusion coefficient and relative dynamic modulus of elasticity. If the
durability check described in Chapter 8 of "Design: General Requirements" is eliminated inaccordance with this Specification by adopting the concrete cover and water-cement ratio shown in
Table 2.1, the concrete cover and water-cement ratio should be provided in design drawings insteadof the characteristic values for durability check. The assumed construction error should also be
provided.

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Part 3 Durability Design

CHAPTER 3
3.1

SIMPLE DESIGN METHOD CONCERNING DURABILITY

GeneralThis chapter describes simple methods for identifying the range of parameters such asconcrete materials, mix proportions and cover that pass the test in the durability check forchloride intrusion, carbonation and chemical intrusion shown in Chapter 8 of "Design:
General Requirements."[Commentary] This chapter presents nomograms and mathematical tables that facilitate theidentification of the range of parameters such as concrete material, mix proportions and cover thatsatisfy various check equations shown in Chapter 8 of "Design: General Requirements". Values
are obtained by back calculation of solutions satisfying the check equations shown in Chapter 8 of"Design: General Requirements" under limited conditions.

3.2
3.2.1

Chloride Attack
Check for steel corrosion due to chloride ion ingress(1) In order to pass the test in the check for the corrosion of reinforcement steel due tochloride ion intrusion under an environment causing chloride ion intrusion, an
appropriate combination of design concrete cover cd and design diffusion coefficient forchloride ion Dd should be specified.
(2) In order to achieve the specified design diffusion coefficient Dd, an appropriate
combination of the width of flexural crack and water-cement ratio of concrete should bespecified.

[Commentary] (1) Figure C 3.2.1 is used to simply find a combination of design concrete cover
cd and design diffusion coefficient Dd for chloride ion that passes the test in durability check, under
the given conditions without using any equations shown in Chapter 8 of "Design: General
Requirements" when conducting durability check for the corrosion of reinforcement steel due tochloride ion intrusion described in Chapter 8 of "Design: General Requirements". Equation (8.3.5)
in the "Design: General Requirements" (iCd/Clim = 1) is effective along the boundary line between
the areas with and without chloride intrusion.
Figure C 3.2.1 can be used as described below.
(i) Chloride ion concentration on concrete surface C0 is specified according to theenvironmental conditions given.
(ii) Limit concentration for the occurrence of steel corrosion Clim is specified.
(iii) Safety factors cl and i are specified.
(iv) cl C0/(Clim/i) is calculated using the values (i) through (iii) above.
(v) The value obtained in (iv) is plotted on the vertical axis. A straight line is drawn from thepoint that cuts the line, parallel to the horizontal axis.

383

Standard Specifications for Concrete Structures-2007, Design(vi) The value of the intersection of the straight line drawn in (v) above and a curve representing
Dd  t .

iCd/Clim = 1 is read on the horizontal line as cd(vii) Service life t for chloride ion intrusion is substituted in cd
obtain c d

Dd  t obtained in (vi) to

Dd . The result is the limit value for the combination of design concrete cover cd anddesign diffusion coefficient for chloride ion Dd that passes the examination in the check(combination of the minimum design concrete cover and the maximum design diffusion
coefficient).
(viii) If cd or Dd is properly specified, the range of the other parameter for passing theexamination in the check may be obtained.
15

γi

10
γcl C 0
C lim
γi

Cd
=1
C lim

Not acceptable
5

Acceptable

0
0

5

10

15
Cd

20

25

30

Dd t

Fig. C 3.2.1 Combination of design concrete cover cd and design diffusion coefficientfor chloride ion Dd that passes the examination for chloride attack

Exp. Table 3.2.1 lists the limit values of parameters that pass the examination in the "check forsteel corrosion due to chloride attack " described in Chapter 8 of "Design: General Requirements".
The table shows the relationships between the parameters on the boundary line between the areas
with and without chloride intrusion in Fig. C 3.2.1, or in the case where (iCd/Clim = 1) is effective
in equation (8.3.5) in the "Design: General Requirements". The objective of the table is also to
simply find a combination of design concrete cover cd and design diffusion coefficient for chloride
ion Dd that passes the test in the check under given conditions without using any equations shown in
Chapter 8 of "Design: General Requirements". The values in the table were obtained under thefollowing conditions. The values should not be used as they are under different conditions.
Chloride ion concentration on concrete surface C0: Value shown in Table C 8.2.2 of the "Design:
General Requirements."
Limit concentration for the occurrence of corrosion of reinforcement steel Clim: 1.2 kg/m3.
384

Part 3 Durability Design

Safety factor cl considering the variation of design chloride ion concentration at the location ofreinforcement Cd: 1.3.

Table C 3.2.1 Maximum design diffusion coefficient for passing the examination for chloride
ingress Dd (approximate value)
designconcrete cover (mm)
かぶりの設計値（mm）
40
50
60
0.123
0.192
0.276
0.128
0.184
0.11
-

70
0.376
0.25
0.15
-

100
0.767
0.511
0.307
0.153

150
1.72
1.15
0.69
0.345

200
3.07
2.04
1.23
0.613

3
3
near
sh oreline 0(C汀線付近（C）)=9kg/m0=9kg/m
25
30
耐用年数
life
time
20年
20
year
30年
30
year
50年
50
year
100年
100yeardesignconcrete cover mm(mm)
かぶりの設計値（
）
35
40
50
60
0.15
0.235
0.338
0.115
0.1
0.156
0.225
0.135
-

70
0.46
0.307
0.184
-

100
0.939
0.626
0.375
0.188

150
2.11
1.41
0.845
0.422

200
3.75
2.5
1.5
0.751

3)
0.1km
from0.1km
coast（(C=4.5kg/m3）
C00=4.5kg/m
海岸から
耐用年数
25
30
life
time
20年
0.14
20
year
30年
30
year
50年
50
year
100年
100year

35
0.191
0.127
-

designconcrete cover mm(mm)
かぶりの設計値（
）
40
50
60
0.249
0.389
0.561
0.166
0.26
0.374
0.156
0.224
0.112

70
0.763
0.509
0.305
0.153

100
1.56
1.04
0.623
0.311

150
3.5
2.34
1.4
0.7

200
6.23
4.15
2.49
1.25

0.25kmfrom coast (C00=3kg/m=3kg/m33）)
海岸から0.25km（C
耐用年数
25
30
life
time
0.216
0.15
20年
20
year
30年
0.1
0.144
30
year
50年
50
year
100年
100year

35
0.295
0.196
0.118
-

designconcrete cover (mm)
かぶりの設計値（mm）
40
50
60
0.385
0.601
0.866
0.256
0.401
0.577
0.154
0.24
0.346
0.12
0.173

70
1.18
0.785
0.471
0.236

100
2.4
1.6
0.962
0.481

150
5.41
3.61
2.16
1.08

200
9.62
6.41
3.85
1.92

3)
0.5km
from coast (C00=2kg/m=2kg/m3）
海岸から0.5km（C
25
30
耐用年数
life
time
20年
0.288
0.414
20
year
30年
0.192
0.276
30
year
0.115
0.166
50年
50
year
100年
100yeardesignconcrete cover (mm)
かぶりの設計値（mm）
35
40
50
60
0.564
0.737
1.15
1.66
0.376
0.491
0.768
1.11
0.226
0.295
0.461
0.663
0.113
0.147
0.23
0.332

70
2.26
1.5
0.903
0.451

100
4.61
3.07
1.84
0.92

150
10.4
6.91
4.14
2.07

200
18.4
12.3
7.37
3.68

3)
1km
from coast (C00=1.5kg/m=1.5kg/m3）
海岸から1km（C
25
30
life
time
耐用年数
0.893
20
20年
year
0.62
0.413
0.595
30年
30
year
50年
0.248
0.357
50
year
100年
0.124
0.179
100yeardesignconcrete cover mm(mm)
かぶりの設計値（
）
35
40
50
60
1.22
1.59
2.45
3.57
0.81
1.06
1.65
2.38
0.486
0.635
0.992
1.43
0.243
0.317
0.496
0.714

70
4.86
3.24
1.94
0.972

100
9.92
6.61
3.97
1.98

150
22.3
14.9
8.93
4.46

200
39.7
26.4
15.9
7.93

3
splashzone 0(C飛沫帯（C）3)=13kg/m0=13kg/m
25
耐用年数
life
time
20年
20
year
30年
30
year
50年
50
year
100
年
100year

30
-

35
-

Extremely small Dd values (0.1 or smaller) have been eliminated.
(2) The characteristic value Dk of chloride ion diffusion coefficient represents inherent
characteristics of concrete. It is dependent on the concrete materials and mix proportions, and canbe obtained by a designated testing method. Additionally, Chapter 5 of "Design: General
Requirements" provides equations for predicting the diffusion coefficient from the water-cement
ratio of concrete in cases where ordinary Portland cement, blast furnace slag cement or silica fumeis used.
Figure C3.2.2 shows the "relationship between water-cement ratio and design diffusion
coefficient" calculated using the relation between the water-cement ratio and concrete chloride ion
diffusion coefficient (C5.2.25) shown in Chapter 5 of "Design: General Requirements" and the385

Standard Specifications for Concrete Structures-2007, Design

design value of diffusion coefficient Dd [cm2/year]

equation for predicting diffusion coefficient considering flexural cracking (8.3.8) shown in Chapter
8 of "Design: General Requirements". As the calculation conditions, concrete cover c was 50 mm,
allowable crack width wa was 0.2 mm, concrete material coefficient c was 1.0, and the constantrepresenting the effect of cracking on the transfer of chloride ions in concrete D0 was 200 cm2/year.
Cases were assumed where the crack width was 0.5, 0.75 or 1.0 time the allowable crack width.
This figure shows combinations of the maximum flexural crack width and the maximum
water-cement ratio for achieving the target design diffusion coefficient. In cases where theconditions are somewhat different from the above calculation conditions, the qualitative tendency
between the two parameters is more or less the same, so the figure is applicable. The values in the
figure, however, should not be used as they are.
10.0
limit
許容ひび割れ幅wa=0.2mm
value of crack width wa=0.2mm

]N
・
2/
m
[c
d 1.0
D
・
・
W
・
U
g・
・

withoutcrack
ひび割れなしw=0.5wa
w=0.75wa
w=wa

0.1
0.20

0.30

0.40

0.50

0.60

0.70

0.80

水セメント比W/C
water-cement
ratio W/C

Fig. C3.2.2

Effects of water-cement ratio and crack width on diffusion coefficientExp. Fig. 3.2.2 can be used as described below.
(i) A crack width is specified for control purposes, and the curve to be used is determined. (Asan example, w is set to be 0.15 mm, or 0.75 wa).
(ii) The value of design diffusion coefficient Dd used for checking for steel corrosion is plottedon the vertical axis. Then, a straight line is drawn from the point cut by the vertical axis, parallel tothe horizontal axis.
(iii) Water-cement (W/C) ratio is obtained from the intersection of the straight line drawn in (ii)above and the curve at w = 0.75 wa.
(iv) The water-cement ratio obtained in (iii) above is the upper limit of allowable water-cement
ratio.
Table C3.2.2 is a mathematical table for simply obtaining the maximum water-cement ratio andcrack width required for achieving the target design diffusion coefficient Dd. The values in the tableshould not be used as they are under different conditions than those in this table.

386

Part 3 Durability Design

Table C3.2.2 Design diffusion coefficient Dd calculated from crack width andwater-cement ratio
W/C
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
0.70

(mm)
crack
width (mm)
ひびわれ幅
0.1
0.15
0.2
without
crack
ひび割れ無
0.20
0.271
0.429
0.751
0.35
0.413
0.567
0.873
0.57
0.633
0.782
1.08
0.89
0.95
1.1
1.38
1.33
1.39
1.53
1.81
1.90
1.96
2.1
2.37
2.60
2.65
2.79
3.05
3.39
3.45
3.58
3.84
4.24
4.29
4.42
4.68

Calculation conditions
Type of cement: Ordinary Portland cement
Concrete cover c: 50 mm
Allowable crack width wa: 0.2 mm
Material coefficient for concrete c: 1.0
Constant indicating the effect of cracking on the transfer of chloride ions in concrete D0: 200
cm2/year

3.2.2

Specification of coefficient of chloride ion diffusion in concrete

Coefficient of chloride ion diffusion in concrete may be obtained by any of thefollowing methods.
(1) Use of the relationship between water-cement ratio and apparent diffusion
coefficient(2) Laboratory tests using electrophoresis or soaking method, or weathering tests(3) Investigations of actual structures[Commentary] The coefficient of chloride ion diffusion in concrete is affected by the material
and mix proportions used, and also by the environmental conditions. The diffusion coefficient
may vary even if the same material and mix proportions are adopted. The methods for obtaining
diffusion coefficients subjected to various effects include the use of the relationship between thewater-cement ratio and apparent diffusion coefficient from existing data, implementation oflaboratory tests, and use of core samples collected from existing structures that are under the similar
natural conditions and expected to be subjected to similar actions to those for the structure to be
designed, or of exposed specimens.
(1) Several regression equations have been developed based on the surveys of distributions ofchloride ions in existing concrete as equations for predicting the apparent diffusion coefficient fromconcrete material and mix proportions. Section 5.2.12 of "Design: General Requirements" provides
equations for predicting the apparent diffusion coefficient from water-cement ratio in cases where
ordinary Portland cement, blast furnace slag cement or silica fume is used.
(2) For obtaining chloride ion diffusion coefficient in laboratory tests, refer to JSCE 571:
Method for Testing Effective Diffusion Coefficients of Chloride Ions in Concrete byElectrophoresis (draft) and JSCE 572: Method for Testing Apparent Diffusion Coefficients ofChloride Ions in Concrete by Soaking (draft). When using core samples collected from actual387

Standard Specifications for Concrete Structures-2007, Design

structures, refer to JSCE 573: Method for Measuring the Distribution of Chloride Ions in Concretein Actual Structures (draft).
Laboratory tests (refer to Table C3.2.3) are beneficial because they enable the direct acquisitionof diffusion coefficients for the material and mix proportions related to material design. The
degree of freedom increases in using concrete materials and mix proportions. Laboratory tests are
therefore effective for using new types of materials in particular.

Table C3.2.3 Methods for obtaining diffusion coefficients in laboratory tests
Test method

Electrophoresis

Soaking method

Standard

Remarks

JSCE 571: Method for Testing Effective Diffusion
Coefficients of Chloride Ions in Concrete byElectrophoresis (draft)

Conversion of effective
diffusion coefficient toapparent diffusion coefficientis required.

JSCE 572: Method for Testing Apparent Diffusion
Coefficients of Chloride Ions in Concrete by Soaking(draft)In the soaking method, concrete specimens are soaked in salt water with increased density for adesignated period of time, the specimen is sliced to obtain chloride ion concentration in concrete atdifferent depths and the diffusion coefficient is calculated from the distribution of chloride ion
concentrations. One of the benefits of the method is the direct acquisition of apparent diffusion
coefficients used for checking as stipulated in the specifications. The test, however, requires
several months. The test period is expected to be more than one year for concrete with a low
water-cement ratio of 40% or lower. In cases where chloride ions enter concrete only near theconcrete surface while the soaking method is adopted because of a low water-cement ratio, thedistribution of concentrations should be obtained for calculating the apparent diffusion coefficient,in accordance with JSCE G574: Planar Analysis Method for Elements in Concrete by the EPMA
Method (draft).
In electrophoresis, chloride ions are forced to move by applying direct current constant voltage
to concrete, and the rate of movement is used to obtain the diffusion coefficient. The test isfinished within one month and effective for measuring the diffusion coefficient in concrete with a
low water-cement ratio for which the soaking method requires a long time. Electrophoresis aims
at measuring not the apparent diffusion coefficient shown in specifications but the effective
diffusion coefficient that represents the ease of movement of chloride ions in concrete micro poresolution. The values obtained by electrophoresis cannot be used as they are for checking thespecifications. The effective diffusion coefficient is converted to the apparent diffusion coefficientfor checking purposes because two are theoretically correlated to each other.
When using the specimens for weathering tests, electrophoresis is effective because it canreflect the environmental conditions of the structure to be designed relatively properly. The
weathering period increases at a low water-cement ratio as for the soaking method.
(3) A method is available for measuring chloride ion distribution in concrete in a structure
separate from the methods of chloride ion diffusion coefficient testing in laboratory. In thismethod, samples are collected from structures and chloride ions in samples are analyzed to
specifications, and the apparent diffusion coefficient is calculated based on the measured
388

Part 3 Durability Design

distribution of chloride ion concentrations. The diffusion coefficient in concrete in an actual
structure obtained can be reflected direct in a new structure.

3.2.3

Chloride ion concentration on concrete surface

The chloride ion concentration used for chloride intrusion checking may be specified
according to the volume of flying salt in the study area.

[Commentary] When checking the chloride intrusion by the method described in Chapter 8 of"Design: General Requirements", the effects of flying salt on the volume of chloride ion intrusion isconsidered based on the chloride ion concentration on concrete surface C0. Chloride ion
concentration on concrete surface C0 has been known to vary according to the climate of the area
where the structure is constructed, topography surrounding the structure and element of thestructure. Using the value of chloride ion concentration on concrete surface C0 based on theexisting records and measurements for similar structures is desirable because the concentration well
represents the environmental conditions of the structure.
The volume of flying salt that affects the chloride ion concentration on concrete surface has
been known to be determined not only by the distance from the seashore or elevation but also by theregional characteristics, e.g. whether the region is located on the coast of the Japan Sea or the
Pacific Ocean. The past surveys have revealed that the volume of flying salt is higher along thecoast of the Japan Sea in the Hokkaido, Tohoku and Hokuriku regions than in the coastal areas inother regions. In Okinawa Prefecture, the volume is also high. A conceivable reason may be thepassage of winter monsoon or typhoons. Chloride ion concentration on concrete surface should
therefore be specified according to the meteorological conditions of the region under study.
Section 8.2 of "Design: General Requirements" provides a mathematical table for specifying
chloride ion concentrations on concrete surface according to the region where the structure islocated, distance from the structure to the seashore and elevation (Table C8.2.2). The surface
chloride ion concentrations in the table may be used if the past records or measurements for similar
structures are not used.
The chloride ion intrusion into concrete is affected by the volume of flying salt that adheres toconcrete surface. The volume of chloride ions on concrete surface may sometimes be higher on
the sea side of a bridge that is parallel to the coastal line than on the land or mountain side. The
salt that adheres to concrete surface may sometimes be removed by rain, wind or snow. The values
shown in Table C8.2.2 in Chapter 8 of "Design: General Requirements" do not reflect such local
conditions but are for the elements of a structure susceptible to chloride intrusion because of a large
volume of flying salt.

3.3

Carbonation

For checking steel corrosion due to carbonation, an appropriate combination of design
concrete cover cd and water-cement ratio should be selected according to theenvironmental conditions.

