Standard Specificationsfor Steel and Composite Structures【 First Edition 】

I General Provision, II Structural Planning, III Design

December, 2009

Japan Society of Civil EngineersThis document is an English translation of the original Japanese text. JSCE assumes no responsibility
or liability for errors or inaccuracies that may occur due to use or application of the information provided
herein.

Foreword
Japan Society of Civil Engineers (JSCE) was established as an incorporated association in 1914
entrusted with the mission to contribute to the advancement of scientiﬁc culture by promoting the ﬁeldof civil engineering and the expansion of civil engineering activities. Committee on Steel Structuresof JSCE was reorganized in 1971 aiming to research and investigate steel materials, steel structuresand composite structures, and to contribute to the progress of science and technology in a ﬁeld of civilengineering. Since its establishment, the committee has organized a lot of subcommittees and they haveproduced a lot of outcomes related to steel materials, steel structures and their technological standards.
The internationalization of technological standards and the performance-based design are paid toattention in recent years. In the performance-based design, the improvement of transparency and accountability, the reductions of cost and negative environmental impact, and securing the quality and theperformance, etc. are basic requirements. The committee resolved to make the ”Standard Speciﬁcationfor Steel and Composite Structures” including hot technologies in 2004 as the JSCE speciﬁcation does
not fall behind the world trends. The speciﬁcations consist of 6 volumes. ”General provision”, ”Basic
Planning” and ”Design” were published in 2007, ”Seismic design” was issued in 2008, and ”Construction”
was also come out in 2009 in Japanese. ”Maintenance” will be also appeared soon. These are the ﬁrst
standards by the committee on steel structures made as the performance-based design format and thelimit state design method. I think that it is very meaningful to have completed the speciﬁcations using
the performance-based design format at this time when a technological standard of western countries
aims at the world standard.
It is expected that the contents of the speciﬁcations does not reveal only a state of the latest technologyof the steel structure but also the direction of activities that the committee should aim. This English
version was translated from the Japanese originals of ”General provision”, ”Basic Planning” and ”Design”
of ”Standard Speciﬁcation for Steel and Composite Structures”. I hope that the speciﬁcations will be
useful and helpful for the design of steel and composite structures in the world.
Finally, warm acknowledgment is expressed to all of the members of the Sub-Committee on Standard
Speciﬁcation for Steel and Composite Structures and the Committee on Steel Structures for their eﬀorts
to preparation of the speciﬁcations and their invariable suggestions to the contents of the speciﬁcations.

December, 2009

MORI Takeshi
Chairman, Committee on Steel Structures
Japan Society of Civil Engineers

Preface
In 1987, the Committee on Steel Structures published two design codes based on Allowable Stress
Design Method. They are ”Design Code for Steel Structures PART-A: Structures in general” and ”Design
Code for Steel Structures PART-B: Composite structures”. The newly revised above versions based on
Limit State Design Method were published in 1997.
In 2000, the committee on Steel Structures organized a sub-committee for investigation of theperformance-based design method. Its activity was to prepare and recommend a new design format,
performance-based design for steel structures, coping with globalization. The report entitled ”Towards
performance-based design method for steel structures” was published in 2003. The committee on Steel
Structures has recognized that the basic design format for steel structures of the next generation wasestablished. After the publication of the above report, the committee on Steel Structures organized the
sub-committee on Standard Speciﬁcations for Steel and Composite Structures in 2004. Its role is not
only to incorporate latest research fruits but to publish an innovative and competitive performance-based
limit state design method for steel and steel-concrete composite structures of the next generation.
It consists of 6 volumes namely ”General provision”, ”Basic Planning”, ”Design”, ”Seismic design”,”Construction” and ”Maintenance”. The three volumes including ”General provision”, ”Basic Planning”
and ”Design”, were issued in 2007. It is based on the performance-based limit state design method,and is the ﬁrst time publication for the design of steel and composite structures in civil steel structural
engineering ﬁeld in Japan. The volume of ”Design” deals with not only steel structures but also concreteslabs and steel-concrete composite girders for composite girder bridge design. Many of the provisions forsteel structures are from those in ”Design Code for Steel Structures PART A: Structures in General”
published in 1997. Even though we seldom design composite girder bridges in Japan, hybrid structures
including composite girders have been recognized to be worldwide competitive alternatives. For global
competition, the provision for composite girders is inevitable. In addition to introducing the design
formulae by AASHTO LRFD or EC given in PART-B, the original formulae developed by Japaneseyoung researchers were incorporated. This is also the ﬁrst time action in Japan after the publication ofPART-B in 1997. I hope the revising work continues towards global-top design of the next generation.
The preparation of an English version including three volumes started in 2007 by many of code writers
on a voluntary basis. First of all, I would like to express my sincere gratitude to all writers for their
devoted contribution. I also have to express my sincere gratitude to JSCE Research Fund, Committee
on ISO Aﬀairs in Civil Engineering, Prof. Yoda of Waseda University and Prof. Nogami of Tokyo
Metropolitan University for their ﬁnancial supports on publication of the English version. I would liketo give my sincere thanks to all members of the committee on Steel Structures and of the sub-committee
on Standard Speciﬁcations for Steel and Composite Structures for their valuable comments.

December, 2009NAGAI Masatsugu
Chairman, Subcommittee on Standard Speciﬁcations for Steel and Composite Structures
Committee on Steel Structures
Japan Society of Civil Engineers

Committee for Steel structures
Adviser
ChairmanVice-chairman
Secretary general
Member
Ikuma M.,
Echigo S.,
Okamoto T.,
Kainuma S.,
Kiyomiya O.,
Sakano M.,
Sumi M.,
Nagai M.,
Nishikawa K.,
Fukada S.,○ Honma K.,
Murakoshi J.,
Yamamoto H.,: Abe H.,
Sakai H.,: Mori T.
: Takagi S.
: Sasaki Y.