[Commentary] In order to pass the test for carbonation checking, the design thickness ofcarbonated concrete (thickness of carbonated concrete at the end of design service life) should notreach the limit thickness for the occurrence of steel corrosion. To that end, concrete cover should
be increased to increase the limit thickness for the occurrence of steel corrosion or concrete should389

Standard Specifications for Concrete Structures-2007, Design

be made resistant to carbonation by reducing the water-cement ratio of concrete.
Figure C3.3.1 shows a sample area where the design concrete cover cd and water-cement ratio
W/C of concrete used for environmental conditions check meet the requirements in carbonation
check. The figure is drawn while standard safety factors are used (cb = 1.15, c = 1.0, i = 1.0 and p= 1.0), constant representing the environmental conditions e is 1.6 (likely to get dry), service life
for carbonation t is 100 years, concrete cover minus thickness of carbonated concrete ck is 10 mm
and the diameter of reinforcement steel is 25 mm. If these parameters have different values, thisfigure is inapplicable without modifications.
If concrete with a low water-cement ratio is used, the requirements can generally be met incarbonation check even with a thin concrete cover. Concrete cover should, however, not be less thanthe diameter of reinforcement steel.

design concrete cover used in verificati
of durabilitycd [mm]

70
60
50

combination of design concrete cover c d
and water-cement ratio W/C that pass theexamination

40
where

30



y d   i  cb  c  p e t  3.57  9.0 WC

γcb =1.15, γc =1.0, γi =1.0,
γp =1.0, βe =1.6, t =100year

20
10
0
0.35

cd   i  y d  ck

lower limit of design concrete coverin case that bar diameter is 25mm
0.40

0.45

0.50

0.55

0.60

0.65

water-cement ratio W/C

Fig. C3.3.1

3.4

A sample relation between the thickness of carbonated concrete andwater-cement ratio

Damage from Freezing and Thawing

For checking damage from freezing and thawing, an appropriate combination of aircontent in concrete and water-cement ratio should be selected according to theenvironmental conditions.

[Commentary] To check damage from freezing and thawing, it should be verified in freezing andthawing tests that the design relative dynamic modulus of elasticity Ed exceeds i Emin (where i is a
structure factor and Emin is the minimum limit value of relative dynamic modulus of elasticity infreezing and thawing tests). In the design phase, therefore, a design value may be specified higher
390

Part 3 Durability Design

than the minimum limit value of relative dynamic modulus of elasticity that meets the performancerequirements for concrete structures against damage by freezing and thawing, referring to Table
8.4.1 in Chapter 8 of "Design: General Requirements". If a high relative dynamic modulus ofelasticity of 100% is specified as the design value, for example, the requirements for checking may
be met but the conditions for mix proportions become severe during the production of concrete. For
reference, plotted on Fig. C3.4.1 are relationships between water-cement ratio and relative dynamic
modulus of elasticity in freezing and thawing tests available in existing researches. The polygonalline in the figure shows a relationship for the maximum water-cement ratio for achieving thedesignated relative dynamic modulus of elasticity shown in Section 5.2.8 of "Design: General
Requirements". The air content of concrete varies from 4 to 7%.

relative dynamic modulus
相対動弾性係数(%)
of elasticity (%)

100
90
80
70
混 和材 無しwithout
admixtures
フライア
fly
ash ッ シ ュ混 入Cha
r 5, .2.8
Table 5.2.8
5章pte表5

60
50
20

30

40
50
60
水セメント比(%)
water-cement ratio (%)

70

Fig. C3.4.1 Relationship between water-cement ratio of concrete andrelative dynamic modulus of elasticity in freezing and thawing test

In cases where the characteristic value for the relative dynamic modulus of elasticity is 90% or
higher in the freezing and thawing tests for an ordinary structure, or where water-cement ratio is
45% or lower and air content is 6% or higher where the structure is affected by chlorides in deicing
agents or sea water, the check for damage by freezing and thawing may be eliminated.
In cases where the structure is required to maintain high level of durability, or maintain theinitial soundness without losing its aesthetic value during its service life, the relative dynamic
modulus of elasticity and mass of the specimen should not be reduced in freezing and thawing tests.
The design relative dynamic modulus of elasticity during freezing and thawing testing should
sometimes be set at 95% or higher.

3.5

Chemical Attack
The design depth of chemical attack should be set below the design concrete cover.

[Commentary] If the design concrete cover has been specified under certain design conditions,the check requirements can be met by specifying the design depth of chemical attack below thedesign value of concrete cover. Then, instructions should be given to manufacture concrete so as
to meet the specified depth of chemical attack. For the concrete structures constructed against
391

Standard Specifications for Concrete Structures-2007, Design

expected chemical attack, it should be verified that the concrete is sufficiently resistant to chemical
attack based on the results or records of existing researches or the results of experiments.
When specifying the depth of chemical attack during the service life first, check requirements
may be met by specifying the design concrete cover larger that the depth of chemical attack. Then,however, the maximum value among the design values of concrete cover specified under different
conditions should be specified as the design concrete cover.

392

Part 4 Thermal Stress Analysis

PART 4

THERMAL STRESS ANALYSISCHAPTER 1
1.1

GENERAL

Scope

This Specification presents examples of thermal and stress analyses required forverifying whether the cracking due to cement hydration affects the performance of theconcrete structure or not as stipulated in Chapter 12 of "Design: General Requirements".
Examples of analysis models and standard values representing the thermal andmechanical properties of materials required for analysis are also presented.

[Commentary] For verifying whether cracking occurs or not owing to cement hydration andchecking crack width, the heating due to cement hydration, resultant concrete temperature
variations and changes in volume of concrete due to temperature variations and autogenous
shrinkage should be identified accurately. The stress of concrete caused by volumetric change
should be calculated accurately. With the remarkable improvement of arithmetic processing
capacity of computers in recent years, analytical processing now requires less time than before andvarious analysis methods and models are available. The analysis methods and models have bothadvantages and disadvantages. The most appropriate analysis method and model should be selectedconsidering various conditions. This Specification shows standard analysis methods for verifying
whether the initial cracks due to cement hydration affect the performance of concrete structures ornot. Chapters 2 and 3 present standard methods for thermal analysis and stress analysis of concrete,respectively. Chapter 4 describes the mechanical and thermal properties of concrete and the thermal
properties of soils and rocks that are required for the above analyses.

393

Standard Specifications for Concrete Structures-2007, Design

CHAPTER 2

THERMAL ANALYSIS

2.1 Analytical Methods
The thermal analysis of concrete shall be conducted using adequate methods inaccordance with factors such as the type and configuration of the structure.

[Commentary] The methods of the thermal analysis of concrete include numerical methods suchas finite element method, finite difference method, simplified numerical method such as Schmidt orCarlson method, and simplified calculation methods with the use of figures and tables, whichever
can be used. Thermal analyses of concrete can also be classified into linear analyses, which assume
that heat generation characteristics and thermal properties are not dependent on temperature, andnonlinear analyses, which allow for temperature dependence. However, since each method has
limitation in its application, it is necessary to select the most adequate method considering therequired accuracy of the analysis and various conditions of the structures subjected to the analysis.
In thermal analysis, it is necessary to determine a valid analytical model and boundary conditions inaccordance with environmental and other conditions of the objective structure. Calculation oftemperature changes and thermal stresses may be conducted until the temperature change becomespractically stationary.

2.2

Boundary and Initial Condition

The boundary and initial condition used in the thermal analysis of concrete shall be
determined adequately considering such factors as the configuration of the structure, theconditions of heat dissipation and the initial temperature of the concrete.

[Commentary] The determination of boundary conditions is as fundamental as that of theanalytical model and has a significant influence on the results of the analysis. The heat transfer
boundary is a boundary where heat is transferred between the concrete and atmosphere and thefixed temperature boundary is a boundary where the temperature is kept constant. In general,
radiation can be ignored in the thermal analysis of concrete.
The heat transfer boundary shall be characterized by the coefficient of heat transfer. The
coefficient of heat transfer shall be determined considering such factors as the use or nonuse of
concrete forms, their type and thickness, the time from placement until stripping, curing method andwind speed.
Dealing directly with convection and diffusion of air layers near the boundary is one way toaccurately reflect the characteristics of the heat transfer boundary. Characteristics of the heattransfer boundary, however, can be easily reflected in analyses by using a coefficient of heattransfer reflecting the average effect of those characteristics. The coefficient of heat transfer has asignificant influence on concrete temperature at and near the surface of members, and also on thetemperature rise in the interior when the thickness of the member is relatively thin. The influence ofwind velocity on the exposed surface of concrete is generally expressed as 12-14 W/m2 ºC in termsof the coefficient of heat transfer per 2-3m/s of wind velocity. The coefficient of heat transfer
increases as wind velocity increases at a rate of 2.3 to 4.6 W/m2 ºC per m/s of wind velocity. When
determining the coefficient of heat transfer considering the influence of such factors as the forms
394

Part 4 Thermal Stress Analysis

and curing method, the following equation may be used:



1
1





(C2.2.1)

dF i

F i

where,
η : modified coefficient of heat transfer, (W/m2˚C)
β : coefficient of heat transfer at surface exposed to atmosphere, (W/m2˚C)(generally taken as 12-14W/m2˚C )dFi : thickness of curing material, (m)λFi : thermal conductivity of curing material, (W/m2˚C)

The reference data of the coefficient of heat transfer are shown in Table C2.2.1.
Table C2.2.1
No.
1
2
3
4
5
6
7

2.3

Reference value of coefficient of heat transfer ηCuring method

Metal frame
Water sprinkling（sprinkling water depth: less than 10mm）
Water sprinkling（Sprinkling water depth10mm~50mm）
Including ....curing
Water sprinkling (Sprinkling water depth: 50mm~100mm）
Plywood
Sheet
Curing mat
Water sprinkling＋Curing mat，
Water sprinkling + Sheet
Styrene foam（Thickness: 50mm）+ Sheet2oη （W/m

C）

14
8
8
8
6
5
2

Rate of Heat Generation of Concrete

The rate of heat generation used in the thermal analysis of concrete shall be modeled,considering the age of concrete and concrete temperature depending on portion in the
structure. If, however, the minimum member size is not smaller than 0.5 m, it may be
assumed in the thermal analysis that the adiabatic temperature rise of concrete isregarded as common characteristics of concrete throughout the structure.

[Commentary] The rate of heat generation in concrete is strongly influenced by temperature.
Since temperatures in a structure are usually not uniform, different parts of the structure usually
generate heat at different rates. In a thermal analysis, therefore, it is desirable that thermal
properties be determined from mix parameters such as the type of cement, chemical andnonchemical admixtures, cement content and water-cement ratio, and calculated rates of heatgeneration reflecting temperature dependence be used. At present, however, few thermal analyses
are conducted in that way.
395

Standard Specifications for Concrete Structures-2007, Design

If the minimum member size is not smaller than 0.5 m, the rate of heat generation in most partsof a concrete member except its exposed surface is almost same as that of adiabatic heat generation.
In such cases, it has been analytically confirmed that accuracy of thermal analysis does not suffer
even if the adiabatic temperature rise characteristics of the concrete for the placing temperature aretaken as its heat generation characteristics, the rate of heat generation in the concrete is determinedaccordingly, and it is assumed to be uniform throughout the structure. At present, however, it iscommon practice to use this approach even when the minimum member size is smaller than 0.5 m.
The mixing method used may influence the rate of heat generation several hours after the
manufacture of concrete, but usually the influence on the calculation of the thermal cracking index
is not substantial. In cases where hydration is retarded by the type and dosage of chemical
admixtures, close attention needs to be paid to early-stage characteristics.

396

Part 4 Thermal Stress Analysis

CHAPTER 3
3.1

STRESS ANALYSIS

Analytical Method

Stresses due to volume changes of concrete shall, in general, be calculated, bydetermining volume changes of restraints such as concrete, reinforcing steel and rock,soil or foundation, so that the boundary and compatibility conditions and the equilibrium
condition are satisfied.

[Commentary] Since mass concrete structures are usually more rigid than ordinary concrete
structures, simplification of the compatibility conditions including the boundary conditions may
result in lower accuracy of analysis. It is desirable, therefore, to use an analysis method in which
both the compatibility and equilibrium conditions are satisfied and volume changes and unsteadymechanical properties of concrete can be considered (e.g., finite element method). Results offinite element analysis may vary depending on element resolution, analytical domain and boundary
conditions, and the properties of the restraining body and the restrained body. If the finite element
method is used, therefore, it is important to determine these parameters carefully, paying attention
to past analysis data, so that the required level of accuracy is achieved. In the analysis considered
here, σt(t) is defined as the maximum value of principal tensile stress in the concrete member at
an age of t.
There are various approximation methods that can be used as a means of calculating stresses inmass concrete structures in which volume changes due to temperature changes are predominant
over those due to autogenous shrinkage. One of those methods is the CP (CL) method described
below.
In general, the restraining actions causing thermal stresses consist of the internal and external
restraining actions. The external restraining action is classified into the one against axial
deformation and the one against flexural deformation.

Deformation due toexternal restraint
Free thermal deformation

Compensation line shifts from AA’
to BB’ due to external restraint

Axial force

Axial force

Bending moment

Bending moment
Rock foundation

Axial force

Fig. C3.1.1

Bending moment

External restraint condition

When free thermal deformation is caused in a concrete block, the deformation is separated into
deformation in an axial direction, i.e., expansion and contraction, and flexural deformation in a397

Standard Specifications for Concrete Structures-2007, Designvertical direction as shown in Fig. C3.1.1. Hence, two kinds of external restraining effects are
considered concerning the restraint of these deformations. Therefore, induced stress is regarded toconsist of the stress components due to the internal restraint, that due to the external restraint
against axial deformation and that due to the external restraint against flexural deformation. Eachstress component is calculated as follows:
When temperature distributions at ages of ti-1 and ti are obtained in mass concrete shown in Fig.
C3.1.2, the distribution of changes in thermal strain can be obtained by multiplying temperature
difference by the coefficients of thermal expansion a. The stress due to internal restraint occurs
where the concrete block subjected to temperature change is free from any restraint of rock or otherobjects, but it is not caused by external axial forces or flexural moments. The stress therefore canbe obtained by drawing the compensation line that represents an axial force of 0 and a flexural
moment of 0. Increment of stress due to the internal restraint can be determined by Eq.(C3.1.1)
from the difference between the compensation line and temperature strain distribution curve(shaded part of Fig. C3.1.2).

 It  E (ti )(T   comp )(C.3.1.1)

where, comp is a strain value at a point of the compensation line.
Curvature increment  i of free thermal deformation is obtained from the inclination of thecompensation line, and so the increment of free axial strain  i from the strain at the center of gravity
on the compensation line.
Compensation line

Concrete

StrainRock or soil foundation

Fig. C3.1.2

Compensation line application

Restraining axial force and flexural moment occurring from age ti-1 to age ti are obtained by Eq.
(C.3.1.2) and Eq. (C.3.1.3), respectively.
N Ri  RN E (ti ) A i(C.3.1.2)

M Ri  RM E (ti ) Ii

(C.3.1.3)

Increment of stress due to the external restraint can be determined by the following equation:

 Ri 

N Ri M RiyAI(C.3.1.4)

where,
A: cross sectional area of mass concrete block,
I: moment of inertia of mass concrete block,
Y: distance from the center of gravity of mass concrete block398

Part 4 Thermal Stress Analysis

RN, RM: factors to represent the effects of restraining bodies such as a rock bed which
restrains free thermal deformation of mass concrete block, with RN for the degree of axial
deformation restraint and RM for that of flexural deformation restraint.
Thermal stress at each age is provided by Eq. (C3.1.5) as the summation of these stressincrements.

   (  It  Ri )(C.3.1.5)i

The values of RN and RM particularly depend on such factors as the difference of stiffness
between the restraining body and the mass concrete block, and the ratio of the bottom length to theheight (L/H) of the mass concrete block. An example of RN and RM are shown in Fig. C3.1.3 (forslabs) and Fig. C3.1.4 (for walls), which were obtained from the results of numerical calculation by
a 3-dimensional finite element method. These coefficients of external restraint can be used as
described in Table C3.1.1 (Usage of Coefficient of External Restraint).

Table C3.1.1

Application of external restraint factor
External restraint factor used for calculation

Slab structures

Soil foundation，rockfoundation
Soil foundation，rockfoundation

Restraining
body

Wall structure

Type ofstructure

Lift division

Axial restraint factor

Bending restraint factor
Before reversing

After reversing

RN(Fig. C3.1.3(a))

RM1(Fig.C3.1.3(b))

RM2(Fig. C3.1.3 (c))

1 liftRN(Fig. C3.1.3(a))

RM1(Fig.C3.1.3(b))

RM2(Fig. C3.1.3 (c))

At least
2 lifts

0.8RN(Fig. C3.1.3(a))

0.8RM1(Fig.C3.1.3(b))

0.8RM2(Fig. C3.1.3 (c))

Footing

RN(Fig. C3.1.3(a))

RM1(Fig.C3.1.3(b))

RM2(Fig. C3.1.3 (c))

1 LiftRN(Fig. C3.1.4(a))

RM1(Fig.C3.1.4(b))

RM2(Fig. C3.1.4 (c))

At least 2 lifts

RN(Fig. C3.1.4(d))

RM1(Fig.C3.1.4(e))

RM2(Fig. C3.1.4 (f))

No

Yes

399

Standard Specifications for Concrete Structures-2007, Design(b) Bending restraint factor RM1(ΔΦ before reversing)(a) Axial restraint factor RN(c) Bending restraint factor RM2(ΔΦ after reversing)Fig. C3.1.3

External restraint factor (Slab structures）

400

Part 4 Thermal Stress Analysis(a)Axial restraint factor RN( First lift)(b) Bending restraint factor RM1(First lift: ΔΦ before reversing)(c) Bending restraint factor RM2(First lift: ΔΦ after reversing)(d) Axial restraint factor RN(Second lift)(e) Bending restraint factor RM1(Second lift: ΔΦ before reversing)(f) Bending restraint factor RM2(Second lift: ΔΦ after reversing)Fig. C3.1.4

External restraint factor (Wall structures)

401

Standard Specifications for Concrete Structures-2007, Design

3.2

Consideration of Autogenous Shrinkage

In cases where autogenous shrinkage cannot be ignored, stresses shall be calculated
considering both volume changes due to heat of hydration and autogenous shrinkage.
Autogenous shrinkage shall be determined by means of a test or formula with provenapplicability and accuracy.

[Commentary] Volume changes at the construction stage are usually influenced mostly bytemperature changes. There are cases, however, where autogenous shrinkage due to hydration
cannot be ignored depending on the type of cement or admixture or the mix proportion of concrete.
In such cases, the accuracy of stress analysis can be improved by considering the effect of volume
changes due to both temperature change and autogenous shrinkage. This section describes a method
for considering the effects of autogenous shrinkage and temperature change.

In such cases, stresses may be calculated, on the assumption that thermal expansion andautogenous shrinkage are not dependent on stress, from effective strains calculated from Eq.
(C3.2.1), taking into account the unsteady mechanical properties of concrete.

 ij , ef   ij   ij ,t   ij , ag

(C3.2.1)

where,
εij: total strainεij, ef: effective strainεij, t: thermal strain =αΔTδij
α: coefficient of thermal expansion
δ: Kronecker delta
εij, ag: autogenous shrinkage of concrete; may be taken as a function of time.
Autogenous shrinkage is influenced by many factors including the water-cementitious material
ratio, type of cement, type and replacement rate of admixture, and temperature. If a concrete mix
containing a large quantity of fine blast-furnace slag is used, autogenous shrinkage may become
un-ignorably large relative to volume changes due to temperature changes even when the cement
content is low as in the case of mass concrete. Since autogenous shrinkage can also be influenced
by the use or nonuse of spray curing, it is important to take the effect of the construction method
into consideration.
At present, it is still difficult to predict strains due to autogenous shrinkage, taking all of thesematerial- and construction-related factors into consideration. A choice is permitted, therefore,
between a laboratory test and an estimation formula depending on the design and construction
requirements. If an estimation formula is used, it is recommended to use a formula that allows for
cement composition, concrete mix proportions and concrete temperature.
In the case of mass concrete, drying shrinkage occurs only near the concrete surface exposed tothe air, so Eq. (C3.2.1) does not allow for drying shrinkage. When the minimum member size issmaller than about 400 mm, temperature changes, autogenous shrinkage and drying shrinkage,
which occurs later than the first two, may become too great to ignore. In such cases, it is desirable
to consider the effect of drying shrinkage as well as autogenous shrinkage.