Ito M.,
Nishimura N.,

Igarashi H.,
Oga M.,
Ogawa A.,
Kasuga A.,○ Sakai S.,
Shito K.,
○ Tachibana Y.,
Nakazawa M.,○ Nogami K.,
Fujii K.,
Maekawa K.,
Mori K.,
Yukawa M.,

Usami T.,
Watanabe E.

Ichikawa A.,
Ogaki K.,
Okui Y.,
Kamihigashi Y.,
Keira K.,
○ Sugimoto I.,
Tatsumit M.,
Nakajima A.,
Nozawa S.,
Fujino Y.,
Masuda N.,○ Yaginuma Y.,
Yoda T.

Kato M.,

Kuranishi S.,

Iwasaki E.,
Ota K.,
Oshita S.,○ Kaneko S.
Goto Y.,
Sugiura K.,○ Tateishi K.,
Naganuma T.,
Hayashikawa T.,
Fujiwara H.,
Miki C.,
Yamaguchi E.,

Iwanami M.,
Otori Y.,
Ono K.,
KItada T.,
Konishi T.,
Sugiyama T.,
Tanaka M.,
Nara S.,
Hirabayashi Y.,
Hotta T.,
Murakami S.,○ Yamaguchi T.,○：Organizer

Sub-committee for Standard Specificationsfor Steel and Composite Structures
Chairman
Secretary general
Member
Ikuma M.,
○ Ichikawa A.,
Ogaya S.,
Sakano M.,
Tateishi K.,
Nozawa S.,
Miki C.,
Yokota H.,：Nagai M.
：Yamaguchi E.

Ito N.,
Inokuma Y.,
Okui Y.,
Sugiura K.,
Tamaoki T.,
Hayashikawa T.,○ Murakoshi J.,
Watanabe E.,

Suzuki E.,
Iwakuma T.,
Ono K.,○ Sugiyama T.,
Nara S.,
Hino S.,○ Mori T.,
Park Y.S.,

Hakamada F.,○ Usami T.,
Kitada T.,○ Sumi M.,○ Nishimura N.,
Hujino Y.,
Yamamoto H.,
Kyung K.S.,

Abe M.,
Okamoto T.,
Goto Y.,
Takagi S.,○ Nogami K.,
Hotta T.,
○ Yoda T.,
Ha D.H.∗○：Organizer* ：Observer

Sub-committee for Standard Specificationsfor Steel and Composite Structures
General Provision WG
Chairman：Sugiyama T.

Member
Ikeda M.,
Nogami K.,

Ichikawa A.,
Mori T.,

Usami T.,
Yamaguchi E.

Okui Y.,

Nishimura N.,

Structural Planning WG
Chairman：Ichikawa A.

Member
Ikeda H.,
Katsuchi H.,
Morino M.,○ Ikeda M.,

Sugiyama T.,
Yamamoto H.,

Ito A.,
Takagi S.,
Yokota H.

Ogaki K.,
Hosaka T.,

Ono K.,
Hota T.,

old member : Inokuma Y.
○：Organizer

Design WG
Chairman
Secretary general
Member○ Akimoto R.,○ Ishikawa T.,
Ogaki K.,
○ Kitahara T.,○ Sugiyama T.,
Nakasu K.,○ Huruya N.,○ Murakami S.,○ Yoneyama H.

：Yoda T.
：Nogami K.

Arima N.,○ Uchida D.,○ Okada J.,
Kumagai Y.,○ Tanaka K.,○ Nakahara T.,
Maeda K.,
Yanagawa H.,○ Iura M.,○ Ikariyama H.,○ Ikeda M.,○ Urata M.,○ Ota M.,

○ Ota K.,

○ Okui Y.,○ Kainuma S.,○ Kawabata A.,

Sato N.,○ Tanaka C.,○ Nakamura S.,○ Miura Y.,○ Yabuno M.,○ Saito N.,○ Suzuki S.,○ Tsuruta H.,○ Nakazawa M.,○ Nakamura S.,○ Nagai M.,○ Minami K.,○ Murakami M.,○ Yamaguchi E.,○ Yamaguchi T.,

old organizer : Ikeda D.
○：Organizer

Sub-committee for Standard Specificationsfor Steel and Composite Structures
Writing author of Design WG
Chapter 1, 2

○ Sugiyama T.∗ ,Akimoto R.∗∗ ,Chapter 3, 5

○ Nakamura S.∗ , ○ Okada J.∗∗ ,∗Chapter 4, 6

Ikeda M.,
Okui Y.,

Huruya N.

∗∗○ Yamaguchi E. , ○ Ishikawa T. ,Tanaka K.,

Nakazawa M.,

Akimoto R., Iura M.,
Saitou N.,
Murakami S.,
Yamaguchi T.

Chapter 7○ Kitahara T.∗ ,Urata M.∗∗ ,Ota M.,

Chapter 8○ Kainuma S.∗ ,Minami K.∗∗ ,Tsuruta H.

Chapter 9

Sugiyama T.∗ ,∗Chapter 10, 12
Chapter 11○ Saitou N. ,Miura Y.,

Yabuno M. ,Murakami M.

○ Yamaguchi T.∗ ,Chapter 14
Chapter 15○ Murakami S. ,Yoneyama H.