402

Part 4 Thermal Stress Analysis

3.3

External Restraining Body

The part of the external restraining body to be considered shall fully cover the part
where stresses due to volume changes of the restraining body cannot be ignored. Suchextent shall, in general, be verified in advance by calculation. In case that the external
restraining body is hardened concrete and rock, restraining effect may be consideredassuming that there is no slip between the restraining body and concrete.

[Commentary] The part of the external restraining body to be considered is difficult to define
because it is somewhat dependent on the calculation method. Usually, the part to be consideredis two to five times as large as the restrained body in the horizontal and vertical directions, and thesize requirements are dependent on the stiffness ratio between the concrete and the restraining body.
In principle, these conditions require a three-dimensional stress analysis of the entire system
including the restraining body, but in reality it is often cumbersome and not easy to do. The
recommended practice, therefore, is to use the CL method or the CP method as a means ofanalyzing this kind of restraining effect easily and accurately.

Even when the external restraining body in contact with the structure is highly rigid,
deformation of the restraining body and displacement along the interface may result. Thisboundary characteristic has not yet been accurately modeled, but because it usually reduces
autogenous stresses, a general rule is to assume perfect restraint (i.e., no displacement).

3.4

Effect of Restraining by Reinforcement

In cases where the restraining effect of reinforcing steel cannot be ignored, stresses
shall be calculated assuming that deformation of reinforcing steel and concrete at thesame location are identical.

[Commentary] Usually, concrete and reinforcing steel have similar coefficients of thermal
expansion. Therefore, in cases where volume change due to temperature is the only concern, therestraining effect of the reinforcing steel on the concrete can be ignored. However, both autogenous
shrinkage and drying shrinkage are restrained by reinforcing steel, if a large amount of steel is used,additional tensile stresses that occur when concrete deformation of these types is restrained by steel
are allowed for.

403

Standard Specifications for Concrete Structures-2007, Design

CHAPTER 4
4.1

MATERIAL PROPERTIES

Mechanical Properties

4.1.1

Tensile strength of concrete

The tensile strength of concrete to be used for the calculation of the cracking index
shall, in principle, be determined by splitting tensile strength test using specimens.

[Commentary] Because of such factors as the degree of drying, loading rate and differences insize, tensile strengths of concrete in structures, differing from that obtained through tension tests
using small and wet test specimens, are greatly influenced by the manufacturing inconsistency andconstruction performance. Manufacturing inconsistency was taken into account when thecharacteristic compressive strength of concrete was determined. Other influences are consideredindirectly by introducing a factor of safety (γcr) associated with the probability of occurrence of
cracks. Therefore, the splitting tensile strength of test specimens in accordance with JIS A 1113 may
be taken as the tensile strength to be used for the calculation of the cracking index.

In general, development of the tensile strength with respect to concrete age can be estimated by
the compressive strength. Examples are shown in Eq. (C4.1.1) and Eq. (C4.1.2). On theright-hand side of Eq. (C4.1.1), f'ck is indicated as characteristic compressive strength, but for such
purposes as post-completion reviews, experimentally determined or other compressive strength
values, if available, may be used instead.
The reason why the relation between tensile strength and compressive strength indicated here is
not identical to the relation indicated in the Standard Specification for “Design: General
Requirement” is that accuracy, particularly for young concrete, is pursued here. Although theseequations have been proved to be reliable for ordinary strength concrete, formulae for high-strength
concrete with characteristic compressive strengths of 50 N/mm2 or more need to be determined
separately by referring to test data and other information.
td (i ) f ' cka  bt

(C4.1.1)

f tk (t )  c f ' c (t ) ・(C4.1.2)

f ' c (t ) 

where,
f 'c (t ) : compressive strength of concrete at an age of t days (N/mm2)
f tk (t ) : tensile strength of concrete at an age of t days (N/mm2)
f ' ck : design strength of concrete (N/mm2)
t : age, in day
i: reference age for characteristic compressive strength (in days; i = 28 or 91)
a, b: values in Table C4.1.1 are used in standard practice, though they vary with type of
cement. Where blast furnace slag cement B is used, moderate the values equivalent to404

Part 4 Thermal Stress Analysis

those for heat portland cement may be used. No constants can be given for fly ash
cement B because only insufficient data have been accumulated. Values should bespecified based on the past records.
c: taken as 0.44 in standard practice, though it varies with such factors as degree of dryingof concrete.
d: increasing ratio of compressive strength of 91days against that of 28days. Standard
values of d(28) is shown in Table C4.1.1. d(91)=1 regardless of the type of cement.

Table C4.1.1

Values of a,b,d in Eq.(C4.1.1)

Type of Cement
Ordinary Portland Cement
Moderate Heat Portland Cement
High Early Strength Portland Cement

4.1.2

a
4.5
6.2
2.9

b
0.95
0.93
0.97

d(28)
1.11
1.15
1.07

Young’s modulus of concrete

The effective Young’s modulus of concrete to be used in calculating thermal stresses
shall be given with proper consideration for the effect of the age and drying.

[Commentary] Since the magnitude of thermal stress is determined by the temperature gradientin the structure, the ratio of stiffness between the restraining body and the restrained body andirreversible stiffness changes of concrete, it is necessary to evaluate the mechanical properties andvolume changes of hardening concrete of the restrained body by sequential stress analysis. As amethod for equally dealing with stiffness changes due to hydration and stress relaxation due tocreep, the method of calculating thermal stresses by using effective Young's modulus, which isdefined by extending the average Young's modulus for the cross section of the restrained concrete toallow for stiffness reduction due to creep, relaxation, etc., was proposed. Young’s modulus ofconcrete of the restrained body gradually increases with age, which is also influenced by the mix
proportion. On the other hand, the stress relaxation of the concrete due to its creep or relaxation
phenomenon is observed much remarkable at early ages.

According to the results of previous studies, when load is applied at an age of 2 days, the creep
coefficient becomes 1.5-2.0 times greater than that when the load is applies at an age of 28 days.
Where the temperature of concrete is kept high, the creep coefficient becomes larger, too. Becauseof these, it is common practice to simply estimate Young's modulus from the compressive strength
determined according to maturity and reduce Young's modulus in consideration of creep orrelaxation at the corresponding age. In this case, compressive and tensile creep characteristics are
identical.
When a simplified method to estimate the effective Young’s modulus is needed, Eq. (C4.1.3)
can be used. However, since creep characteristics of concrete with characteristic compressive
strengths exceeding 50 N/mm2 are not well clarified yet, they should be determined through creeptest.
E e t   t x 4.7 x10 3

f ' c (t )（C4.1.3）

where, E e t  : effective Young’s modulus at the age of t days, in N/mm2,405

Standard Specifications for Concrete Structures-2007, Designφ(t): compensating factor taking account of creep during concrete temperature increasingfor up to 3 days:φ=0.73
for after 5 days:φ=1.0
from 3 days to 5 days: linear interpolation can be used.
f 'c (t ) : estimated compressive strength of concrete at an age of t days using Eq. (C4.1.2), in
N/mm2.

In cases where the effect of stress changes due to temperature changes, autogenous shrinkage ordrying shrinkage cannot be ignored, it is desirable to determine the concrete stress  t i  bycalculating creep strains corresponding to changing stresses. A simpler method is to calculate
concrete stress from Eq. (C4.1.4), using the effective Young's modulus Ee(ti, tj) corresponding to theeffective strain increment  ef (t j ) at age tj at the time of loading. The effective Young's modulus

Ee(ti, tj) may be taken as Eq. (C4.1.5), in which different creep coefficients are used according to theage of concrete at the time of loading.

 t j   Ee t i , t j   ef t j 
E e (t i , t j ) (C4.1.4)

E c (t j )(C4.1.5)

1  { E c (t j ) / E c } (t i , t j )where, σ(ti): concrete stress at age ti
 ef (t j ) : effective strain increment at age tj
Ee(ti, tj): effective Young's modulus at ti of concrete loaded at age of tj
Ec : Young's modulus of concrete at age of 28 days (standard curing period)φ(ti, tj): creep coefficient calculated from Ec at ti of concrete loaded at age of tj

4.2

Thermal Properties

4.2.1 Thermal Properties of Concrete
The adiabatic temperature rise of concrete shall be adequately determined consideringsuch factors as the materials and mix proportion of concrete used and concretetemperature at placing. The thermal properties to be used in thermal analysis, i.e.,thermal conductivity, thermal diffusivity and specific heat, shall be adequately determinedconsidering the mix proportion of concrete used.

[Commentary] The design value of adiabatic temperature rise of concrete is expressed by Eq.
(C4.2.1) unless either chemical admixtures or admixtures that are highly effective for retarding
hydration are used.

Qt   Q 1  e rt(C4.2.1)

where,
Q : ultimate adiabatic temperature rise to be determined by testing,406

Part 4 Thermal Stress Analysis

r : constant for rate of temperature rise to be determined by testing,t : age (days),
Q(t) : adiabatic temperature rise at an age of t (ºC).
If the type of cement, cement content and the temperature at the time of placement are given,Q and r may be estimated by the regression equations shown in Table C4.2.1 as examples. The
committee for revising the "Cracking Control Guidelines for Mass Concrete" of the Japan Concrete
Institute proposes Eq. (C4.2.2) to express the characteristics of adiabatic temperature rise morefaithfully.

Qt   Q 1  e r t t 0 s

(C4.2.2)

where, t0 and s are the base and the speed of temperature rise, which are introduced to specify
the equation expressing the proposed adiabatic temperature rise as a regression equation based on
the existing data, and vary according to the temperature at the time of placement. The value of s is 1
for cement other than low-heat Portland cement. The equation gives Q , r, t0 and s (in the case of
low-heat Portland cement only) according to the temperature during placement for a cement content
of 250 kg/m3 to 450 kg/m3 or 450 kg/m3 to 700 kg/m3. These should be referred to as required.

Table C4.2.1 Standard values of Q and r in Eq. (C4.2.1)

Type of cement

TemperatureduringplacementQt   Q 1  e

Q

a
0.12
0.11
0.11
0.11
0.10
0.11
0.13
0.13
0.13
0.11
0.10
0.10
0.13
0.13
0.13
0.15
0.14
0.14



 C  b 1)

b
11.0
13.0
12.0
6.0
9.0
9.0
15.0
12.0
10.0
4.2
8.0
9.4
13.2
11.9
10.9
3.7
4.5
4.5

 rt


r  gC  h 1)g0.00150.00380.00400.00030.00150.00210.00160.00250.00140.00060.00120.00190.00130.00180.00230.00110.00190.0030h
0.135-0.036
0.337
0.303
0.279
0.299
0.478
0.650
1.720
0.105
0.071
0.055
0.034
0.148
0.396
0.107
0.213
0.487

10
20
30
10
Moderate-heat Portland
20
cement30
10High early strength20
Portland cement30
10Low-heat Portland cement
20
30
10
Blast furnace slag cement
20
type 2)30
10
Fly ash cement type 3)20301) C: Cement content (kg/m3)
2) In cases with 40% of blast furnace slag (Blaine fineness: 4200 cm2/g). For other percentages,
refer to existing data or conduct testing.
3) The percentage of fly ash is 18%.
Ordinary Portland cement

The thermal properties of cement paste vary depending on the progress of hydration and thewater content. The thermal properties of concrete, however, may be assumed to be constant because407

Standard Specifications for Concrete Structures-2007, Design

the thermal properties of aggregate, which accounts for a major part of concrete volume, areconstant. Thermal constants of concrete generally depend on the mix proportion of concrete,especially on such factors as the property and unit content of aggregate, and the moisture content of
concrete. Therefore, the constants are recommended to be determined considering the effects ofthese factors.
For concrete to be used in ordinary concrete structures, the thermal conductivity, specific heatand thermal diffusivity may be taken as 2.6-2.8 W/mºC, 1.05-1.26 kJ/kgºC and 0.83-1.1×10-6 m2/s,
respectively. Once the thermal conductivity and density are determined, the other constants can be
estimated by the following equations.

4.2.2

h2c=3.34×10-7λc(C4.2.3)

Cc=3.03×103/ρ

(C4.2.4)

Thermal properties of soil and rockIn cases where thermal analysis requires the thermal properties of soil, rock or othermaterials, such properties shall be determined conservatively by, for example, referring toavailable data.

[Commentary] In general, mass density, thermal conductivity and specific heat of rock may betaken as 2600-2700 kg/m3, 1.7-5.2 W/m℃ and 0.71-0.88 kJ/kgºC, respectively.

408

Part 5General Structural Details

PART 5 GENERAL STRUCTURAL DETAILSCHAPTER 1
1.1

GENERAL

Scope

This Specification presents details of reinforcement arrangement that meets therequirements in Chapter 13 of "Design: General Requirements."[Commentary] The details of arrangement of reinforcement in structures are important
prerequisites for the performance verification. The data validity on the reinforcement arrangement
is generally related only to part of the longitudinal reinforcement and shear reinforcement in the
study cross section. At present, no performance can be verified directly that is related to numerous
reinforcing bars details.
This Specification shows a standard method of reinforcement arrangement that meets therequirements in Chapter 13 of “Design: General Requirements.”
Complying with thisSpecification therefore is expected to meet the requirements stipulated in the related sections of
Chapter 13 of “Design: General Requirements.” The details of reinforcement arrangement inmembers and structures are described in Chapters 7 through 13 of this Specification in cases where
the design methods based on the linear analysis shown in Part 1 of “Design: Standards Methods”
are applied.

409

Standard Specifications for Concrete Structures-2007, Design

CHAPTER 2

CONCRETE COVER(1) The minimum depth of concrete cover shall be the larger of the diameter ofreinforcement "and" the concrete cover that meets the requirements in Sections 8.3 and10.7 of "Design: General Requirements" plus a margin of construction error. This
concrete cover shall be clearly presented in design drawings. For the regions requiring
no fire resistance, it is not necessary to meet the requirements in Section 10.7 of "Design:
General Requirements."(2) The margin of construction error should be specified considering the construction
conditions for members or regions and the construction management system forreinforcing bar works.
(3) The concrete cover that meets the requirements in Section 8.3 of "Design: General
Requirements" may be calculated in accordance with "Design: Standards Part 3."(4) For footings or important members of structures placed directly against earth, it isrecommended that the concrete cover should not be less than 75 mm.
(5) For reinforced concrete placed in water, without using antiwashout underwater
concrete, it is recommended that the concrete cover should not be less than 100 mm.
(6) In cases that concrete is likely to be subject to abrasion by running water, etc. it isrecommended that the concrete cover should be appropriately increased.

[Commentary] (1) For determining the minimum concrete cover, the larger of the diameter ofreinforcement steel and the concrete cover that meets the durability requirement in which no fire
resistance is required, plus a margin of construction error shall be taken into consideration, as
shown in Fig. C2.1. The concrete cover here means the distance from the outermost steel toconcrete surface. If joints are used for the reinforcement, the distance from the outermost edge ofthe joint zone should be defined as the concrete cover. In the case of deformed reinforcement, theconcrete cover may be calculated regarding a nominal diameter of the deformed reinforcement as
the diameter of the reinforcement. In order to secure bond strength, the distance to concretesurface should not be shorter than the sum of the diameter of the reinforcement and a margin of
construction error for all the reinforcement.
It is important that the actual concrete cover after construction is not smaller than the larger ofthe diameter of the reinforcement and the concrete cover that meets the durability requirement.
The margin of construction error should be properly specified considering the actual construction
conditions. The design drawings should clearly present the concrete cover and the margin of
construction error for each region.

410

Part 5General Structural Details
Any of the larger values

Bar diameter
Cover

≧

+

Construction error

Cover that meets the
durability requirements

Corrosion of reinforcing bars
due to cracks
Corrosion of reinforcing bars
due to carbonation
Corrosion of reinforcing bars
due to chloride attack
Effect of frost attack
Effect of chemical attack

Fig. C2.1

Calculation of concrete cover (in cases where no fire resistance is required)

When a group of parallel deformed bars act as a unit and are bundled in contact, the unit may betreated as a single bar having an equivalent diameter derived from the equivalent total area, for the
purpose of determination of cover requirements (Fig. C2.2).
Concrete CoverNot less than bar diameterφ’ norvalues indicated in Table 9.2.1
Not less than 20mm, nor 4/3 of the
Horizontal
maximum size of coarse aggregate,clear distancenor bar diameter φ’φ’

Vertical clear distanceNot less than 20mm
nor bar diameter φ’Concrete Coverかぶりφ'’：Diameter of single bar with theequivalent total area of bundled bar

Fig. C2.2 Concrete cover and clear distance for bundled bars(2) A margin of construction error should be taken into consideration when specifying theconcrete cover because the construction error occurs at the time of reinforcement assembly.
The margin of construction error should be specified for each region because the method ofassembly varies from region to region. The margin of construction error is also determined by the
management system or management values for reinforcing bar works during construction. These
points should be taken into consideration when specifying a margin of construction error. The
margins of construction error based on the results of surveys of margins of construction error andthe construction management systems are shown in “Design: Standards Part 3.”(5) Because of the difficulty in ensuring sufficient compaction, and the possibility of concrete
not being able to reach all the narrow spaces between the formwork and the bars, and the fact thatexamination of the condition of concrete placed in water is difficult, the concrete cover in cases
411

Standard Specifications for Concrete Structures-2007, Design

when concrete is placed under water without using antiwashout underwater concrete shall not beless than 100mm to ensure safety of the structure. In the case of cast-in-situ concrete piles
considering the ease of placing, irregularity of the inside face of drilled earth, and installation of
cages, it is recommended that concrete cover be around 150 mm.
(6) Where concrete is subjected to abrasion, for example upper side of a slab without effective
protection, it is recommended that the concrete cover be increased by at least 10 mm compared tothe standard value determined in accordance with the provisions of this section, in order to ensurethat design strength is not decreased even after abrasion.