Akimoto R.∗∗ , ○ Kitahara T.,∗∗∗

Chapter 13

Urata S.

Iura M.,

Miura Y.∗∗ ,Yoneyama H.

Ishikawa T.,

Nakamura S.,

Tanaka K.,

Minami K.

∗∗

Murakami M. , Kitahara T.,
Nakazawa M.,
Nakamura S.
○ Kawabata M.∗ ,Ikariyama H.∗∗ , Nakamura S., Ota K., Uchida D.,
Tanaka C.,
Nakahara T., Suzuki S.,
Akimoto R.
∗∗∗○ Okui Y. ,Ota M. , ○ Okada J., ○ Huruya N., Yabuno M.,○ Nagai M., ○ Nakamura S., ○ Nogami K.
∗∗∗：Chief：Organizer○：Member who translated into English

Volume I

General Principles

Standard Specifications for Steel and Composite Structures【 General Principles 】
Contents
Chapter 1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Fundamental Philosophy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.3 Scope. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2
1.4 Documents concerning Design, Construction and Maintenance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.5 Meanings of Descriptive Words and Clauses in These Specifications . . . . . . . . . . . . . . . . . . . . . . . 4
1.6 Ability and Responsibility of Engineers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.7 Check at Structural Plan and Design Stages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.8 Terms and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Chapter 2 Basis for Structural Planning, Design, Construction and Maintenance . . . 10
2.1 Purpose of Structural Planning, Design, Construction, and Maintenance . . . . . . . . . . . . . . . . . 10
2.2 Verification of Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Performance Level and Importance of Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

（ 1）

1

Chapter 1 General
1.1 Fundamental Philosophy
The fundamental philosophy of these speciﬁcations is that performance veriﬁcation methods
shall be applied to all of structural plan, design, construction, and maintenance of steel andcomposite structures and engineers’ ethics shall be observed at every stage.
【 commentary 】

These Standard Speciﬁcations for Steel and Composite Structures are based on performance veriﬁcation methods in which the required performance of a structure is speciﬁed ﬁrst and then actual performance is veriﬁed at all stages: structural planning, design, construction and maintenance.
Consequently, the fundamental philosophy behind these speciﬁcation is that performance veriﬁcation
methods should be applied at the structural planning, design, construction, and maintenance stages ofsteel and composite structures, while fully observing engineering ethics at every stage. Within these
speciﬁcations, the actual articles relating to the observance of engineering ethics can be considered the
1 accountability for structural planning, design, construction, and maintenance work; 2following: 
traceability of reasons for decision-making after the fact; and 
3 compliance. Currently, some performance requirements of structures are not explicitly veriﬁed, so some parts of the speciﬁcations are notfully complete.

1.2 Composition
These speciﬁcations are composed of six volumes; that is, General principles volume, structuralplan one, design one, seismic design one, construction one, and maintenance one.
【 commentary 】

The six volumes of these speciﬁcations apply to the structural planning, design, construction, andmaintenance of structures.
A structure’s various performance requirements should be upheld throughout the design working
life of the structure and this must be conﬁrmed. It is necessary to succeed to the information relatingto ”performance requirements and methods of achieving them” and/or ”purpose and achievement
method” at each stage of structural planning, design, construction, and operation and maintenanceto the next stage certainly. That is, all stages should correlated with each other closely as shownin Fig.C1.2.1. At the structural planning and design stages, assumptions are made about the typeand size of structure and then the performance level required of this assumed structure is veriﬁed.
Immediately after construction is completed, it should be checked whether this required performancelevel is satisﬁed or not. At the maintenance stage, the performance level of the in-service structureis estimated based on information collected through inspections, because the performance level ofa structure generally decreases over time. Based on this estimate, a judgment as to the structuralsoundness of the structure - that is, whether the performance level of the structure is equivalent to or
exceeds the a priori determined required performance - is made and the result is later fed back into
the operation and maintenance plan.

2Standard Specifications for Steel and Composite Structures [General principles]

As noted above, checking and conﬁrmation of the performance level of a structure continues throughall stages of structural planning, design, construction, and operation and maintenance. Thus, these
speciﬁcations include ﬁve volumes corresponding to structural planning, design, construction, andmaintenance of structures, respectively. It should be noted that design is separated into a Designvolume and a Seismic Design volume. This is because it is generally recognized that design philosophy
and veriﬁcation techniques relating to seismic design are diﬀerent from those of other areas of structuraldesign and that a separate explanation of seismic design may be convenient for design engineers.

Level of performance

Marginal level of Performance(use beginning)
Planning
Assumption

No

Performa

Fig.C1.2.1

Production

Operation

Maintenance
Yes
PerformanceNo
Yes
Correction
Yes
Review ofmaintenanc(check)(check and measures)
Passing
Check result
Forecast ofConfirmation of
performanceNo
Measures(repair andPerformance of structure during its life cycle

1.3 Scope
These speciﬁcations shall be applied to the structural plan, design, construction, and maintenance of steel structures, composite girders, and composite columns (described as ”steel andcomposite structures” hereafter).
【 commentary 】

These speciﬁcations apply to the structural planning, design, construction, and maintenance of steel
structures, composite girders, and composite columns ﬁlled with concrete. Composite columns aretreated explicitly only in the Seismic Design volume. The structures considered in these speciﬁcations
are general steel structures in which structure of the main members consists of steel and composite
girders and columns composed of both steel and concrete. As for composite girders, references [JSCE
2002a] and [JSCE 2002b] may be referred to instead of these speciﬁcations.
Highway and railroad bridges are the main focus of these speciﬁcations, although port and harbor
structures, river structures, and electric power facilities are also considered. Each of these structureChapter 1

General3

types also has its own speciﬁcations or standards for planning, design, construction, and maintenance.
However, as each of these speciﬁcations or standards is codiﬁed for a speciﬁc type of structure, there issome possibility of diﬃculty in attempting to plan, design, construct, and maintain a speciﬁc structurethat does not have a speciﬁc applicable speciﬁcation or standard. Here, not only are the normal
techniques for structural planning, design, construction, and maintenance relating to speciﬁc steel andcomposite structures such as highway and railway bridges speciﬁed, but their applicability to the otherstructures is also considered.
Where the articles of these speciﬁcations are insuﬃcient and/or inappropriate for dealing withthe structural planning, design, construction, and maintenance of a speciﬁc individual structure type,it may not be necessary to apply these speciﬁcations if the eﬀectiveness, appropriateness, accuracy,
and applicable scope of another selected technique can be certiﬁed. Even in this case, however, thestructural planning, design, construction, and maintenance of the structure may be implemented while
taking account of the substance of these speciﬁcations.

1.4 Documents concerning Design, Construction and Maintenance(1) Design documents, drawings, construction procedure documents, maintenance documents,and other relevant documents shall include the description that compliance with relevant
regulations has been fulﬁlled at every stage of structural plan, design, construction, andmaintenance. These documents also shall be lodged.
(2) Design documents, drawings, construction procedure documents, maintenance documents,and other relevant documents shall be presented in an appropriate manner satisfying therequirements for oﬃcial information and/or documents. In case that required items are notshown, these documents should be made based on the rules such as Japanese Industrial
Standards.
【 commentary 】

As already noted, the fundamental philosophy of these speciﬁcations is that performance veriﬁcation
methods should be applied to the structural planning, design, construction, and maintenance stages ofsteel and composite structures with full observance of engineering ethics at every stage. Given this, full
attention should be paid to the following points when producing design, construction, and maintenancedocuments.

1 The design document should describe and give the reasons for selecting particular structural
types, structural materials, construction methods, etc. at the structural planning and design
stages. (The accountability requirement)
2 In cases where the articles of these speciﬁcations are not applied, the engineering justiﬁcationof the appropriateness of this decision relating to the performance veriﬁcation method should
be explained in the design document. If a newly developed performance veriﬁcation approachis adopted, both the title of the third party institution that has certiﬁed the appropriatenessof the new method and the results of certiﬁcation should be provided in the design document.
Moreover, construction documents should be prepared so as to ensure that construction work
satisﬁes all of the performance requirements of the design stage.
3 In cases where structural types, structural materials, construction methods, etc. are determined
through consultation among the persons concerned and/or on the direction of the owner becauseof the absence of speciﬁc requirements, not only should details of the determinations (including
the decision-making process) be written down in design, construction, and maintenance documents, but also the names of participants in the consultation and/or the director(s). (The4Standard Specifications for Steel and Composite Structures [General principles]

traceability requirement)

1.5 Meanings of Descriptive Words and Clauses in These Specifications
Meanings of descriptive words and clauses in these speciﬁcations are classiﬁed as shown in Table
1.5.1.
Table 1.5.1 Meanings of descriptive words and clauses
Meanings of descriptive words and clauses

General examples for descriptive words and clauses【 Requirement 】∼ shall (be)items that shall be necessarily satisfied according∼ should (be)to these specifications∼ is to (be)【 Recommendation 】

item that might be the most commendable among∼ shall preferably (be)several alternatives【 Possibility】

item that is one of the acceptable alternatives∼ may (be)【 commentary 】

In order to ensure that the meaning of each article is clear, the phrasing used in these speciﬁcations
is classiﬁed largely into the three categories shown in Table 1.5.1. This classiﬁcation has been adopted
with reference to [JSCE 2003] and [Japan Highway Agency 2002].

1.6 Ability and Responsibility of Engineers(1) The engineers who take part in the structural plan, design, construction, and maintenanceof steel and composite structures shall be the experts in the relevant ﬁeld.
(2) The engineers who take part in the structural plan, design, construction, and maintenanceof steel and composite structures may be desirable to be the persons qualiﬁed by the publicagencies in the relevant ﬁeld.
(3) The engineers who take part in the structural plan, design, construction, and maintenance ofsteel and composite structure shall be responsible for ensuring of public safety and beneﬁt,preservation of environment, and so on.
(4) The engineers who take part in the structural plan, design, construction, and maintenanceof steel and composite structure shall have accountablity for both decision making results
and evidence of performance-based veriﬁcation.

【 commentary 】

This article is prescribes the skills required of engineers who take part in the structural planning,
design, construction, and maintenance of steel and composite structures as well as their responsibilities.
The quality of structural planning, design, construction, and maintenance outcomes depends generally
on the skills of the engineers involved in these activities, because they often have to make decisions
based on their technical knowledge and/or experiences at every stage of structural planning, design,
construction, and maintenance. Consequently, engineers who carry out the structural planning, design,Chapter 1

General5construction, and maintenance of steel and composite structures should be experts with experience inthe relevant ﬁelds. In other words, the engineers should preferably be persons certiﬁed in the relevant
ﬁeld by public agencies such as the Japan Society of Civil Engineers, the Institution of Professional
Engineers Japan, and so on.
The structures of greater safety, economy, and durability structure can be planned, designed, constructed, and maintained through the contribution of skilled and experienced engineers in the relevant
ﬁeld.
The design, construction, and maintenance documents produced according to Article 1.4 should
be lodged appropriately by the engineers involved in structural planning, design, construction, andmaintenance so that everyone can refer to the adopted standards, references, minutes, etc. throughout
the durable lifetime of a structure.