412

Part 5General Structural Details

CHAPTER 3
3.1

CLEAR DISTANCE

Clear Distance(1) Lateral clear distance between longitudinal reinforcements in beams shall neither
be less than 20 mm, nor less than 4/3 times the maximum size of coarse aggregate, norless than the diameter of the bar. The lateral clear distance shall also be such that aninternal vibrator can be inserted for compacting the concrete.
Vertical clear distance for longitudinal reinforcement arranged in two or more layers
should neither be less than 20 mm nor less than the diameter of the bar (See Fig. 3.1).
(2) Clear distance for longitudinal reinforcement in columns shall neither be less than
40 mm, nor less than 4/3 times the maximum size of coarse aggregate, nor less than one
and a half times the diameter of the bar.
(3) In cases when the diameter of the deformed bars used is less than 32 mm and thearrangement of bars is complicated to the extent that sufficient compaction of concrete
may not be possible, two longitudinal bars in members such as beams, slabs, etc. may bebundled vertically and two or three vertical longitudinal bars in members such ascolumns, walls, etc. may be bundled (See Fig. 3.2).
(4) The spacing of reinforcement should be verified whether the requirements forconcrete construction performance are met or not.

c : Concrete covera : Clear distance(a) Beam

Fig. 3.1

Clear distance and concrete coverFig. 3.2(b) Column

Bundled bars

[Commentary] (1) In order to ensure that concrete surrounds the tensile reinforcement
appropriately a minimum lateral clear distance for longitudinal reinforcement in beams isprescribed here to be neither less than 20 mm, nor less than 4/3 times the maximum size of coarse
aggregate. Considering the site-conditions, the design clear distance should be greater than thevalues specified here by an appropriate margin. Experience has shown that sufficient bonddevelops in cases when the lateral clear distance is about equal to the diameter of the bar, provided
the tensile reinforcement is well covered by the concrete. The lateral clear distance shall also be
such that an internal vibrator can be inserted for compacting the concrete. Clear distance forsplices in reinforcement may be provided in Section 13.7 (4) in “Design: General Requirements.”(2) Clear distance for longitudinal reinforcements in columns has been specified in a manner
similar to that for beams, though the values are somewhat greater than those in the case of beams
since it may be more difficult to place concrete in columns.
413

Standard Specifications for Concrete Structures-2007, Design(3) Placing and compacting concrete using an internal vibrator may become difficult in cases
when the reinforcement ratio of primary horizontal reinforcement in beams, slabs, etc. and verticalreinforcement in columns, walls, etc. is high. In such cases, two or three bars may be bundled forease of placement and compaction of concrete, to prevent segregation in concrete, and to produce
dense concrete.
Since it may be difficult to place and compact concrete if the bundled bars come apart or move,it is important to tie the bars securely and use suitable spacers to keep the bundled bars in position
during construction. Since bond with concrete decreases in the case of bundled round bars, only
deformed bars can be bundled.
When bars are bundled, there may be cases when mortar does not adequately surround thereinforcement unless the concrete is sufficiently compacted. It is, therefore, necessary to carry out
the construction carefully, and it is recommended that the clear distance between reinforcement be
widened to an extent for inserting internal vibrators.
(4) At the time of design, the verification should be made whether the requirements for concrete
construction performance are met or not using the slump assumed based on the concrete mix
proportions. For the relationship between the spacing of reinforcement and the concrete slump,refer to Chapter 4 of “Construction: Standard.”

3.2

Clear Distance of Prestressing Tendon(1) Clear distance shall be provided between tendons or between sheaths, or between
the tendon or sheath and the reinforcement to ensure that concrete adequately surrounds
the tendons and sheaths and that concrete is fully compacted.
(2) Clear distance between sheaths for post-tensioning tendons should satisfy thefollowing requirements:(i) Horizontal and vertical clear distances between sheaths should not be less than 4/3
times the maximum size of the coarse aggregate.
(ii) In areas where an internal vibrator is to be inserted, the horizontal clear distance of
sheaths or groups of sheaths shall be the space necessary to be able to insert the internal
vibrator.
(iii) Small size sheaths may be arranged in contact with each other in cases it isunavoidable. Even in such cases, in vertical direction, not more than two sheaths shallbe allowed to be in contact.
(iv) When the sheaths in contact with each other are curved, the vertical clear distance
between the sheaths or groups of sheaths in the bend portion should not be less than the
diameter of a sheath.
(v) The horizontal clear distance between the longitudinal reinforcement and sheathshould neither be less than 20 mm, nor less than 4/3 times the maximum size ofaggregate, nor less than the diameter of the bar.
(vi) The vertical clear distance between the longitudinal reinforcement and sheathshould neither be less than 20 mm nor less than the diameter of the bar.
414

Part 5General Structural Details(3) Clear distance between sheaths for pre-tensioning tendons should satisfy thefollowing requirements:(i) The horizontal and vertical clear distances between prestressing tendons at the endof a member should not be less than 3 times the diameter of the tendon. Furthermore,
the horizontal clear distance should not be less than 4/3 times the maximum size of thecoarse aggregate.
(ii) When the prestressing tendons are bundled in a region other than the member end,
the numbers of the layers and the tendons in a group shall not exceed 2 layers and 4
tendons, respectively, and the clear distance between such groups shall not be less than
4/3 times the maximum size of the coarse aggregate.

[Commentary] (2) (i) and (ii) The horizontal clear distance should be provided to insert aninternal vibrator to ensure that concrete adequately surrounds the tendon or sheath and is fullycompacted. For compacting concrete, an internal vibrator with a diameter of approximately 50
mm is generally used. Then, the horizontal clear distance of sheaths should not be less than 60mm.
(iii) and (iv) Allocating numerous sheaths in contact with one another should be avoided
inasmuch as possible. In cases where sheaths need to be arranged in contact with one to provide
space for inserting an internal vibrator because of a limited member thickness, sheath groups may
be used in which two layers of small sheaths are placed only after special considerations. Herein
the small sheath indicates the one of which the diameter is less than around 70 mm. In addition,
the special considerations indicate the ones with regard to the cross-sectional dimensions forcalculating the stress, the interval of the bend up locations, the concrete quality and the placing
procedures, etc.
When sheaths are curved, the concrete between the sheaths needs to resist bearing stress of
tendons acting on the sheath wall surface. If the clear distance is small in cases where no grout isinjected into the sheath at the bend up location in the direction of the bearing stress, as illustrated inFig. C3.1(a), the concrete or sheath may be damaged. In practice, as mentioned in the clear
distance between the sheaths at the bend up location should not be less than the diameter of a sheath.
(see Fig. C3.1(b))

Fig. C3.1

Arrangement of curved sheaths(3) In the pre-tensioned concrete structure, a large bond stress acts along the length of theprestressing tendons especially at the end of the concrete member. Therefore, adequate clear
distance should be provided to ensure sufficient compaction of concrete, which facilitatesdevelopment of adequate bond.

415

Standard Specifications for Concrete Structures-2007, Design

CHAPTER 4

BEND CONFIGURATIONS OF REINFORCEMENT(1) Inside radius of bend for bent bars shall be not less than 5 times the diameter of thebar (see Fig. 4.1). When reinforcing bars within a distance of 2Φ+20 mm from the surfaceof concrete member are used as bent bars, the inside radius of bend of such
reinforcement shall not be less than 7.5 times the diameter of the bar.
(2) Inside radius of bend for reinforcement along the outer side of a corner in a rigid
frame shall not be less than 10 times the diameter of the bar diameter (see Fig. 4.2).
(3) Reinforcement along the inner side of a haunch or a corner in a rigid frame shall not
be tensile reinforcement bent from a slab or a beam, but separate straight reinforcement
provided along the inner side of a haunch (see Fig. 4.2).
Not less than 10
Stirrup
Not less than 5

Not less than 5

Reinforcement
for haunch

: Diameter of reinforcement
tie

Fig. 4.1

Inside radius of bend
for bent bar

Fig. 4.2

Reinforcement along inner side of
haunch corner in rigid frame, etc.

[Commentary] (1) Inner radius of the bend for bent bars should be determined such that it does
not generate large bearing stresses in concrete. Where bend bars are within 2φ+20 mm from thesurface of a concrete member, the bearing strength of concrete around the bend points is decreased.
Therefore, inner radius of the bend for bent bars should be greater to reduce the bearing stresses
around the bend points. When high strength deformed bars are used, the inner radius of the bend
for bent bar should be as large as possible.
(3) As shown in Fig. C4.1, in haunches or rigid frames it is possible for concrete to peel-off
along the inner side, as a bent tension reinforcement tends to straighten under the action of tensileloads. Separate additional reinforcement should be provided in such cases, as per the provisions of
this section. In cases when bending tensile reinforcement along the inner side of a haunch cannot be
avoided, stirrups or ties should be provided at the bent.

ハンチ部分のConcrete at the
コンクリートhaunch spalls off
がはげ落ちる

Fig. C4.1

Unfitting bar arrangement at haunch416

Part 5

CHAPTER 5
5.1

General Structural Details

DEVELOPMENT OF REINFORCEMENT

GeneralIf one of the following methods is used for providing anchorage at the end of
reinforcing bars, the development length for reinforcing bars should be specified as
described in this chapter.
(i) To embed reinforcing bars into concrete and develop through bond stress between
the reinforcement and concrete.
(ii) To embed reinforcing bars into concrete and provide an anchorage using standard
hooks.

[Commentary] Standard hooks should be applied in accordance with Table C5.1. The standard
hooks should be installed in the tension reinforcing bars of slabs and beams, longitudinal
reinforcing bars of piles and longitudinal reinforcing bars arranged at the corners of columns. If
adequate development length can be secured for the longitudinal reinforcing bars of piles, no hookshould be installed.
The shapes of standard hooks are shown in Fig. C5.1. The dimensions of standard hooks forthe longitudinal reinforcing bars are listed in Table C5.2 (a) and (b). The dimensions of standard
hooks for stirrups and hoops are shown in Table C5.3 (a) and (b).

Table C5.1

Application of hooks

Semicircular Acute-angled Right-angled
hook
hook
hook
Ordinary round bar

○

×

×

×

Longitudinal
reinforcing bar

○

○

○

○

Stirrup

○

○

○

×

Hoop

○

○

×

×

3

2

1

r2

r'3
r3

D
D1

a

Deformedbar

With nohookscb

L 1= a + 1

Semicircular hook

Fig. C5.1

L 3= c + 3

Acute-angled hook

Shapes of standard hooks1)

417

L 2= b + 2

Right-angled hook

Standard Specifications for Concrete Structures-2007, Design

Table C5.2 (a)Bardiameter
D10
D13
D16
D19
D22
D25
D29
D32

Dimensions of standard hooks for longitudinal bar (SD295, SD345) (mm)

D
50
70
80
100
110
130
150
160

Table C5.2 (b)Bardiameter
D10
D13
D16
D19
D22
D25
D29
D32

D
60
80
100
120
140
150
180
200

Table C5.3 (a)Bardiameter
D10
D13
D16
D19
D22
D25
D29
D32

D1
60
83
96
119
132
155
179
192

Semicircular hook
a
l１
L1
94
66
160
130
70
200
151
79
230
187
83
270
207
93
300
243
107
350
281
119
400
302
128
430

2L1
320
400
460
540
600
700
800
860

Right-angled hook
b
l2
L2
47
123
170
66
164
230
75
195
270
94
236
330
104
266
370
123
307
430
141
349
490
151
389
540

r2
25
35
40
50
55
65
75
80

2L2
340
460
540
660
740
860
980
1080

Dimensions of standard hooks for longitudinal bar (SD390) (mm)
D1
70
93
116
139
162
175
209
232

Semicircular hook
a
l１
L1
110
60
170
146
64
210
182
68
250
218
82
300
254
96
350
275
105
380
328
122
450
364
136
500

2L1
340
420
500
600
700
760
900
1000

r2
30
40
50
60
70
75
90
100

Right-angled hook
b
l2
L2
55
125
180
73
156
230
91
199
290
109
231
340
127
273
400
137
303
440
164
356
520
182
388
570

2L2
360
460
580
680
800
880
1040
1140

Dimensions of standard hooks for stirrups and hoops (SD295, SD345) (mm)

D
40
60
70
80
90
100
120
130

Semicircular hook
D1
a
l1
L1
50
79
61
140
73
115
65
180
86
135
65
200
99
156
84
240
112 176
94
270
125 196 104 300
149 234 116 350
162 254 136 390

2L1
280
360
400
480
540
600
700
780

r3
20
30
35
40
45
50
60
65

Acute-angled hook
r’3
c
l3
L3
25
59
61
120
37
87
83
170
43
101
99
200
50
118 122 24056
132 138 270
63
148 152 300
75
177 183 360
81
191 199 390

2L3
240
340
400
480
540
600
720
780

Table C5.3 (b)Dimensions of standard hooks for stirrups and hoops (SD390) (mm)Bar
diameter
D10
D13
D16
D19
D22
D25
D29
D32

Semicircular hook
D1
a
l1
L1
60
94
66
160
83
130
70
200
96
151
79
230
119 18783
270
132 20793300
155 243 107 350
179 281 119 400
192 302 128 430

D
50
70
80
100
110
130
150
160

2L1
320
400
460
540
600
700
800
860
418

r3
25
35
40
50
55
65
75
80

Acute-angled hook
r’3
c
l3
L3
30
71
69
140
42
99
81
180
48
113
97
210
60
141 119 260
66
156 134 29078
184 156 340
90
212 178 390
96
226 194 420

2L3
280
360
420
520
580
680
780
840

Part 5General Structural Details

Development lengths of reinforcing bars of various shapes are shown in Fig. C5.2. The
development lengths in cases of mechanical anchorage are shown in Fig. C5.3. Examples formembers with a shown in Section 13.6.3 (1) of “Design: General Requirements” are shown in Table
C5.4 (a) and (b). Basic development lengths at a = 1 are shown in Table C5.4 (c). The basic
development length of each member ldo can be obtained by multiplying the value of shown in
Table C5.4 (a) and (b) by the basic development length shown in Table C5.4 (c).
Mechanical anchorage should be applied in accordance with the “2007 Guidelines forAnchorage and Joints for Reinforcing Bars” prepared by the Japan Society of Civil Engineers. In
cases where the anchorage is provided at regions that cannot be handled as massive concrete or only
thin concrete covering is available in the anchorage zone in particular, whether the hook should be
replaced with mechanical anchorage or should not be determined by conducting tests in which thedimensions and stress conditions in the anchorage zone are simulated.
If the descriptions in Section 13.6.3 (1) (III) of “Design: General Requirements” are applicable(see Fig. C5.4), the basic development length for reinforcement ld should be set 1.3 times thedevelopment length obtained as stipulated in the section. Using concrete that induces no bleeding,however, the development length should not be corrected for the depth of concrete placement.

Right-angled
hook
Right-angled
直角フックによる定着
hook

Without
フックなし定着
hook

半円形フックによる定着
Semicircular hook

Acute-angled
鋭角フックによる定着
hook

do

ldo－
do10φ

端部にフックなしの場合
Without
hook at bar end（異形鉄筋）(deformed bar)
15φ

do-10φdo-10φ端部にフックありの場合
With
hook at bar end（異形鉄筋）(deformed bar)
10φFig. C5.2

Anchorage lengths for reinforcement of various shapes

Mechanical anchorage

Mechanical anchorage

Mechanical anchorage

Development
lengthDevelopment
lengthDevelopment
lengthThread impacted typeFig. C5.3

Friction and pressure welded typeBar end enhanced type

Anchorage lengths in cases of mechanical anchorage

419

Standard Specifications for Concrete Structures-2007, Design

Concrete surface after the placement
Not greaterthan 300mm

300mm以下

Not less thanthat should be longer 300mm以上
Re-bars
基本定着長を延伸する鉄筋
300mm
basic development length

Fig. C5.4

コンクリートの打ち込み高さDepthof concrete placement

Reinforcing bars with prolonged basic development length

Table C5.4 (a)Examples of  for beams, columns and bridge piers

Concrete coverLongitudinal bar diameter
D16
D19
D22
D25
D29
D32
20
0.8
0.9
0.9
0.9
1.0
1.0
25
0.7
0.8
0.9
0.9
0.9
0.9
30
0.7
0.8
0.8
0.9
0.9
0.9
35
0.6
0.7
0.8
0.8
0.9
0.9
40
0.6
0.7
0.7
0.8
0.8
0.9
45
0.6
0.6
0.7
0.7
0.8
0.8
50
0.6
0.6
0.6
0.7
0.7
0.8
60
0.6
0.6
0.6
0.6
0.7
0.7
70
0.6
0.6
0.6
0.6
0.6
0.7
*1 Transverse reinforcement should be D13. The spacing and clear distance of thelongitudinal reinforcement should be 250 mm or less, and double of the concrete
cover or larger, respectively.

Table C5.4 (b)Examples of for slabs

Concrete coverLongitudinal bar diameter
D16
D19
D22
D25
D29
D32
20
0.9
0.9
1.0
1.0
1.0
1.0
25
0.8
0.9
0.9
1.0
1.0
1.0
30
0.8
0.8
0.9
0.9
0.9
1.0
35
0.7
0.8
0.8
0.9
0.9
0.9
40
0.6
0.7
0.8
0.8
0.9
0.9
45
0.6
0.7
0.7
0.8
0.8
0.9
50
0.6
0.6
0.7
0.8
0.8
0.8
60
0.6
0.6
0.6
0.7
0.7
0.8
70
0.6
0.6
0.6
0.6
0.7
0.7
*1 No transverse reinforcement is assumed to be used because the longitudinal
reinforcement is located closest to the surface.
*2 Clear distance of longitudinal reinforcement should be double of the concrete cover orlarger.

420

Part 5

Table C5.4 (c)

D10
D13
D16
D19
D22
D25
D29
D32
*1

General Structural Details

Basic anchorage length ld0 (mm) ( = 1.0)

Design strength of concrete f’ck (N/mm2)
21
24
27
30
SD345 SD390 SD345 SD390 SD345 SD390 SD345 SD390
526
595
481
544
445
503
415
469
684
773
626
707
578
654
539
610
842
952
770
871
712
805
664
750
1000
1130
914
1034
845
956
788
891
1157
1308
1059
1197
979
1107
912
1031
1315
1487
1203
1360
1112
1257
1037
1172
1526
1725
1396
1578
1290
1459
1203 1360
1684
1903
1540
1741
1424
1610
1327 1500

γc＝1.3, γs＝1.0

Examples of the development lengths obtained based on the diameter of reinforcement to be
developed, At/s and cb are listed in Table C5.5. The type of reinforcing bar to be developed isSD345, and the design strength of concrete f'ck is set to be 21 N/mm2 or greater. In cases where
SD390 is anchored, the development length in the table should be multiplied by 1.13. In cases
where the design strength of concrete f'ck is 24, 27 or 30 N/mm2, the development length in the tableshould be divided by 1.1, 1.2 or 1.3, respectively.

Table C5.5
Bar
diameter
D10

D13

D16

D19

D22

At/s
2.0
1.5
1.0
0.5
0.0
2.0
1.5
1.0
0.5
0.0
2.0
1.5
1.0
0.5
0.0
2.0
1.5
1.0
0.5
0.0
2.0
1.5
1.0

Calculated development length for reinforcing bars (times)
10
32
32
32
42
47
32
32
42
47
53
32
37
42
47
53
37
42
47
53
53
42
47
47

20
32
32
32
32
37
32
32
32
37
42
32
32
37
42
47
32
37
42
47
47
37
42
42

30
32
32
32
32
32
32
32
32
32
37
32
32
32
37
42
32
32
37
42
42
32
37
37
421

40
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
37
32
32
32

cb

50
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32

60
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32

70
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32

80～
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32
32

Standard Specifications for Concrete Structures-2007, Design

0.5
53
47
42
37
32
32
32
32
0.0
53
53
47
42
37
32
32
32
2.0
42
37
37
32
32
32
32
32
1.5
47
42
37
32
32
32
32
32
D25
1.0
47
47
42
37
32
32
32
32
0.5
53
47
42
42
37
32
32
32
0.0
53
53
47
42
37
37
32
32
2.5
42
42
37
32
32
32
32
32
2.0
47
42
37
37
32
32
32
32
1.5
47
47
42
37
32
32
32
32
D29
1.0
53
47
42
42
37
32
32
32
0.5
53
53
47
42
42
37
32
32
0.0
53
53
47
47
42
37
37
32
2.5
47
42
37
37
32
32
32
32
2.0
47
42
42
37
32
32
32
32
1.5
47
47
42
42
37
32
32
32
D32
1.0
53
47
47
42
37
37
32
32
0.5
53
53
47
47
42
37
37
32
0.0
53
53
53
47
42
42
37
32
*1 The value cb is of smaller among the concrete cover and 1/2 of the clear distance of the bars.
*2 γc = 1.3, γs = 1.0, *3 The value of cb may be subjected to linear interpolation.