1.7 Check at Structural Plan and Design Stages
An appropriate check shall preferably be made in order to ensure the required technologicallevel and quality of structural plan and design.
【 commentary 】

So as to ensure that a structure is of the required quality, appropriate reviews of whether the
structural types, structural materials, and structural details adopted at the structural planning anddesign stages are reasonable and whether adequate performance veriﬁcation is taking place should
preferably be carried out by an authorized third-party institution. If no such institution is yet available,
it is acceptable for these reviews to be carried out by another design company.

1.8 Terms and Definitions
The terms used commonly in these speciﬁcations are deﬁned as follows.
(1) General terms relating to structural plan, design, construction, and maintenance1) Performance-based design method: design method in which no restrictions are applied
to the structural types and materials, design methods, construction methods if thedesigned structure has only to keep the required performance level. In other words,
design method in which the speciﬁed performance of the structure may be ensured atevery stage of structural plan, design, construction, and maintenance once the objective
and function of structure is deﬁned clearly and the performance of structure is speciﬁed
so as to fulﬁll its function.
2) Regulation-based design: design method in which structures or structural members aredesigned based on the speciﬁc design codes where the proper procedures such as design
calculations, the kind of structural materials and their size, etc. are speciﬁed.
3) Deemed-to-satisfy regulation: regulations in which one or more of solutions that areconsidered to satisfy the required performance is illustrated. These regulations may be
adopted in case that veriﬁcation method of structural performance is not necessarily
speciﬁed. The kind of structural materials and their size, the procedures such as design
calculations that have been regarded as proper empirically, etc. are speciﬁed in theseregulations.
4) Reliability-based design method: design method in which the possibility that structures/structural members lead to limit states is estimated based on the probabilistic

6Standard Specifications for Steel and Composite Structures [General principles]

theory.
5) Limit state design method: design method in which limit states to be veriﬁed is speciﬁed
clearly and partial factor design format is adopted as the veriﬁcation format. Partial
factor design format is classiﬁed into Level 1 veriﬁcation format from the reliabilitybased design viewpoint. Strictly speaking, partial factor design format is not equivalent
to limit state design method although both are sometimes regarded equivalent in Japan.
6) Partial factor design format: design format in which some partial factors are incorporated in order to consider the uncertainties or scatter relating to actions, geotechnicalparameters, size of structural members, structural analysis methods, etc..
7) Life cycle cost: the total amount of cost that is spent for structural plan, design, construction, maintenance, and demolition of structure; in other words, the total amountof cost invested during the life cycle of structure.
8) Design working life: assumed period for which a structure is to be used for its intended
purpose without major repair being necessary. During design working life, originallyplanned regular inspection and repair are continued. Design working life is determinedat design stage.
9) Durable lifetime: the period from the service start to a point in time when the performance of structure becomes down due to fatigue, corrosion, material deterioration, etc.
and structure leads to its limit states.
10) Objective: commonly used expression of the reason why the structure is constructed. It
may be desirable that the objective is expressed by using the word such as client/user
as the subject.
11) Basic requirements: the clauses to be observed relating to the use and function of
structure, environmental conservation, and safety of work. These clauses relating to
the required size/space and acts such as design and construction, etc. are enacted basedon the relevant laws.
12) Function: the role that structure has to play in accordance with its objective.
13) Check: the conduct that is carried out by a authorized third party institution in orderto scrutinize whether the design process compounded from determination of objective
to veriﬁcation is proper or not.
14) Authorization: determination of the third party that is able to perform the check.
15) Certiﬁcation: act that the authorized third party institution checks the structural design
and issues the certiﬁcate if the design is proper.
(2) Terms relating to performance
1) Performance: ability that the structure has to demonstrate in accordance with its
objective or requirements.
2) Required performance: performance that the structure has to keep in order to achieve
its objective.
3) Performance item: item into which the required performance is subdivided. One veriﬁcation index to which one limit state generally corresponds is determined to eachperformance item.
4) Performance level: the level of performance that is required to each structure. Performance level is determined for each required performance depending on its necessity.
5) Safety: ability of a structure to ensure the lives and assets of users and the third party.
6) Serviceability: ability of a structure to perform adequately so that the users do not
perceive any intolerable unpleasantness or unease.
7) Durability: ability of a structure or structural element to resist the deterioration causedby repeating variable action and/or environmental action. In case of steel and com-

Chapter 1

Generalposite structures, corrosion of steel members caused by environmental action, fatigue
phenomenon caused by repeating variable action, and material and strength deterioration of concrete members are considered.
8) Repairability: ability of structure to be restored to the originally speciﬁed performancelevel when intended actions attacks structure and then its performance level may decrease.
9) Societal and environmental compatibility: ability of structure not only to contribute to
the sound societal, economic, cultural, etc. activities but also to minimize the infection
upon the surrounding social and natural environment.
10) Constructibility: ability to keep construction work safe and certain during fabricationand erection.
11) Initial soundness: ability of structure that its performance just after completion is notbelow the level intended at design stage.
12) Maintainability: easiness of maintenance of structure.
(3) Terms relating to limit state
1) Limit state: a state beyond which the structure or structural element no longer satisﬁes
the required performance.
2) Safety limit state: a state associated with collapse, or with other similar forms of structural failure caused by large deformation, large displacement, vibration, etc.. Safety
limit state is used as the limit state corresponding to the structural safety. The words”ultimate limit state” are adopted in Seismic Design Volume as this expression often
used instead of ”Safety limit state”.
3) Serviceability limit state: a state that corresponds to conditions beyond which speciﬁedservice requirements for a structure or structural element are no longer met. Serviceability limit state is used as the limit state corresponding to the serviceability.
4) Repair limit state: a state which corresponds to conditions beyond which repair ofstructure is not possible with current applicable repair technology, with reasonable
cost, nor within reasonable period and structure is not able to be under service. Repair
limit state is used as the limit state corresponding to the repair easiness. In Seismic
Design Volume, the words ”Damage limit state” is adopted instead of ”Repair limit
state”.
5) Fatigue limit state: a state associated with fatigue failure of structure or structuralmember caused by repeating variable action. Fatigue limit state is used as the limit
state corresponding to the fatigue durability.
(4) Terms relating to veriﬁcation
1) Performance veriﬁcation: activities performed in order to verify if the designed structure
satisﬁes all of the performance requirements or not. In case that limit state design
method is adopted, judgment is made by comparing response value S with limit valueof performance R.
2) Veriﬁcation index: index to express a performance item as a physical quantity. Veriﬁcation indices are utilized in performance veriﬁcation. ．
3) Response value (Demand) S : physical quantity caused in the structure by action.
4) Limit value of performance (Capacity) R : allowable limit physical quantity towards
corresponding structural response. This value is determined based on required performance level.
5) Statistical characteristic value: a value corresponding to a priori speciﬁed fractile ofthe statistical distribution of random variable such as material property and action.
Expected value and mode of random variable are regarded as statistical characteristic

78Standard Specifications for Steel and Composite Structures [General principles]values.
6) Optimization: activities performed in order to obtain an optimal solution so that theobjective function including the required performance, performance item, etc. as thesubordinate variables may take the smallest or the largest value under some restraint
conditions.
7) Partial factor: a factor assigned to each design value in order to consider its uncertainty.
Five partial factors, i.e. action factor, material factor, factor for structural analysis,factor for structural member, and factor for structure are generally adopted.
8) Factor for structure: a factor in order to consider the importance of structure, societal
and economic inﬂuence caused by the failure of structure, and so on.
(5) Terms relating to actions
1) Action: all causes which draw deformation, displacement, constraint, and deteriorationof structure or structural element.
2) Load: an assembly of mechanical forces directly acting on a structure which are converted from actions through the analytical model. Load is used as an input datum fordesign calculation of stress resultant, stress, displacement, and so on.
3) Design value of action: a value obtained by multiplying the action factor to the characteristic value of corresponding action.
4) Direct action: an assembly of concentrated or distributed mechanical forces acting ona structure.
5) Indirect action: the cause of deformations imposed on the structure or constrained init.
6) Environmental action: mechanical, physical, chemical or biological action which may
cause deterioration of the materials constituting a structure.
7) Permanent action: action which is likely to act continuously throughout a given reference period and for which variations in magnitude with time are small compared withthe mean value.
8) Variable action: action for which the variation in magnitude with time is neither negligible in relation to the mean value nor monotonic.
9) Primary variable action: one or one set of variable actions considered as the most primary one in case that load combination is taken into account in performance veriﬁcation
activities.
10) Subsidiary variable action: a action which is considered as the subsidiary one among
variable actions and which is additionally combined with the combination of primaryvariable action and accidental action.
11) Accidental action: action that is unlikely to occur with a signiﬁcant value on a given
structure over a given reference period and which may cause a serious damage for astructure if once occurs.
12) Action modifying factor: a factor to convert the standard or nominal value of action
into characteristic value.
13) Action factor: a factor to consider the unfavorable deviation of statistical characteristic
value of action, uncertainty relating to action model, change of action characteristics
during a given reference period, the inﬂuence of action characteristics on the relevant
limit state of structure, variation of environmental action, and so on.
(6) Terms relating to structural materials
1) Characteristic value of material strength: a value corresponding to an a priori speciﬁed
fractile of the statistical distribution of material strength. Statistical distribution isdetermined based on the statistical data which are obtained from the standardized

Chapter 1

General9material strength test.
2) Standard value of material strength: a value of material strength adopted in otherstructural design speciﬁcations/standards except ”Standard Speciﬁcations for Steel andComposite Structures”.
3) Material strength modifying factor: a factor to convert the standard value of material
strength into characteristic value.
4) Material factor: a factor to consider the unfavorable deviation of statistical characteristic value of material strength, the diﬀerence of material properties between experiment
specimen and real structure, the inﬂuence of material properties on the relevant limit
state of structure, change of material properties during a given reference period, andso on.
5) Design value of material strength: a value obtained by dividing the characteristic valueof material strength by the corresponding material factor.
(7) Terms relating to calculation of response value
1) Factor for structural analysis: a factor to consider the accuracy of structural analysis
methods which are applied in the calculation of stress resultant, etc, the uncertainties
relating to modeling procedure of structure, and so on.
2) Design value of response: a value obtained by multiplying the factor for structural
analysis to the response value. Response value is calculated by using the values ofactions which are multiplied by their corresponding action factors.
(8) Terms relating to calculation of limit value of performance
1) Factor for structural member: a factor to consider the accuracy of structural resistanceanalysis methods which are applied in the calculation of load-carrying capacity, variation of structural member size, importance of the role of structural member, and soon.
2) Design limit value of performance: a value obtained by dividing the limit value of performance by the factor for structural member. Limit value of performance is calculated
by using the design values of strength materials.
【 Commetary 】