5.2

Development of Longitudinal Reinforcement(1) At least 1/3 of the positive moment reinforcement in slabs or beams shall be
extended beyond the support without bending and embedded.
(2) At least 1/3 of the reinforcement provided for negative moment in slabs or beams
shall be extended beyond the point of inflection, and be either embedded in acompression zone, or continued to the neighboring reinforcement provided to resist
negative moments.
(3) A bent bar should be extended as main reinforcement, or the end of a bent bar
should be embedded in the compression zone with minimum concrete cover.
(4) Without leading to abrupt change in the amount of reinforcement, and taking ls as
the effective depth of cross-section, critical sections to check development length of thelongitudinal tension reinforcement in flexural members shall be set as given below.
(i) The development length should not be shorter than the reduced anchorage length lomeasured from the point ls away from the cross section where the bending moment is at
the extreme.
(ii) When bending the reinforcing bar in the cross section where part of the reinforcing
bar is not required from the calculation, the bar should be bent at the point ls away in the
direction toward the smaller bending moment from the cross section where part of the bar
is not required to resist the calculated bending moment.
(iii) Development length for a bent bar anchored in the compression zone of concreteshould not be less than 15 for the cases when hooks are not provided, and 10 for cases
when the hooks are provided, where  is the diameter of the bar.
(iv) In principle, the tensile reinforcement should be anchored in portions of concrete
422

Part 5General Structural Details

not subjected to tensile stresses. However, it may be anchored in portions of concrete
subjected to tensile stresses, provided the provisions (a) or (b) given below are satisfied.
In such cases, the tensile reinforcement shall be extended by (l d  l s ) beyond the section
where the bar is no longer required to resist calculated flexure, where ld and l s may betaken as the basic development length and the effective depth of the cross section in
general, respectively.
(a) The design shear capacity between the point where the bar is terminated and thesection where it is no longer required to resist calculated flexure shall not be less than 1.5
times the design shear force.
(b) The design moment capacity of continuing reinforcement at a point where adjacentreinforcement terminates shall not be less than 2 times the design moment and the design
shear capacity between the point of bar cutoff and the section where the bar is no longer
required to resist calculated flexure shall not be less 4/3 times the design shear force.
(v) Where positive moment reinforcement in a slab or beam is developed beyond the
support at the end, the development length of the reinforcement shall not be less than thedevelopment length lo for stress in reinforcement at a section which is at the distance of ls,
which may be taken as the effective depth, from the center of the support and shall be
extended to the end of the member.
(vi) At the fixed end of a cantilever, development length should not be smaller than the
reduced development length that should be from a point inside the anchorage zone by thesmaller among 1/2 of the effective depth of the cross section and 10 times the bar
diameter in cases where the end of the tensile reinforcing bar is confined horizontally inthe anchorage zone. In cases where the end of the tensile reinforcement is not confinedhorizontally in the anchorage zone, development length should be from a point inside theanchorage zone by the effective depth of the cross section.
(vii) At the bottom end of a column, development length should not be smaller than thebasic development length ld that should be from a point inside the footing by the smaller
among 1/2 of the effective depth of the column cross section and 10 times the bar
diameter.
(viii) If the thickness or depth of the cross section in the member to be developed issmaller than that of the existing member, the reinforcing bar should be prolonged to theend of the member to be developed. Methods of the development of the reinforcement
and methods of the arrangement of reinforcing bars at the connections of the member
should be examined so that the anchorage zone may transmit the stress acting on theexisting member to the member to be developed.
(ix) If the thickness or depth of the cross section in the member to be developed ismuch larger than that of the existing member, development length may be calculated by
an appropriate method considering the characteristics of bond between the reinforcement
and concrete, rather than complying with Section 13.6.3 of "Design: General
Requirements."(x) The l s in members with variable depth of the cross section for Section 5.2 (4) (i)may be taken to be equal to the effective depth, d at the section of maximum moment, for423

Standard Specifications for Concrete Structures-2007, Design

the Section 5.2 (4) (ii) it may be taken to be the effective depth, d at the section where thereinforcement is no longer required to resist calculated flexure.

[Commentary] (3) In cases such as continuous and fixed beams, the extension of a bent bar isused not only for anchoring the bent bar but also as reinforcement to resist positive or negative
moments. When the extension of a bent bar is not used as positive or negative moment
reinforcement, the end of bent bar should be embedded in the compression zone of concrete.
However, when embedding in the tension zone is unavoidable, provisions of Section 5.2 (4) (iv)shall be satisfied.

hhDevelopment length should not be less than 15 in cases with no standard hooks that isembedded in the compression zone of concrete. Development length should not be less than 10
in cases where standard hooks are provided. Since no stress or tensile stress, however, acts near
the top fiber at the support of a beam, no anchorage should be provided within 0.8 h of the support
at the end of members, or within 1.6 h around the support of the central portion of members (see Fig.
C5.5).
15φ

不良
Fault

0.8h

0.8h

良
Good

h

h

Support at（端支点部）
the end of member

1.6h

Fig. C5.5

不良
Fault

1.6h

良
Good

（中central
央支 点部）
Support at the
portionof member
Examples of arrangement of bent reinforcing bars(4) A sudden change in the longitudinal reinforcement content across a cross-section, such as in
the portion where the bars may be cutoff, could lead to a sharp drop in the load carrying capacity,and render the member susceptible to failure at the section, even if the adequate development lengthis provided for. Thus, only a gradual reduction is recommended in cases when the longitudinal
reinforcement content needs to be changed.
Figure C5.6 gives examples of critical sections for extension of reinforcement. Bars "A", "B",and "C" in Fig. C5.4 (a) respectively are illustrative the examples for the following cases:
Bar "A" indicates a tension reinforcement anchored in concrete subjected to tensile stresses. In
such cases in accordance with the provisions of Section 5.2 (4) (i), since the maximum stress in Bar"A" on account of flexure occurs at the cross-section ‘1’, the tension reinforcement shall extend at
least to point "a", which is at a distance ls from the cross-section ‘1’. However, this requirement is
424

Part 5General Structural Details

bound to be satisfied as Section 5.2 (4) (iv) requires that the reinforcement be extended up to thepoint marked "c", which is at a distance of more than ( ld + ls ) from the cross-section ‘2’, where theBar "A" is no longer required to resist calculated flexure.
Bar "B" indicates a bent bar. According to Section 5.2 (4) (ii) a point "d" should be at a
distance of at least ls from the cross-section 3, where the Bar "B" is no longer required to resist
calculated flexure. In addition, according to Section 5.2 (4) (ii) the bent point "d" should be at the
distance of lo from the point "b" which is the point of maximum stress in the Bar "B". However,these two requirements are usually satisfied in many cases, and therefore further examination may
be unnecessary. Bent deformed reinforcing bars should be anchored as shown in Fig. C5.7.
Bar "C" is an example of tension reinforcement anchored beyond the support. In such cases,
the development length shall be neither less than lo③, between point "f" (the terminal point to the
Bar "C") and the point "d" (the point of maximum stress in the Bar "C"), nor, be less than lo④ inaccordance with Section 5.2 (4) (v) between the point "f" and point "e".

Calculated
momentMomentshifted by ls

Bar A
Bar B
Bar C

(a) Beam

Any of the smaller values
among d/2 and 10, where  isthe diameter of the bar.

Any of the smaller values among d/2 and 10,
where  is the diameter of the bar.

(c) Cantilever (Case 1)(b) Column(d) Cantilever (Case 2)

Fig. C5.6

Examples of critical sections for development of reinforcementb ≧ 15φFig. C5.7

b ≧ 12φb ≧ 12φExamples of arrangement of bent reinforcing bars1)

425

Standard Specifications for Concrete Structures-2007, Design

Where,‘1’ : Cross section corresponding to the peak bending moment‘2’ : Cross section where Bar "A" is no longer required as per calculations.
‘3’ : Cross section where Bar "B" is no longer required as per calculations.
loⓝ : Reduced development length according to the stress in the reinforcement insection “n”.
lb : Development length of bent bar

The ls in member with variable depth for Section 5.2 (4) (i) may be taken to be equal to theeffective depth, d at the section of maximum moment, for the Section 5.2 (4) (ii) it may be taken to
be the effective depth, d at the section where the reinforcement is no longer required to resist
calculated flexure.
(iv) In cases when the tension reinforcement is anchored in concrete subjected to tensile stresses,
the reinforcement should extend beyond the section where it is no longer required to resist
calculated flexure in accordance with the provision in Section 5.2 (4) (ii), by an amount equal to ls,
and embedded there. In order to prevent harmful cracks caused at the end of the bar, provisions(a) and (b) in this section shall be satisfied in the region between the end of the bar and the crosssection where the bar is no longer required to resist calculated flexure. Provisions (i) and (ii) in
this section have been laid down on the basis of experimental results.
In cases when a member with reinforcing bars anchored at an intermediate point is subjected tocyclic loads, the flexure capacity becomes discontinuous at the location where the reinforcement isanchored. Flexural cracks that often occur at that location may grow into diagonal cracks. If
such a member undergoes cyclic loads with displacements in excess of levels that cause thereinforcement to yield, the load carrying capacity may be significantly reduced. In cases when thedisplacement exceeds twice yield displacement, the decrease in the capacity may be very significant.
Therefore, it shall be ensured that the performance of the intermediate portion containing theanchored reinforcement is not lower than that of the portion where is corresponding to maximum
force.
Note that maximum cross-sectional force induced during an earthquake depends on actual
strengths of materials and actual cross-sectional area of re-bars provided in a section. Therefore,
this point should be carefully taken into account in the assumptions used in computation of design
flexural moment and design shear force. For example, it is assumed that column members inbridge piers or column and beam members in frame structures reach plastic region, when structures
are designed to satisfy the Seismic Performance 2 for level 2 earthquake ground motion.
Maximum flexural moment caused in columns or beams depend on actual arrangements and actual
strengths of longitudinal re-bars. Furthermore, the flexural moment increases with increase instress of the re-bars if the re-bar strain reaches strain hardening zone. Hence, the flexural momentand shear force should be computed using the characteristic strength of materials and member factor.
They are taken into consideration since shear force in the response analysis relates to the flexural
moment. The condition of development of longitudinal re-bar described here is shown in Fig.5.8.

426

Part 5General Structural Details

V1: Design shear force that could beoccurred.
Vyd1 : Design shear capacity at thetermination point of re-bar
Md : Design bending moment that
may be occurred. In general,
this may be set as the design
flexural capacity of the member
at the bottom end, Mud
M1 : Bending moment at thetermination point of re-bar
Mud1：Design flexural capacity at thetermination point of re-bar

Termination
point oflongitudinalbarFig. C5.8

Requirement for the development of longitudinal re-bar(v) In cases then the positive moment reinforcement in a slab or beam is anchored beyond the
support, the development length shall satisfy not only the present provision but also the provisionsof Section 14.4 of “Design: General Requirements,” regarding the structural details for arrangementof reinforcement in the support.
(vi) and (vii) For the development of longitudinal reinforcing bars for a RC member,development length should be secured by determining the start point of anchorage considering theeffects of major loads acting on the member and the stress condition in the anchorage zone.
Figure C5.6 (b) illustrates the development length of reinforcement at the base of the column.
In general, the reinforcement should be extended close to the bottom of the footing.
Figure C5.6 (c) illustrates the development length of reinforcement at the fixed end of a
cantilever, where the reinforcement is confined upward and downward.
Figure C5.6 (d) illustrates the development length of reinforcement at the fixed end of a
cantilever where the extended reinforcement is not confined upward. In such cases, it isrecommended that the reinforcement be extended to the other end of the connecting member
without terminating.
The development length of longitudinal reinforcing bars in a cantilever is specified considering
the concrete confinement and stress conditions surrounded the existing longitudinal reinforcement.
The development length of longitudinal reinforcing bars in a column, on the other hand, should bespecified considering the stress condition of the existing member and the length of insufficientdevelopment due to bond deterioration during an earthquake as a major load. In this stipulation,
the length of longitudinal reinforcement that suffers bond deterioration during the plastic
deformation of a column is specified based on the existing test results. The stipulation is based on
the assumption that no excessive cracks occur in the existing member.
Where the thickness or the depth of the base of the column or the member jointed with thecantilever is less than that of the column or the cantilever in Figs. C6.5 (b) to (d), the reinforcement
may be extended to the end of the base of the column or the member jointed with the cantilever.
(ix) When the longitudinal reinforcing bars in the column are developed to the massive concrete
footing, in which no damaging cracks are likely to occur, development length may be calculated
separately considering the characteristics of bond between the reinforcement and concrete. Herein,
the development length may be calculated considering the relationship among bond stress, sliding
and strain2). In cases where earthquakes or other loads repeatedly cause high strain after yielding427

Standard Specifications for Concrete Structures-2007, Designof longitudinal reinforcing bar that is developed in the concrete, the regions where the development
is not effective in the member should be taken into consideration.

5.3

Development of Transverse Reinforcement(1) Stirrups shall be provided so as to enclose positive or negative moment
reinforcement in a manner that the ends are embedded in the compression zone.
(2) At the end of ties or hoops, a semicircular or an acute-angled hook, enclosing
longitudinal reinforcement, shall be provided.
(3) Spiral reinforcement shall be anchored at each of its ends by 11/2 turns of the spiral.
Within the plastic hinge section, however, the ends of spiral reinforcement should beoverlapped so as to wrap the concrete twice or more times.

[Commentary] (1) When a diagonal crack is formed, the two portions of a beam tend to separate
from each other. Stirrups are provided to prevent this separation of the two parts and to serve as
vertical tension member in a Howe truss. Thus, the development of a stirrup should be ensured
using a hook enclosing a compression bar. When compression reinforcement is used, stirrups
should enclose such reinforcement. This ensures a proper anchorage for the stirrups and prevents
the buckling of compression reinforcement (Fig. 5.9).
In cases where one set of stirrups is insufficient to encircle all the longitudinal reinforcement
because of a large member width, multiple sets of stirrups should be used to encircle thereinforcement (Fig. 5.10).
(2) Tie bars, hoops and intermediate ties should be provided to prevent primary reinforcing bars
from buckling, to ensure toughness and adequate distribution of stresses, and to serve as shear
reinforcement. When lap splices are used in these reinforcements, sometimes the tie or hoop
reinforcements fail to discharge its function in cases of cracking due to bending and spalling of
cover concrete. Therefore, tie bar, hoop and intermediate tie should be embedded with a hookenclosing longitudinal reinforcement (Fig. 5.11).
(3) Within the plastic hinge section, the anchorage of the end of the spiral reinforcement may beinadequate, so the spiral reinforcement should wrap the concrete twice or more times, and the ends
should be mechanically connected to each other or should be developed to internal concrete using
acute-angled hooks at the end of the reinforcement.

428

Part 5General Structural Details(Compression side)(Tension side)

Fig. C5.9 Shape of stirrup end

Fig. C5.11

Shape of tie end

Distribution reinforcement
配力鉄筋
軸方向鉄筋
Longitudinal
reinforcement

Sirrup
せん断補強鉄筋スターラップLongitudinal reinforcement
軸方向鉄筋

配力鉄筋
Distribution reinforcement

Fig. C5.10

Example of reinforcement arrangement when multiple sets of stirrups are used429

Standard Specifications for Concrete Structures-2007, Design

CHAPTER 6
6.1

SPLICES IN REINFORCEMENT

GeneralSplices should be installed for longitudinal reinforcement in accordance with Section
6.2, and for transverse reinforcement in accordance with Section 6.3.

[Commentary]
this Chapter.

6.2

In the case when no special discussion is conducted, splices may be provided as

Splices for Longitudinal Reinforcement(1) In cases when the provided reinforcement is not less than 2 times the amountrequired by design calculations, and, the ratio of spliced reinforcement to total
reinforcement is not greater than 1/2, length of lap splice shall not be less than the basic
development length, l d .
(2) When both of the two conditions in (1) are not satisfied, length of lap splices shallnot be less than 1.3 l d and transverse reinforcement shall be provided for the lap splices.
(3) When neither of the two conditions in (1) are satisfied, length of lap splices shall not
be less than 1.7 l d and transverse reinforcement shall be provided for the lap splices.
(4) Length of lap splices shall not be less than 20 times the diameter of the bar.
(5) Spacing between ties, intermediate ties and hoops at lap splices shall be not morethan 100 mm as shown in Fig. 6.1.
(6) Length of lap splices for concrete in water shall not be less than 40 times thediameter of the bar.
(7) Lap splices shall not be provided in plastic hinge zones subjected to repeatedstresses.

less than
100mm

Fig. 6.1

Spacing between ties, intermediate ties and hoops at lap splices

430

Part 5General Structural Details[Commentary] (1) Since lap splices are similar to development of anchorages in terms of stresstransfer, the length of lap splice has been specified in relation to the basic development length foranchorages.
Lap splices are easy to provide but their strengths could decrease considerably, resulting frominadequate compaction of concrete, segregation of concrete, or poor quality of concrete in theneighborhood of splices. Also, without the presence of a sufficient amount of transverse
reinforcement, concrete surrounding lap splices may split along the reinforcing bars, causing brittle
failure, if subjected to high tensile stresses or cycles of high stress. Therefore, splices should belocated in areas subject to relatively low stresses and need to be sufficiently reinforced bytransverse reinforcement.
(2) Such cases are commonly encountered, and it is recommended that to ensure the safety, therequired development length should be not less than 1.3 times the basic development length, and thesplices be reinforced with transverse reinforcement.
(3) This clause is provided according to (2) above.
(6) Requirements for a longer development length for concrete in water has been given
considering that the bond strength may decrease due to the presence of water-clay slurry or
bentonite slurry. When any adverse effect by the slurry is not foreseen, and normal bond strengthis expected, the requirement may be waived.
(7) Lap splices should not be used in members subject to low-cycle fatigue, such as columns
subjected to repeated stresses due to seismic loads. In cases providing lap splices become
unavoidable, they shall conform to the requirements stated herein. In cases where lap splices need
to be used in the plastic hinge section, the length of splice should not be less than 1.7 times the baseanchorage length ld, hooks should be installed and the splice zone should be reinforced by spiralre-bars or other splices reinforcement metals.

6.3

Splices for Transverse Reinforcement(1) Splices for stirrups
No lap splices should be used for stirrups.
(2) Splices for ties(i) If ties are spliced, they shall be connected such that splices can transmit fullstrength of the bare bars.
(ii) If lap splices are used, they should be staggered such that the spliced portions are
not connected.