Terms commonly used in these speciﬁcations are deﬁned based on [JSSC 2001], [JSCE 2003], andso on. Terms peculiar to each volume are deﬁned in the relevant volume.
As for the term ”Safety limit state” as speciﬁed in (3) 2), it is used here to clarify the relation
between required performance and the relevant limit state; the term ”Ultimate limit state” is commonlyused instead of this term. The term ”Safety limit state” is adopted in these speciﬁcations because it
incorporates the concept of public safety, durability in a broad sense, initial soundness, etc. in addition
to the idea of ”Ultimate limit state” in the Design volume.
References in Chapter 1
Japanese Society of Steel Construction (2001) ：Performance design guidelines for Civil Engineering Steel Structures, JSSC Technical Report No. 49.
Japan Society of Civil Engineers (2002a) ：Standard Specification for Concrete, Volume of Structural Performance Verification ．
Japan Society of Civil Engineers (2002b) ：Guidelines for Performance Verification of Hybrid Structures (tentative) ．
Japan Road Association (2002) ：Specifications for Highway Bridges and Commentary, I Common Specifications Volume, II Steel Highway Bridges Volume ．
Japan Society of Civil Engineers (2003) ： Comprehensive Design codes (tentative) code PLATFORM ver.1 ．

10Standard Speciﬁcations for Steel and Composite Structures [General principles]

Chapter 2 Basis for Structural Plan, Design,
Construction and Maintenance
2.1 Purposes of Structural Plan, Design, Construction and
Maintenance
After the most suitable kind and type of structure are selected and the outline of its dimensions
are determined at the structural plan stage, steel and composite structures shall satisfy all of therequired performances such as safety, serviceability, durability, repairability, societal and environmental compatibility, etc. at every stage of design, construction, and maintenance throughout agiven reference period.
【 commentary 】

Steel and composite structures should be ﬁt for purpose and should not only be safe but alsofunctional. Therefore, once an appropriate plans for steel and composite structures (or structuralmembers) have been developed, they should be designed, constructed, and maintained so as to ensure
adequate safety against various actions and to be functional during their construction and service
periods. Steel and composite structures should also be durable and compatible with their surroundings.
For example, bridges are constructed to allow roads, railways, etc. to cross rivers, straits, roads, andrailways and so that persons and goods can be transported over them. Although the most important
performance requirement for bridges is structural safety, it is also important to secure good structural
durability to ensure the long-term structural soundness of the bridge. Furthermore, bridges shouldbe acceptable to nearby residents and should not aﬀect those residents with uncomfortable vibration
and/or noise radiation that may be caused by the passage of vehicles over them. A further requirement
is that bridges should have excellent aesthetic qualities.
At the structural planning stage, a bridge should be compatible with its purpose, while 
1 legal2 economic eﬃciency should be considered.
restrictions on the use and function of the bridge and also 
The performance requirements, meaning 
3 safety, 
4 serviceability, 
5 durability, 
6 social and environ7 earthquake inﬂuence, 
8 constructability, and 
9 maintenance, should also bemental compatibility, 
discussed at the structural planning stage. Multiple alternatives with respect to structural type should
be compared and discussed based on a consideration of the above-mentioned performance requirements
in order to determine the optimal type.
At the structural design stage, comparison and discussion of various matters such as structural
material selection, corrosion protect method, determination of cross sections, etc. is carried out.
Although these comparisons and discussions are based on economic eﬃciency, the optimal alternative
should be determined not from the viewpoint of minimum initial construction cost but rather inconsideration of minimum life-cycle cost. In other words, ease of maintenance should be taken into
account so as to ensure that the bridge is durable as a semi-permanent structure.
The design working life of a structure can be considered from three points of view, as follows:a) economic working life corresponding to economic life according to asset depreciation;b) functional working life corresponding to the period until the structure fails to fulﬁll its socially
expected function;c) physical working life corresponding to the absolute end when the structure itself malfunctions.
In structural design, it is generally assumed that the physical working life is greater than the otherChapter 2

Basis for Structural Plan, Design, Construction and Maintenance11

two measures of working life
Minimizing the life-cycle cost means that economic eﬃciency is investigated through considerationof both economic working life and physical working life. No quantitative estimation method has yet
been established for doing this, although society has recently come to expect the establishment of such amethod. The term ”functional working life” represents the time until the structure is considered uselessbecause of changing social and economic activity. Taking account of the present level of structural
engineering development, it may be impossible to determine this functional working life. However,structures should be designed so that the physical working life is longer than any predicted functional
structural life. Design working life is set in the range 60 to 100 years in the current design speciﬁcations
for highway and railway bridges. As many existing bridges have been in service for more than 100
years, design working life is generally established as 100 years at present.

2.2 Verification of performance(1) At every stage of structural plan, design, construction, and maintenance, required performances of steel or composite structure shall be determined deﬁnitely. In general, safety,
serviceability, durability, repairability, societal and environmental compatibility are to berequired as required performances.
(2) At the design stage, performance level shall be shown against each of performance item
which corresponds to the relevant required performance and performance veriﬁcation shallbe carried out for every performance item.
(3) In the performance veriﬁcation of steel and composite structures, veriﬁcation indices andtheir corresponding limit values of performance shall be determined ﬁrst, and then the
check whether structural response value obtained through an appropriate numerical analysis
method is less than or equal to the limit value of performance is to be carried out in general.
(4) Conﬁrmation through experiments, etc. or observance of regulations relating to structural
types, structural materials, etc. may be substituted for the veriﬁcation method described in
the above (3).
(5) At the structural plan and design stages, veriﬁcation shall be performed so that response
value is less than or equal to the limit value of performance throughout both construction
period and working life. Speciﬁc veriﬁcation methods are illustrated in Structural Plan
Volume, Design Volume, and Seismic Design Volume.
(6) At the end of construction stage, just completed structure shall fulﬁll the all of required
performances considered in its design. Speciﬁc veriﬁcation methods are illustrated in Construction Volume.
(7) During working life of structures, an appropriate inspection or examination method, a propercountermeasure against damage, etc. shall be selected so as to satisfy all of the required
performances. Speciﬁc veriﬁcation methods are illustrated in Maintenance Volume.