[Commentary] (1) Lap splices based on the bond between the reinforcement and concrete should
not be recommended for use in stirrups, as cracks along stirrups may occur in some cases.
Because stirrups are arranged near concrete surface, in the case that lap splices are used for stirrups,
cracking or spalling of concrete cover will cause the bond between the reinforcement and concrete
to be lost and adversely affects stress transfer between them. In addition, the progress of cracking
may induce large stress locally or deteriorate the bond, however, predicting the locations to beaffected is difficult, and the weak points in stirrups may induce unexpected contingencies. No lap
splices should therefore be used for stirrups.
431

Standard Specifications for Concrete Structures-2007, Design

In cases of members with a large cross-section where lap splices may be unavoidable, sufficientlap length as specified herein, should be provided. When a hook is provided at the end of stirrup,
a bar of D13 or larger shall be provided perpendicular to the stirrup as shown in Fig.C.6.1. Incases of hooks at the end of the stirrup, they preferably point inwards in the member. Lap splices
should, however, be used for stirrups only carefully.

Axial reinforcement isarranged inside the hook.

Lap splice of stirrup
StirrupFig. C.6.1

Arrangement of splice for stirrup(2) In seismic performance verification, yielding in longitudinal re-bars is assumed. It is,therefore, specified that closed stirrups, ties or spiral re-bars enclosing longitudinal re-bar should be
used as transverse re-bars. However, re-bar which is often used in wall-type structures todetermine re-bar spaces should not be considered as lateral re-bar because of its insufficientdevelopment. In case of spiral re-bars, it is necessary to verify its safety sufficiently in regard to
rupture or development at the ends. In some members, seismic performance may not be thedominant required performance. In this case, it may not be necessary to refer this specification.
(i) Ties, which enclose all longitudinal re-bars in the area where spalling of cover concrete occurs
with large deformation, should transmit full strength, even if the spalling occurs. The requiredcondition should also be satisfied when splices are provided for ties. Considering this requirement,
flare welding or mechanical coupler are recommended, see Fig. C.6.2. For the matters related toflare welding and mechanical splices, refer to the "Recommendation for Design, Fabrication and
Evaluation of Anchorages and Joints in Reinforcing Bars [2007]".
In cases where the splices zone is in the internal concrete, lap splices may be used while
regarding the ends of the hoop as standard hooks (refer to Fig. C.6.3).
Flare welding

tie

Lap
splicesStandardhooks

Lap splices
with standard
hooks

Flare welding

Fig. C.6.2 Splices of ties byflare welding

Fig. C.6.3 Lap splices of ties

The cross section of flare welding, length of welding, and the shape of welding splices are432

Part 5General Structural Details

described below.
(a) The dimensions of a flare welding joint are shown in Fig. C.6.4. The bead width w should
not be less than a half of the bar diameter. The minimum width should be 6 mm.
(b) The length of welding should not be less than ten times the bar diameter. When changing thelength of welding, welding size, welding materials, etc., the length of welding should be determined
after verifying the performance of the splices.
(c) The shape of flare welding is shown in Fig. C.6.5.
(d) The size of flare welding joint, length of welding and the shape of the splices should bepresented in design drawings.
w≧φ/2，a≧0.39φ－e
where,
w: Bead width (mm)a: Design throat thickness for strength calculation (mm)e: Allowance for length. The following values may begenerally used.
e=2mm（φ≦10mm），
e=3mm（10mm<φ≦22mm）
e=4mm（φ>22mm）
φ: Diameter (nominal diameter) of reinforcement (mm)Fig. C.6.4

Bead width and throat thickness for flare welding spliceflare welding
Reinforcing bar
No boxing

Fig. C.6.5

Welding

No boxing
Reinforcing bar

Shape of flare welding spliceFig. C.6.6 Spliced portion of ties(ii) The reliability of spliced portion is less than the bare bar, and tends to be a weak point fromconstruction viewpoint. They should, therefore, be staggered such that the spliced portions are notconcentrated in member direction. For example, in the case of ties provided in a member withrectangular shape connected by flare welding at a point as shown in Fig. C.6.2, if the first splice
portion of a tie is near the center of side with width “a”, the next tie which provided with intervalsof “s” in the longitudinal direction should be near the center of side with width “b”, and the next
portion width “a” again. When two re-bars are spliced at two side points facing each other, the same
method should be applied (see Figs. C.6.2 and C.6.3). The arrangement of circular or elliptical ties
in members with circular or elliptical section should also be done with the same method (see Fig.
C.6.6).
In cases where the joints of hoops need to be concentrated in one and the same cross section
because of various conditions (splices of medium hoops in the rectangular cross section in Fig.
433

Standard Specifications for Concrete Structures-2007, Design

C.6.3 are examples), " Recommendation for Design, Fabrication and Evaluation of Anchorages andJoints in Reinforcing Bars [2007]" should be honored considering the reliability attributable toconstruction according to the type of splice for hoops as in the case of longitudinal reinforcement
splices.

434

Part 5

CHAPTER 7
7.1

General Structural Details

RE-BAR ARRANGEMENT IN BEAM

General(1) Spacing of stirrups, where compression reinforcement is provided, shall not exceed
15 times the diameter of the compression reinforcement or 48 times the diameter of thestirrups.
(2) In beams with large depth, additional reinforcement shall be provided in thehorizontal direction in the web.
(3) Additional reinforcement shall be provided to prevent cracking in the web near the
support.

[Commentary] (1) To prevent buckling of compression reinforcement, spacing of stirrups has
been specified. Also, it is specified not to exceed 48 times the diameter of the stirrups since wide
spacing of stirrups with small diameter decreases the effectiveness of the stirrups.
(2) In beams with large depth, flexural cracking in the web cannot be prevented only by primary
reinforcement provided at the side of extreme fiber in tension zone. Therefore, horizontal
additional reinforcement is required to restrict the width of cracking. Horizontal additional
reinforcement in the web is effective in preventing cracks which may occur vertically in the web,due to the conditions of construction, temperature change, shrinkage and so forth. It is
recommended to provide reinforcement with an area of more than 0.2 % of area in the web, withspacing not greater than 300 mm.
(3) Since a near vertical cracking can occur close to the support of beam due to the effect ofconcentrated support reaction and so forth, additional reinforcement is required to be arranged
sufficiently both in horizontal and in vertical directions.

7.2

Deep Beam(1) Primary tension reinforcement in simply supported beams shall be provided
continuously between supports and shall be anchored at the supports such that it can
resist tensile forces greater than the maximum tensile force. It is recommended that, ingeneral, primary tension reinforcement should be embedded beyond the support for alength greater than the basic development length.
(2) Positive and negative moment reinforcement in continuous beams shall be
provided throughout the length of beams. Reinforcement provided in the bottom layer
may be lap-spliced at intermediate supports, but shall be anchored at the end supports ina manner similar to simply supported beams. Additional horizontal reinforcement shallbe provided with 1/2 the spacing required by the Clause (3) of this section in regions
within a distance of 0.4 times the span length on both sides from the intermediate
supports.
(3) On both sides of a deep beam, additional reinforcement having an area not less435

Standard Specifications for Concrete Structures-2007, Design

than 0.08 % of the concrete cross sections shall be provided in both the horizontal andvertical directions with the spacing exceeding neither 2 times the width of beam, nor 300mm.
(4) Detailing at supports shall be carried out in accordance with Section 7.3[Commentary] (1) Because primary tension reinforcement is considered to be tension tie
members in tied arches, all amount of the tension reinforcement required for maximum moment
should extend beyond the support and should never be anchored in the spans.
(2) Provision concerning horizontal additional reinforcement to be arranged at the intermediate
supports of the continuous deep beams has been made so as to resist the splitting tensile stresses
caused by support reactions and to prevent cracking in the web under serviceability limit state.

7.3

Corbel(1) In cases when the primary tension reinforcement is arranged in two or more layers,
the reinforcing bars shall be placed within a distance of d 4 from the upper surface ofcorbels (See Fig. 7.1), where d is the effective depth of corbel at the column face.

Fig. 7.1 Effective depth at the loading point
and primary tension reinforcement in corbel(2) Primary tension reinforcement shall be bent horizontally and anchored insupporting members, with the inside radius of bend not being less than 10  . The
distance of the inside loop of primary tension reinforcement shall be the maximum of thefollowing: 13  from the loaded point, 2  from the edge of the loaded plate and cover
thickness in concrete.
(3) In both sides of a corbel, additional reinforcement having area not less than 40 % ofprimary tension reinforcement shall be provided at a spacing not exceeding 300 mm.

[Commentary] (2) Since inadequate end anchorage of primary tension reinforcement causes a
failure as shown in Fig. C 7.1, the end of bars must be looped and anchored extending beyond theloaded point.

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Part 5General Structural Details

Fig. C.7.1 Example of failuresdue to insufficient anchorage oftension reinforcement

Fig. C.7.2 Example of reinforcement
arrangement in corbel(3) Additional reinforcement in side faces of corbels should also be arranged in the zone where
primary tension reinforcement no longer exists so as to prevent the progress of diagonal cracks
produced in the web and the splitting failure at the loaded point. It is recommended for additional
reinforcement to be arranged in such a way to enclose the longitudinal reinforcement in columns towhich corbels are attached.
An example of arrangement of reinforcement in corbels is shown in Fig. C.7.2.

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Standard Specifications for Concrete Structures-2007, Design

CHAPTER 8
8.1

RE-BAR ARRANGEMENT IN COLUMN

Tied reinforced Column(1) At least four reinforcing bars with a diameter not less than 13mm shall be provided.
The cross-sectional area of the longitudinal reinforcement shall be neither less than 0.8 %nor greater than 6 % of the required cross-sectional area of concrete.
(2) Diameter of lateral ties and hoop reinforcement shall not be less than 6mm, and thespacing of lateral ties shall not be greater than the minimum lateral dimension of thecolumn, 12 times the diameter of longitudinal bar and 48 times the diameter of the lateraltie (see Fig. 8.1).
Sufficient lateral ties shall be provided especially at the connections with beams orother members.

Fig. 8.1

Tied reinforced columns[Commentary] (1) Diameter of longitudinal reinforcing bars has been prescribed to be not lessthan 13 mm in the provisions because the reinforcing bars, of which diameters are less than 13 mm
are often unable to straighten out during placing owing to insufficient rigidity of the bars. And,the minimum number of bars has been prescribed to be not less than 4 because no adequate
reinforcement of column can actually be achieved if less than 4 bars are arranged.
(2) Purposes of lateral ties are to prevent the buckling of longitudinal reinforcements, to fully
utilize the compressive strength of concrete by confining the lateral strain of concrete due to axial
compression forces, and to bear a part of shear forces.
Spacing of lateral ties has been prescribed to be not greater than 48 times the diameter of lateral
tie because the purpose of lateral ties cannot be achieved if lateral ties which are too slender are
arranged at wide intervals.
One side of a hoop ci should not be shorter than 48 times the tie diameter and 1 m to prevent the
restraining effect from being deteriorated greatly (Fig. C.8.1). Then, multiple ties should bearranged in combination.

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Part 5General Structural Details

intermediate
ties
ties
(diameter t)ties(diameter t)(a)Fig. C.8.1(b)

Arrangement of ties and intermediate ties in the large cross section

When intermediate ties are used, the same materials, diameter and interval in the longitudinal
direction of the member may be applied as those for ties. In cases where it is necessary to arrange
intermediate ties as shown in Fig. C.8.1 (b), they should be placed directly on the tie and adequate
anchorage should be provided at the end. Care should be exercised not to prevent concrete casting
work because of the arrangement of intermediate ties.

8.2

Spiral Reinforced Columns(1) By providing at least six reinforcing bars with a diameter not less than 13 mm, thecross-sectional area of the longitudinal bars shall be neither less than 1 % nor greaterthan 6 % of the effective cross-sectional area of columns, and, shall also not be less than
1/3 the converted cross-sectional area of spirals.
The converted cross-sectional area of spirals
with following equation

Aspe 

Aspe shall be computed in accordanced sp Asp

where,(8.1)

s

d sp : diameter of the effective cross section of spiral reinforced column

Asp : cross sectional area of spiral reinforcements:spacing of spiral reinforcement(2) Diameter of spirals shall not be less than 6 mm, and the spacing shall not exceed
1/5 of the diameter of effective cross section of columns and 80 mm (See Fig.8.2).
Converted cross-sectional area of spirals shall not be greater than 3 % of the effective
cross-sectional area of columns.
Sufficient spirals shall be provided especially at the connections with beams or othermembers.

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Standard Specifications for Concrete Structures-2007, Design

Ae ：effective cross-sectional area of spiral reinforced columns
Fig. 8.2

Spiral reinforced columns[Commentary] Spiral reinforced column is a reinforced concrete column having longitudinal
reinforcement entwined by spiral bars. Column with longitudinal reinforcement bars hooped bycircular ties instead of spirals may be treated as spiral reinforced column, if reinforcement iscompletely anchored.
(1) Diameter of longitudinal reinforcing bars has been prescribed to be not less than 13 mm
because of the same reason as the case of tied columns set forth in Section 8.1(1). For keeping
proper shape and spacing of spirals, it is necessary to arrange proper numbers of longitudinal
reinforcing bars along the inner circumference of spirals and to tie the bars firmly to spirals. For
this purpose, six longitudinal re-bars are necessary at least and it is desirable to arrange not less than
8 bars. The provisions for limitation of cross-sectional area of longitudinal reinforcement are
installed for the necessity that provides longitudinal reinforcement of considerably large
cross-sectional area in order to realize the effect of spirals sufficiently. It is necessary in practice toprovide them not less than 1/3 the converted cross-sectional area of spirals.
(2) Diameter of spirals has been prescribed to be not less than 6 mm, because the spirals musthave a high rigidity and, in practice, too small spacing of spirals must be avoided. The reason why
the minimum spacing of spirals has been prescribed is to realize the full effect of spirals, which has
been determined from the results of experiments and considerations for actual work.

8.3

Splices of Reinforcement in Column(1) In principle longitudinal reinforcement shall be spliced using gas pressure welded
splices, mechanical connections, pressure joint splices or enclosed welding splices.
When using lap splices, the number of splices at any cross section of the column shallnot be greater than 1/2 the number of longitudinal bars.
(2) When using lap splices in spirals, the length of each lap splice shall not be lessthan one and a half wind of the spiral.

[Commentary] (1) When using lap splices in longitudinal reinforcement of column, lap splices
particularly tend to become the structural weak points. Because of this, splice positions must be
shifted from each other throughout the column. Therefore, above requirements as well as theprovisions of Section 13.7 must be satisfied.

440

Part 5

CHAPTER 9
9.1

General Structural Details

RE-BAR ARRANGEMENT IN A SLAB

General(1) At a section, where the moment is maximum, the spacing of positive and negative
moment reinforcement in slab shall exceed neither two times the thickness of the slab nor
300 mm. For other sections, the above spacing shall exceed neither three times the
thickness of the slab nor 400 mm.
(2) In cases when negative moments may occur near the supports of a simply
supported slab, appropriate reinforcement shall be provided.
(3) When creating an opening in the slab, additional reinforcement should be arranged
so as to provide enough capacity resisting on cracking due to concentration of stresses,
and other reasons, and prevent from excessive cracking.

[Commentary] (1) This Section limits the spacing of primary reinforcement, otherwise behaviorof slab as a reinforced concrete may not be ensured.
(2) When a simply supported slab is loaded at the edge, the additional reinforcement shall be
provided for the negative moment which may occur near the loaded area.
(3) Since openings in slab are inevitable in many cases, harmful cracks may occur due to thestress concentration around the openings. As the degree of stress concentration varies case by case,
it is recommended to take appropriate measures in accordance with numerical analysis, experiments
or observation of cracking in existing structures. Typical example of additional reinforcements isshown in Fig.C.9.1. These reinforcements around corners shall be developed with adequate
anchorage.
The amount of primary and distribution reinforcements interrupted by an opening shall be added
along the sides of the opening.
For slab with large opening, it is recommended to provide measures derived from the numericalanalysis or the test results.

Fig.C.9.1 Additional reinforcements around opening
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Standard Specifications for Concrete Structures-2007, Design

9.2

One-Way Slab

(1) When modeling a one-way slab as a linear member for analysis, adequate
distribution reinforcement should be arranged at transverse direction to the span.
(2) For simply supported one-way slabs subject to uniformly distributed load, theamount of distribution reinforcement per unit length shall not be less than 1/6 the primarytension reinforcement per unit width of slab.
(3) For simply supported one-way slabs subject to a concentrated load, the amount of
distribution reinforcement per unit length shall be at least  times the area of primarytension reinforcement per unit width. Here  shall be as given in (i) and (ii).
(i) Loading in the vicinity of the center of the slab
for distribution reinforcement at the bottom of the slab  1  0.25  l b 1  0.8  b (9.1)

In cases when l b  2.5 ,  shall be computed taking l b  2.5 .
(ii) Loading near the edge of the slab
for distribution reinforcement at the top of the slab  1  2  b  8
where,

l: span of slabb

: width of slab

(9.2)

ν : distribution width of load(4) In cases when slabs are subject to both distributed and concentrated loads,
reinforcement provided shall be the sum of area of reinforcement required for each type ofload.

[Commentary] (1) In cases multiple concentrated loads act on a slab in a manner that theireffective widths overlap, the effect of all the loads shall be adequately accounted for in the design ofeach region. However, in an application where the requirement of the reinforcement varies fordifferent regions, the following simplification may be made. In cases when the variation in therequirement for the different regions is not significant, the reinforcement per unit width, Asd , may
be distributed as shown in Fig.C.9.2 in accordance with the theory of plasticity, except in the case ofskewed slabs for which a separate treatment may be required.

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Part 5General Structural Details

As1 , As 2 ,  As 5 : amount of reinforcement per unit width for each region
l1 , l 2 ,  l 5 : effective width for each load
Fig.C.9.2

Example of reinforcement provided in slabs subject to multiple concentrated loads

Moments in one-way slab occur not only along the direction of the span but also in thetransverse direction.
(2) In cases when the span to width ratio in a slab subjected to uniformly distributed loads is notless than 0.5, the coefficient given in Table C.9.1 may be used instead of 1/6 for distribution toprimary reinforcement ratio.
Table C.9.1

Coefficient for distribution reinforcement

l/b

0.5

0.7

1.0

2.0

β

1/6

0.16

0.13

0.07

(3) In the cases when a one-way slab is subject to a concentrated load, it deforms in a concave
manner in the vicinity of the load, which requires adequate reinforcement in the direction
perpendicular to the primary reinforcement. In cases when a one-way slab is subject toconcentrated load near the edge, negative moment may occur in a portion away from the load.
When such a moment occurs in a slab, it is recommended that distribution reinforcement in thetransverse direction at the top of slab should be provided.

9.3

Two-Way Slab(1) In cases where a two-way slab with a short and long span ratio (lx/ly) of 0.4 or lower
is subjected to a uniformly distributed load, it is assumed that the load is carried only by
the short span. In cases where re-bars are arranged in the direction of the short span as
bar members for which the total width of the slab is assumed to be effective, re-bars
should be arranged as described below in the direction of the long span.
i) For slabs specified in 1), at least one-fourth the primary reinforcement per unit widthof short span shall be provided as distribution reinforcement per unit length of short span.

443

Standard Specifications for Concrete Structures-2007, Designii) For continuous or fixed-end slabs, at least half the primary reinforcement per unit
width of short span, shall be provided at the top at right angles to the direction of theshort span. This reinforcement shall extend more than 1/3 the length of the short spanfrom the front edge of the support.
(2) In end sections on the long side of a fixed or continuous slab, three sides are fixedand one side is left free. For the moment at the fixed end on the short side, additional
reinforcement should be arranged.
(3) In cases when a two-way slab is not built monolithically with the walls or beams, oris discontinuous beyond the slab support, additional reinforcement at the corners of the
top and bottom of slab shall be provided.
i) This additional reinforcement shall be provided over a distance equal to 1/5 of thelonger span from the corner in both directions.
ii) Additional reinforcement shall be placed parallel to the diagonal from the corner at
the top of slab and perpendicular to the diagonal at the bottom of slab.
The
reinforcement specified in this Section may be placed in two bands parallel to the sides ofthe slab.
iii) The area of additional reinforcement per unit width in each direction shall be equal
to the area of positive moment reinforcement per unit width provided at the center of slab
for the short span (See Fig. 9.1).

Fig. 9.1

Additional reinforcement at corners of two-way slab

[Commentary] (1) When two-way slabs with a ratio of shorter span to longer span l x l y , notgreater than 0.4 are subjected to uniformly distributed loads, the magnitude of moment in x
direction is nearly equal to that calculated as a one-way slab in the short span direction. In thiscase, the moment may be computed as a beam with unit width of slab spanning in short span
direction. It is necessary to provide distribution reinforcement for the moment in y direction
accordingly.
(3) When two-way slab is not monolithically built with walls or beams, or discontinuous beyond
the slab support, additional reinforcement shall be provided at corners of the top and bottom of slab
against warping at corners and torsional moment.
444

Part 5

9.4

General Structural Details

Cantilever Slab

(1) The area of distribution reinforcement per unit length of slab shall not be less than
1/6 the area of the primary tension reinforcement per unit width of slab. Reinforcing bars
with a diameter not less than 6 mm shall be provided in the transverse direction at thebottom of the slab with spacing not exceeding three times the slab thickness. For acantilever slab subject to a large concentrated load, distribution reinforcement shall be
increased in accordance with the provisions for a one-way slab.
(2) Primary tension reinforcement in a cantilever slab should be fully anchored.

[Commentary] (2) Hooks shall be provided for primary reinforcement in a cantilever slab.
Where the thickness of slab is not enough to anchor a reinforcing bar shall be bent down at the free
end and extended along the bottom of slab (Fig. C.9.3).

Fig. C.9.3

9.5

Development of primary reinforcement in cantilever slab
subject to large concentrated load at free end

Skewed SlabThe primary, distribution and additional reinforcements shall be provided in skewed
slabs as specified in (1) to (3) below.
(1) Arrangement of primary reinforcement (See Fig 9.2)

Fig. 9.2

Arrangement of primary reinforcement in skewed slab(a) For b / l i  0.75 , the positive moment reinforcement shall be arranged in theskewed direction.
(b)

For b / li＞ 0.75 , the positive moment reinforcement shall be distributed over445

Standard Specifications for Concrete Structures-2007, Design

the center of the slab parallel to the direction of the normal span.
In case of b / li＞ 0.75 and the positive moment reinforcement arranged in theskewed span direction at two free sides, it is safe enough to provide the positive
moment reinforcement required to resist the moment assuming the skewed span
length.
(2) Arrangement of distribution reinforcement(i) For b / l i  0.75 , the amount of distribution reinforcement shall not be less than
1/4 of the positive moment reinforcement and shall be placed in the direction
normal to the positive moment reinforcement or parallel to the edge of support.
(ii) For b / li＞ 0.75 , the amount of distribution reinforcement shall be not less than
1/3 of the positive moment reinforcement and shall be placed parallel to the edgeof support.
(3) Arrangement of additional reinforcement
At the top of obtuse corners of skewed slabs, additional reinforcement parallel to theskewed span and the support shall be provided over a distance equal to 1/5 of the skewed
span length from the edge in each direction, as shown in Fig. 9.3. The additional
reinforcement provided in each direction shall be the product of the positive moment
reinforcement and the coefficient  as specified in Table 9.1.
For b li ≦0.75, reinforcement provided at the top of obtuse corners may be considered
as a part of the distribution reinforcement.
Table 9.1

Coefficient for additional reinforcement at obtuse corner
Skewed angle
90° > θ ≥ 75°75°>θ ≥ 60°60°>θ ≥ 45°

Fig. 9.3

Coefficient（α）
0.6
0.8
1.0

Additional reinforcement at corners of skewed slabs[Commentary] At obtuse corners of the support of simply supported skewed slab, torsional
moments cause the tensile stress in the top of slab in the normal direction to a bisector of the obtuse
corner. The tensile stress varies according to the diagonal angle, ratio between the diagonal spanand slab width and loading condition. Accurately obtaining the tensile stress is difficult. Additional
446

Part 5General Structural Details

reinforcement should therefore be arranged based on the results of approximate studies of tensilestress.
For the additional reinforcement against torsional moment in obtusely angled areas, the range ofarrangement can be properly specified by FEM analysis using shell elements. The arrangement of
secondary reinforcement can also be determined by conventional methods as described below.

9.6

Circular SlabIn principle, appropriate reinforcement should be provided in the radial andcircumferential directions to resist applied moment. Alternatively, in cases where sucharrangement is not appropriate as at the center of the slab or for small slabs, they may beprovided in two orthogonal directions.

[Commentary] This Section specifies for a circular slab that the reinforcing bar shall be provided
in the radial and hoop directions of principal moment as it is the most effective.
When the above arrangement of reinforcement is unsuitable to apply to the members, such as
the center region of slab or small slab, reinforcement may be provided in two orthogonal directions
like a mesh.

9.7

Flat Slab(1) Reinforcement against the moment transferred to the column shall be provided oneach side of the column over a distance equal to the width of column plus 1.5 times the
thickness of slab. (see Fig 9.4)

Fig. 9.4

Flat slab system(2) In cases when moment is transferred to a column, reinforcement shall be provided
at the bottom face of slab near the column head. In cases when the required
reinforcement cannot be calculated using adequate tools of analysis, the cross-sectional
area of reinforcement therein shall not be less than 1/2 that of reinforcement provided at
the top face of slab. The reinforcement shall be provided over an area as given in (1)above.

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Standard Specifications for Concrete Structures-2007, Design

CHAPTER 10

RE-BAR ARRANGEMENT IN SHELL AND WALL

(1) Spacing of longitudinal reinforcement shall not be greater than 2 times the
thickness of shell or 300mm, whichever is smaller. Area of longitudinal bars shall not beless than 0.25 %, nor greater than 5 % of the cross-sectional area of concrete. In
addition, the cross sectional area of transverse reinforcement provided perpendicular to
the reinforcement along the principal axis shall not be less than 1/4 of the latter.
(2) In the portion subject to large tensile forces, longitudinal reinforcement should
preferably be arranged in the same direction as that of the principal stresses due to theaction of permanent loads.
(3) Longitudinal reinforcement in shells at the location of the connection with thesupporting or the end member shall be anchored into the supporting or the end member.
(4) Splices in reinforcement shall not be located at the location of the joint between theshell and the supporting or end members.
(5) Reinforcing bars should be arranged in a wall as described in (a) through (e) below.
(a) The total sectional area of vertical reinforcement in a wall subjected to verticalloading should be between 0.4% and 4% of the total sectional area of concrete.
(b) The total sectional area of vertical and horizontal shear reinforcement in an
earthquake-resistant wall should not be smaller than 0.15% of the total sectional
area of vertical concrete in all directions.
(c) The diameter of the reinforcement in shear walls shall not be less than 13 mm,
and the spacing of bars shall not be greater than 2 times the wall thickness or
300mm, whichever is smaller.
(d) The vertical reinforcement located at both sides of the wall shall be tied to eachother using tie bars.
(e) The diameter of horizontal reinforcement should not be smaller than 13 mm andone-fourth of the diameter of vertical reinforcement. Horizontal reinforcement
should be arranged at intervals of 300 mm.

[Commentary] (1) The minimum spacing of longitudinal reinforcement is based on theexperience of existing shell structures built in the past in order to prevent hazardous cracks due todrying shrinkage of concrete and temperature gradient. The longitudinal reinforcement means thebars arranged in parallel with the curved surface of shell. Usually, these bars are arranged in twolayers orthogonally.
(2) This is the basic concept of the direction of the longitudinal reinforcement since the flow ofstress is very complicated in shell structures.
Longitudinal reinforcement, in general, shall be arranged in the same direction as that ofprincipal stress as much as possible, which depends upon the combination of loads. In practice the448Part 5General Structural Details

direction of reinforcement may be arranged as that of principal stress due to permanent loads.
(5) Lateral ties or tie bars enclosing vertical reinforcements shall be arranged uniformly, such as
in staggers, throughout the wall surface. The bars near the end surface of wall shall preferably bearranged more closely to each other, in accordance with the provisions of columns.

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Standard Specifications for Concrete Structures-2007, Design

CHAPTER 11

RE-BAR ARRANGEMENT IN FOOTING(1) Distribution reinforcement in footings shall not be less than 1/6 of primary
reinforcement.
(2) Compression reinforcement shall not be less than 1/6 of tension reinforcement.
(3) Additional reinforcement should be arranged in the web of the footing as in thebeam.

[Commentary] (1) and (2) Primary tensile reinforcement for a footing is anchored in thecompressive area of concrete. The reinforcement should therefore be bent up from the bottom to the
top of the footing, and down from the top to the bottom (refer to Fig.C.11.1).

Fig. C.11.1

Anchorage of longitudinal reinforcement(3) Additional reinforcement should be arranged in the web of the footing against the tensilestress due to vertical forces such as soil and pile reactions as for beams (refer to Fig. C.11.2).

Additional re-bar
用心鉄筋
D19,
interval shall not be
D19 200mm間隔以下
more than 200mm
Stirrup
スターラップFig. C.11.2

Secondary reinforcement in the web of footing

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Part 5

CHAPTER 12

General Structural Details

RE-BAR ARRANGEMENT IN RIGID FRAME(1) Primary reinforcement in a beam or column should be fully anchored to the joint ofthese members.
(2) The shear reinforcement required for checking should be arranged in a beam orcolumn throughout the span of the member. Tie bars or stirrups should be arranged
densely near the joint between the beam and the column.
(3) Closely spaced lateral ties or stirrups shall be provided in the neighborhood of thejoints between columns and beams.
(4) The joint of the member should be fully reinforced with reinforcing bars or othermaterials so that the designated strength and deformability may fully develop in themember.

[Commentary] (1) The longitudinal reinforcement in a beam or column should be firmly
anchored to the joint of the member. The method of anchorage of longitudinal reinforcement ofeach member may be determined based on the descriptions below on the assumption that thelongitudinal is fully reinforced as described in (4) of this section1). The joint of the member isgenerally determined geometrically according to the dimensions of the member. No adequate
anchorage may sometimes be provided in the joint. Then, providing anchorage using anchor
plates or securing the anchorage zone using slabs should be considered.
(a) Cantilever slab
The longitudinal reinforcement in a cantilever slab is generally prolonged for use as negative
reinforcement in an intermediate slab, or bent for use as positive reinforcement in an intermediateslab. When the reinforcement is anchored without being prolonged, it should be prolonged by d +ld or more from the study cross section, bent downward from the intermediate slab at an angle of 15
degrees, and prolonged by 10 (refer to Fig. C.12.1).

d+ d
d

10φ

15°
30φ

検討断面
Study
cross section

Fig. C.12.1

Arrangement of longitudinal reinforcement in the upper part of a cantilever slab

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Standard Specifications for Concrete Structures-2007, Design

The reinforcement in the lower part of a cantilever slab should double as the haunch reinforcementin the slab. Then, the reinforcement should be prolonged to the negative reinforcement in theupper part of the intermediate slab and anchored using hooks (refer to Fig. C.12.2).

Reinforcement in theupper part of theintermediate
上側鉄筋までslab
≥25
25φ以上

Study
cross
section

検討断面

Fig. C.12.2

Arrangement of primary reinforcement in the lower part of the cantilever slab1)(b) Beam
Examples of anchorage of longitudinal reinforcement in an upper layer vertical and horizontal
beams are shown in Figs. C.12.3 and C.12.4, respectively. An example of anchorage of longitudinal
reinforcement in a middle layer beam is shown in Fig. C.12.5.
h
+ d
2

R=10φ

h
+
2 d

R=10φ

d

Extension to the position at the endoflower re-bar of lateral beam
端横梁下側鉄筋の上まで延ばす

Extension
to above of lower
縦梁下側鉄筋の上まで延ばす
re-bar of vertical beam

Fig. C.12.4 Anchorage of longitudinal
reinforcement in an upper layer horizontal
beam1)

Fig. C.12.3 Anchorage of longitudinal
reinforcement in an upper layer verticalbeam1)

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Part 5General Structural Details≥ 15 and extended to the position of
15φ以上かつlongitudinal
re-bar of column
柱の軸方向鉄筋まで

Straight直線部：12φzone: 12Fig. C.12.5 Anchorage of longitudinal reinforcement in middle layer beam1)(c) Column
An example of anchorage to the upper layer beam is shown in Fig. C.12.6. Hooks are attachedat four corners of the longitudinal reinforcement in the column.
When anchoring to an underground beam, the longitudinal reinforcement in the column should
be prolonged to the reinforcement in the lower part of the underground beam and semicircular or
right-angled hooks should be attached to all reinforcement in principle (refer to Fig. C.12.7).

※※

When anchoring to the footing, the longitudinal reinforcement in the column should be
prolonged to the top of the reinforcement in the lower part of the footing. For the extra length ofanchorage l', the smaller of a half of the column width and 10 ( diameter of longitudinal
reinforcement in the column) should be specified (refer to Fig. C.12.8 (a) and (b)).

dd* Prolonged to the bottom of the primary reinforcement in the upper part of the beam (200 to 300
mm below the slab surface)(a) With haunches
Fig. C.12.6(b) With no haunches

Anchorage of primary reinforcement in column to upper layer beam1)453

Standard Specifications for Concrete Structures-2007, DesigndFig. C.12.7 Anchorage of primary reinforcement in column to underground beam1)
D
D

Smaller one between
D
D/2
or 10
2 または10φのうち小さい方

Smaller one between
D
D/2
or 10
2 または10φのうち小さい方
d

R

d

(a)
Fig. C12.8(b)Anchorage of longitudinal reinforcement in column to footing1)(d) Arrangement of reinforcing bar in beam support
Examples of reinforcement arrangement in a beam support are shown in Fig. C.12.9. The
reinforcement against diagonal tension (lifting reinforcing bars) should be arranged as shown in Fig.
C.12.10 (a) in principle. If necessary, however, the reinforcement may be arranged as shown in
Fig. C.12.10 (b).

dd(a) With no hooks
Fig. C.12.9(b) With hooks

Examples of reinforcement arrangement in beam support1)

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Part 5General Structural Details

Hook
フックをつける
30φ

10φ

45°

1：
1

15°

d≥以上
ld

(a) With no hooks
Fig. C.12.10(b) With hooks

Examples of dimensions of lifting reinforcement1)(e) Underground beam

20φ

An example of anchorage at the end of longitudinal reinforcement in an underground beam isshown in Fig. C.12.11. The top longitudinal reinforcing bar should be bent downward to the topof the reinforcement in the lower part of the beam for anchorage. The bottom longitudinal
reinforcing bar should be bent upward with the straight section exceeding 20  (diameter of thereinforcing bar to be anchored).

Fig. C.12.11

Example of anchorage of longitudinal re-bars in underground beam1)(2) Shear reinforcement in a beam or column of a rigid-frame structure required for checking
should be arranged throughout the length of the member. In the element at the end of the member
or at other locations where a plastic hinge is formed, transverse restraining reinforcement should bearranged to control the buckling of the longitudinal reinforcement. Stirrups for beams or ties forcolumns are arranged as shear and transverse confining reinforcement, respectively. At thecolumns and beams of rigid frame bridges, large moments and shear forces occur at the same time
during earthquakes, and moreover they act to the columns and beams in alternate directions, so it
often results in intersected diagonal cracks of members. In cases where inadequate shear
reinforcement is arranged, cracks rapidly cause failure. In order to increase ductility near theconnection, therefore, adequate ties or stirrups should be arranged effectively. Especially,
sufficient lateral ties shall preferably be provided near the upper portion of the column because
construction joints for successive pours are often provided there, resulting in a decrease of strengthof concrete due to bleeding and so forth. Especially for the columns, the ratio of lateral ties to beprovided in the region from the under part of the beam haunch, of the connection with column andbeam, shall preferably be not less than 0.25 %, and the spacing of lateral ties shall preferably be notgreater than 1/4 of the minimum size of member (See Fig. C12.12). And also, the ratio of lateralties to be provided from the top of footing to the upper point on column, shall preferably be not less455

Standard Specifications for Concrete Structures-2007, Design

than 0.2 %. In the range of beam, the quantity of stirrups shall preferably be not less than 0.2 % or
1.2 times the value obtained through calculations, whichever is larger. And also, the maximum
spacing of lateral ties shall preferably be not greater than 1/4 of the effective height of member.
The same volume of reinforcement steel should be arranged also in the connection for theanchorage of primary reinforcement and for the reinforcement of the joint.
H region H region
Tie
bar
帯鉄筋
D region
Longitudinal
re-barof column
柱の軸方向鉄筋Longitudinal
re-barof beam
梁の軸方向鉄筋

Stirrup
スターラップD regionFig. C.12.12 Reinforcement
arrangement at inter support of rigid
frame structure

Fig. C.12.13

Reinforcement arrangement at
joint(4) The joint of members should maintain sufficient stiffness and strength even in cases wherestrength or plastic deformability develops in members in contact with the joint such as beams andcolumns. To that end, haunches should be installed in members or shear reinforcement should bearranged adequately in the joint so that sufficient strength and stiffness may develop at the joint(refer to Fig. C.12.13). Then, the joint is congested with reinforcing bars. Attention should
therefore be paid also to the ease of concrete construction. Even in cases where strength anddeformability develops in the joint to which members are connected, if sufficient stiffness andstrength in the joint are verified in checking, the cross section and bar arrangement for the joint may
be specified so that sufficient stiffness and strength may be provided. In cases where high strength
reinforcement is used for the longitudinal reinforcement in columns or beams in particular, great
forces act on the connection. Check should therefore be made of the joint by an appropriate
method.

456

Part 5

CHAPTER 13

General Structural Details

RE-BAR ARRANGEMENT IN ARCH

(1) In principle, longitudinal reinforcement in an arch rib should be provided
symmetrically along its top and bottom faces. The gross-sectional area of reinforcement
shall not be less than 600 mm2 per meter of the width of arch rib. Also, the total
reinforcement for both the top and bottom faces shall be not less than 0.15 % of thecross-sectional area of concrete.
(2) Lateral reinforcement, which encases the longitudinal reinforcement, shall be
provided in an arch rib. Diameter of lateral reinforcements shall not be less than 13 mm,
and the center-to-center spacing of these reinforcements shall not be greater than 15
times the diameter of longitudinal reinforcements nor greater than the smallest dimensionof cross-section of arch rib, whichever is smaller.

[Commentary] (1) Relatively large stresses are induced in arch rib due to temperature change,
shrinkage of concrete, displacement of support and so forth. These stresses are released by plastic
deformation of concrete, but stresses vary due to displacement of arch axis. In order to reducethese effects, the minimum amount of reinforcement has been prescribed as above.
(2) The lateral reinforcement is provided to keep the location of top and bottom longitudinal
reinforcement, to resist secondary stresses induced in the normal direction to arch axis and toprevent the buckling of longitudinal reinforcement.

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Standard Specifications for Concrete Structures-2007, Design

CHAPTER 14

RE-BAR ARRANGEMENT IN PRESTRESSTED CONCRETE MEMBER

14.1 Reinforcement of Anchorage Zone
(1) End of the member
Tensile stress damaging concrete at the end of the member may occur depending on
the interval at which anchorages are installed and the sequence of tensioning of tendons.
Re-bars should be applied for protection from the tensile stress.
(2) Intermediate section of the member(i) When installing anchorages in an intermediate section, anchorages should beembedded in concrete and reinforced with reinforcing bars to prevent adverse effects on
the performance of the anchorage zone.
(ii) In cases of anchorage to a projection or notch, reinforcing bars should be applied
for reinforcement to prevent the variation of stress due to sudden change of cross section
from adversely affecting the characteristics of section of the member.
(3) Reinforcing bars behind the anchorage fixture
For the reinforcing bars against the tensile forces occurring behind the anchorage
fixture, reinforcement for the anchorage fixture, spiral reinforcement or reinforcement
arranged in a grid pattern should be used.

[Commentary] In the anchorage zone, multiple anchorages are generally arranged in one and thesame cross section and the stress condition is complicated. In cases where anchorages are installed
in an intermediate section, projections or notches need to be provided in the cross section of themember. Sudden change of cross section frequently causes the stress to concentrate near theanchorage zone. Studies should therefore be made in design to prevent the dimensions of theanchorage zone or stress condition from adversely affecting the characteristics of the cross sectionof the member. Reinforcing bars should be applied if necessary.
(1) Typical stress distributions near the anchorage zone are shown in Figs. C.14.1 (a) and (b).
Near the anchorage zone, tensile stress at right angles to the tendon ((i)), tensile stress at rightangles to the tendon between anchorages ((ii)) or tensile stress at the corner ((iii)) occurs.
Examples of reinforcing bars against these tensile stresses are shown in Figs. C.14.1 (b) and (d).
The method of reinforcement has been set for each method of anchorage. The tensile force at rightangles to the tendon ((i)) may be considered during the design of the anchorage as Fig. C.14.2.
(2) In cases where anchorages are embedded, or used as dead anchors, reinforcement should bearranged not only along the tendon but also in the longitudinal direction of the member.
In the case of projection anchorage, the tensile force indicated in Fig. C.14.3 by an arrow is
expected to act on the concrete near the anchorage zone. Tensile forces T1, T2 and T6 may beobtained by

T1=0.25P（a‐a’）/aT2=0.25P（b‐b’）/b（C.14.1）
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Part 5General Structural Details

T6=P sin awhere, P is the tensioning force used for anchorage, a and b, and a' and b' indicate the sectional
area and size of bearing area of a concrete block cut out of the anchorage zone, respectively (refer
to Fig. C.14.4).
For the coefficients in the equations for T1 and T2, 0.30 instead of 0.25 may sometimes be used.
T1 and T2 may be calculated by other methods.
Tensile force T3 generated at the corner by tensioning force P for anchorage is generally said tobe 10% of P.

P causes high compressive force to act on the concrete at the notch. The compressive force may
sometimes induce tensile force in front of the anchorage zone. At present, no formula has been
proposed for calculating T4. T4 should be calculated on the assumption of a force that is proportional
to P. In a method of anchorage, for example, calculation is made on the assumption of T4 = 0.5P.
T5 may be obtained as the tensile force generated due to the action of P that works as an
eccentric axial compressive force.
An example of reinforcement in the projection anchorage zone is shown in Fig. C.14.5.
Reinforcement F1 is against T1, F2 against T2 and T3, F3 against T4 and T5, and F4 against T6. An
example of reinforcement in the notch anchorage zone is shown in Fig. C.14.6. Reinforcement F1,F2 and F3 are against the tensile force at the notch and F4 is against the tensile force behind theanchorage fixture.
tensile Compress tensile
Compress
ive stressstress (iii) ive stress stress (i)tensile stress (iii)

tensilestress (i)tensile stress (ii)(a) Stress (y) diagram under
1-point concentrate force
crack by tensilestress (iii)
Grid-type or
spiral re-bar(c) Stress (y) diagram under
2-point concentrate force

crack by tensilestress (iii)
crack by tensilestress (ii)re-bars for tensilestress (ii)(iii)

re-bars for re-bars fortensile stress (iii) tensile stress (i)(b) Arrangement of re-bars
for 1-point concentrate force

Dead anchor

re-bars for tensile stress (i)(d) Arrangement of re-bars
for 2-point concentrate force

Fig.C.14.1 Stress distribution in concrete at thevicinity of anchorage and example of reinforcement459

PC tendonRe-bars
Front of the anchorage Behind the anchorage
解説 図 14.2

埋殺し定着部の補強例
Fig.C.14.2
Example ofreinforcement by dead anchorage

Standard Specifications for Concrete Structures-2007, Design

Corner ofintersection

Where, P: preseressed forcee : eccentricity of Pc : length of rib-anchorage
R : bending radius of tendon

Tendonα : bending angle of tendon

Front of the anchorage Behind the anchorage

T1 : tensile force occurring behind the anchoragein z-direction (vertical to this paper)
T2 : tensile force occurring behind the anchoragein y-direction
T3 : tensile force at the corner of intersection
T4 : tensile force generating in front of anchorage
T5 : tensile force induced by bending moment
occurred by prestress force(Me =P･e)
T6 : tensile force generating at the bending sectionof tendon = P･sinα

Fig.C.14.3

Tensile force at rib-anchorage

Fig.C.14.4
Concrete block解説
図 14.4 コンクリートブロック
Front of the anchorage Behind the anchorage

解説 図 14.5
突起定着部の補強例
Fig.C.14.5
Exampleof reinforcement
at rib-anchorage
解説 図 14.6
切欠き定着部の補強例
Fig.C.14.6
Exampleof reinforcement
at anchorage with cut-out portion

460

Part 5General Structural Details(3) Tensile force of tensile stress (i) shown in Fig. C.14.1 acts behind the anchorage fixture.
Against the tensile force, reinforcement for the anchorage fixture, spiral reinforcement orreinforcement arranged in a grid pattern should be applied. The reinforcement is specified
according to the method of anchorage. The reinforcement should be arranged in accordance with“the Recommendations for Design and Construction of Prestressed Concrete” or other documents.
Stirrups or other materials arranged in the member should double as the reinforcement against
tensile forces.
When using large anchorage fixtures, the area and arrangement of reinforcement should be
examined by FEM analysis or other means.

References
1) Railway Technical Research Institute: Guidelines for Reinforcing Bar Arrangement, DesignStandards for Railway Structures, Nov. 2004.
2) e.g. Shima, Zhou and Okamura: Bond characteristics of deformed reinforcing bars after yielding,
Proceedings of the Japan Society of Civil Engineers, No. 378/V-6, pp. 213-220, Feb. 1987.

461

Standard Specifications for Concrete Structures-2007, Design

PART 6STRUT-AND-TIE MODEL

CHAPTER 1
1.1

GENERAL

Scope(1) This Specification should be applied to cases where the limit state in the case of asectional failure is examined using a strut-and-tie model defined in Section 9.2.2 of"Design: General Requirements."(2) The strut-and-tie model should be applied to examine the ultimate limit state ofstructural concrete in discontinuity regions, such as regions in which the flow of internal
forces changes significantly, regions with abrupt changes of section, regions near frame
corners, regions with openings, regions near steel anchorages, or regions where thegeneral beam or plate theory is not applicable, when proof experiments for the ultimate
capacity or analyses with high accuracy are not performed.
(3) When using the strut-and-tie model to estimate the ultimate capacity of structuralmembers, it should be ensured that the equilibrium conditions between the compression
in struts and the tension in the ties at all nodes are satisfied.

[Commentary] The strut-and-tie model is a useful structural tool to estimate the resistance of astructure due to the applied load and how the internal forces flow. In this model, concrete
structures or members are discretely modeled into an assembly of one-dimensional struts and ties,
and nodes connecting these struts and ties. The ultimate capacity corresponding to the assumed
flow of forces is calculated based on the static equilibrium conditions and the individual strength of
the struts and ties. The tie is normally modeled on the basis of the resultant force from a layer ofreinforcing bars or prestressing steel. The strut represents the resultant of either a uniform
compressive stress field, such as a compression chord or a diagonal compression strut in webs ofbeams, or a fan-shaped compressive stress field, such as over supports or under concentrated loads(Fig. C1.1). The node represents a certain amount of concrete volume, in which struts either
intersect with ties or are deviated by ties.
C’

C’

C’

C’

xc

xc

(a) Uniform compressive stress field(b) Fan-shaped compressive stress field

Fig. C1.1 Concrete struts
462Part 6 Strut-and-Tie Model

As far as structural members, such as beams, columns, or slabs, whose design and construction
procedures are well established, and structural details of cross-section and detailing of
reinforcement are widely and empirically accepted, are concerned, a reasonably safe design can beachieved by following the provisions laid down in either Chapter 9 of “Design: General
Requirements”, or those in the present Specification. However, examination for ultimate capacityof some of the structural members including those in the regions with abrupt changes of section,
corners of framed structures, or with openings, cannot be carried out using standard methods given
in Chapter 9 of “Design: General Requirements”. The present understanding and practice ofreinforcement arrangement in regions where the flow of internal forces changes significantly are notnecessarily sufficient. In such cases, it is desirable to perform proof experiments or nonlinear
analyses with sufficient accuracy to examine the safety of structural members with an assumed
geometry and material properties. However, once the resisting mechanism for the design load ispredetermined, the design for detailing of the reinforcement and the properties of the materials used,
can be accordingly carried out, using methods such as the strut-and-tie model.
The strut-and-tie model described in this Specification should be applied only to examine theultimate limit state. Since the strut-and-tie model does not strictly consider the compatibility
condition in deformations, when deciding the location of struts and ties, it should be ensured thatthe compatibility of deformations is adequately maintained by providing sufficient deformation
ability to the structural members. This ensures the transfer of forces according to the resistingmechanism assumed in the ultimate limit state.

463

Standard Specifications for Concrete Structures-2007, Design

CHAPTER 2
2.1

STRENGTH OF TIE

Strength of Steel Tie

The strength of steel ties shall be obtained by multiplying the cross-sectional area ofsteel by the design yield strength.

[Commentary] At the ultimate limit state, it may be assumed that the steel of the tie yields.
Therefore, the strength of each tie can be obtained by multiplying the cross-sectional area of steel inthe tension tie by the design yield strength of steel. When high strength steel or prestressing steel
is used and the steel does not yield at the ultimate limit state, the force of tension ties shall be
evaluated using the actual stress in the steel at the ultimate limit state.

2.2

Strength of Concrete Tie

In the case of concrete ties, it shall be examined whether the expected tension
resistance of concrete still remains at the ultimate limit state. If this examination isskipped, it is not allowed to assume concrete ties.

[Commentary] Although reinforcement is normally provided to resist tensile forces in structuralconcrete, the tensile resistance of concrete, such as in the case of planar members without shear
reinforcement or for bond and anchorage of steel, is often expected even at the ultimate limit state.
When concrete ties are assumed, it shall be examined whether the tension resistance of concrete still
remains at the ultimate limit state. This is the prerequisite to apply a concrete tie in the
strut-and-tie model.

464

Part 6 Strut-and-Tie Model

CHAPTER 3
3.1

STRENGTH OF STRUTSStrength of Concrete Strut(1) In calculating the load carrying capacity of concrete struts in the strut-and-tie
model, the effective strength of concrete f ' cd .eff is desirable to be obtained using thedesign compressive strength of concrete f 'cd but appropriately reducing it using factors
to account for the presence of cracks in a member, crack width and geometricdisturbances. Equation (3.1) may be used the calculation of the effective strength.

f ' cd .eff  v・
1 v・
2 f ' cd

(3.1)

where, v1 is a reduction factor to consider the difference between the compressive
strength of concrete in a structural member and the strength determined using laboratory
specimens and may be taken to be 0.85. The reduction factor v2 may be taken as
follows:(a) v 2  1.00

for uncracked struts with uniform strain distribution.

(b) v 2  0.80

for struts with cracks parallel to the strut or for struts intersecting
bonded transverse reinforcement; the strength of struts shall be
reduced considering the disturbances due to the transverse tension or
the irregular crack surfaces.

(c) v 2  0.60

for struts transferring compression across cracks, such as in webs ofbeams.

(d) v 2  0.45

for struts transferring compression across large cracks, such as inmembers with axial tension or flanges in tension.

(2) The load carrying capacity of a concrete strut FRcd shall be obtained using theeffective strength of concrete f ' cd .eff and the area of a concrete strut.

FRcd  A・
c f ' cd .eff /  bwhere,

Ac
xc
b

b

:
:
:
:

(3.2)

area of a concrete strut (= x・c b)
depth of a concrete strut
thickness of a concrete strut
generally, may be taken as 1.3(3) The depth of a concrete strut xc shall be determined considering the stress
distribution and the direction of intersecting reinforcement.

[Commentary] (3) When a uniform stress distribution can be assumed as shown in Fig. C3.1, thedepth of a concrete strut may be estimated as xc  z・cos  , where  is the inclination angle
between the resultant compressive force and the member axis. When a concentrated load isapplied near the support (Fig. C3.2), a fan-shaped stress distribution occurs over the support and thedepth of a concrete strut changes depending on the location. In this case, if the minimum depth
determined from the width of a support is used as the strut depth xc , a conservative estimation for
the ultimate capacity can be obtained. When transverse reinforcement intersecting a strut is465

Standard Specifications for Concrete Structures-2007, Design

provided (Fig. C3.3), the change of strut depth due to the location may be considered. Figure C3.4
is a typical example of a strut-and-tie model considering the arrangement of reinforcement aroundthe anchorage of prestressing steel. It shows the steel ties required for the division of concrete struts,
which support the tensile force in the prestressing steel and the approximation of tension forces T of
the ties.

z

xc

z
A w f wy  cot sVFig. C3.1

Concrete strut for uniform compressive stress field
a
r
V

c

x/2



x

z

xc


d1
V
r

Fig. C3.2

Concrete strut for a concentrated load near a support
a

F

F
tie

tie

Fig. C3.3

Strut-and-tie model with horizontal reinforcement

T ≈ 0.25P

Fig. C3.4

T ≈ 0.50P

Strut-and-tie model around the anchorage of prestressing steel

466

Part 6 Strut-and-Tie Model

3.2

Strength of Concrete Strut with Reinforcement(1) Reinforcements may be considered effective in compression struts only when they
are placed parallel to the strut. Flexural compression reinforcement in a beam andlongitudinal reinforcement in a column are examples of such reinforcement.
(2) These reinforcements shall be surrounded with adequate transverse reinforcement
to provide the required resistance to buckling.
(3) The load carrying capacity of a concrete strut with reinforcement may be taken to
be the sum of the load carrying capacity of the concrete strut and that of thereinforcement as shown in Eq. (13.3.3).

FRcd  A・・f yd /  bs
c f ' cd .eff /  b  Asc(3.3)

where,  b and  bs may be taken to be 1.3 and 1.1, respectively.

3.3

Strength of Confined Concrete Strut

The load carrying capacity of a concrete strut may be increased by providing sufficientand proper transverse reinforcement to confine the concrete strut. In this case, theincrease in strength should be appropriately assessed.

3.4

Reduction in Strut Thickness(1) If a strut of thickness b is intersected by ducts or bars such that the sum of theirdiameters is larger than b / 6 , the resisting force of the strut shall be calculated using a
reduced thickness br.

br  b     
where,













(3.4)

  : sum of the diameters of ducts or bars
  : coefficient depending on the stiffness of ducts or bars; the value shallbe taken to be 0.5 and 1.2 for grouted ducts or bonded bars and for
ungrouted ducts or unbonded bars, respectively(2) The load carrying capacity of the strut shall be calculated as given by Eq. (3.5).

FRcd  ( x・c br ) f ' cd .eff /  bwhere,

xc

:

(3.5)

depth of the strut(3) If the load does not act uniformly throughout the thickness of a member or the
thickness of a member is not uniform, the reduced thickness of struts shall be used to
calculate the load carrying capacity in compression.

467

Standard Specifications for Concrete Structures-2007, Design

CHAPTER 4
4.1

STRENGTH OF NODES AND ANCHORAGES OF REINFORCING BARSGeneral(1) The nodes shall be designed in a manner that all forces are appropriately balanced
and any ties are securely anchored.
(2) Appropriate additional reinforcement should be provided at the anchorage to takecare of transverse tensile stresses that are likely to be carried by tensile resistance inconcrete. In cases such reinforcement is not provided, the ultimate capacity of concretein the anchorage region shall be thoroughly re-examined.

[Commentary] (1) Any anchorage of reinforcement in the anchorage zone produces transverse
tension, which is often resisted by concrete tensile stresses. The stresses in concrete in a structuralmember could be biaxial or triaxial. For example, in the plane stress condition, the concrete is inbiaxial compression stress state in C-C-C nodes (C = compression force in strut) connecting struts
and is in biaxial tension-compression stress state in C-C-T or C-T-T nodes (T = tension force in tie).

The following verifications shall be carried out during the design of the nodes:(a) verification for the anchorage of ties in nodes(b) verification that the maximum compressive stress does not exceed the effective
compressive strength of concrete

4.2

Compression Node(1) In nodes connecting only compression struts, the increase in compressive strengthof concrete under multiaxial compressive stress state may be taken into account whenestimating the ultimate capacity. The increase in compressive strength of concrete
under multiaxial compressive stress state shall be based on adequate and reliable
experimental evidence.
(2) In special cases, such as in the anchorage zones of prestressing force, higher local
strength of concrete may be utilized, if adequate confining reinforcement is provided inthis portion.

4.3

Anchorages of Reinforcing Bar

The reinforcing bars shall be anchored in accordance with the provisions of Chapter 13
of “Design: General Requirements.”[Commentary] The ties have to be securely anchored to ensure that the reinforcement in the ties
actually yields, as assumed in the design provisions. However, the real structures, where thestrut-and-tie model is often applied, have a geometric layout that makes appropriate arrangement ofreinforcement quite difficult. Therefore, if the provisions for the standard structural detailing
468

Part 6 Strut-and-Tie Modelcannot be followed, the performance of the anchorage should be verified in accordance with
Chapter 13 of “Design: General Requirements.”
In cases where the performance of the anchorage zone cannot be achieved by the method
specified in Chapter 13 of “Design: General Requirements,” the performance of the anchorage zone
should be verified in accordance with the “2007 Guidelines for Anchorage and Joints for
Reinforcing Bars.”469