【 commentary 】(1) The ﬁrst step at the structural planning and design stages is to determine the required performance of the steel or composite structure. However, there remain at present various opinions
and arguments regarding the deﬁnition and classiﬁcation of required performance; as yet, noconsensus on these matters has been reached.
In [Ministry of Land, Infrastructure, Transport and Tourism (2002)], three performance requirements - that is, safety, serviceability, and restorability - are deﬁned as the fundamental
required performance of a structure. These three are subdivided according to the function of12Standard Speciﬁcations for Steel and Composite Structures [General principles]the structure. In the subdivisions, the performance requirement ”durability” occurs commonly.
It is very important for the durability of a steel or composite structure to be ensured at every
stage of structural planning, design, construction, and maintenance, because the physical working life of the structure is signiﬁcantly aﬀected by how deterioration of structural performancewith time under repeated variable actions and/or environmental actions is controlled. For thisreason, durability is deﬁned as one of the performance requirements in these speciﬁcations.
Social and environmental compatibility is a recent requirement associated with changing social and economic circumstances. This new fundamental performance requirement may become
crucial from now on, although techniques for deﬁning and estimating the relevant limit state are
inadequate at present [JSCE (2003)].
Further, performance during the construction stage is to be carefully considered at every stageof structural planning, design, and construction. This performance requirement is deﬁned as”workability” and is regarded as one of the performance requirements in these speciﬁcations.
In summary, the performance requirements adopted in these speciﬁcations are safety, serviceability, durability, restorability, social and environmental compatibility, and workability. Table
C2.2.1 shows the performance items corresponding to each performance requirement. These performance requirements and performance items are applicable not only to structural planning anddesign but also to the maintenance of structures in service.
(2) When verifying performance requirements at the design stage of steel and composite structures, it
is usual to verify whether the designed structure will reach each of the limit states corresponding
to the a priori established level of required performance. The term ”limit state” means thestate assumed as the extreme margin of each performance item (the itemized of performancerequirements). This means that, if each of these limit states is clearly established, performance
veriﬁcation based on the limit state design method is possible. The performance items and theircorresponding limit states are prescribed in each volume.
The basis of performance veriﬁcation according to performance-based design in these speciﬁcations is that the design value of demand, S, should be less than the design value of capacity, D,for every performance item, where both S and D are calculated using partial factors. Fig.C2.2.1
illustrates the framework for performance veriﬁcation. In cases where it is not possible to establish a limit state, performance veriﬁcation is carried out by optimizing an objective function
such as cost, utility, etc., which is a function of the design variables [JSCE (2001)].
At present, it is possible to establish relevant limit state(s) for some performance requirements.
For others, it is not easy to do so. For the former, performance veriﬁcation is carried out
quantitatively. On the other hand, in the latter case, optimization of the objective function is
attempted instead of a quantitative performance veriﬁcation.

Verification for each performanceverification

Level of action
Death and live-load
Environmental
action etc.

index
Response Performan limit
value
value

Structurallevel
Load-proof and levelof the lesion
Use period etc.
Calculation of demand

Fig.C2.2.1

Sectional force, stress, anddisplacement and transformation
Cost and environmental impact, etc.

Power-proofof section
Rigidity
Generation
cost etc.

Calculation of capacity

Framework of performance verification(3) In calculating response values, it is necessary to choose a structural model as well as a structural

Chapter 2

Table C2.2.1
Performancerequirement
SafetyExamples of performance requirements of structuresand related performance items in these specifications

Performance item

Example of check item

Handling with book

Structural safety

resistance of structural member, resistance of whole structure, stability, deformation performance, etc.
injury to users and third parties(falling objects etc.)
vehicle operating performance underusual conditions (soundness and rigidity of road)train operating performance and ride
comfort under usual conditions
pedestrian comfort under usual conditions (walking-induced vibration)level of damage (ease of restoration)

DesignvolumePublic safety
Vehicle operating
performance
Serviceability

Restorability

Pedestrian comfort
Restorability after earthquake
Fatigue resistance

Durability

Socialandenvironmental
compatibility

Workability

13

Basis for Structural Plan, Design, Construction and MaintenanceCorrosion resistanceResistancetomaterial deterioration
Maintainability
Socialbilitycompati-fatigue durability against variable actions
rust prevention and corrosion protection performance of steel material
concrete deteriorationease of maintenance (inspection, painting, etc.) and ease of restoration
appropriateness of partial factor (consideration of social importance ofstructure)social utility during life cycle of structurenoise, vibration, environmental impact(CO2 emissions), aesthetics, etc.
safety during construction

Economic rationality
Environmental
compatibility
Safetyduringconstruction
Initial soundness

material quality, welding quality, etc.

Ease of constructionease of fabrication and construction
work

DesignvolumeStructuralplanning
volumeSeismic
designvolumeMaintenancevolumeDesignvolumeDesignvolumeDesignvolume・Construction
volumeanalysis method that estimate structural performance appropriately. Many highly advanced
structural analysis methods are available now as a result of remarkable development in computer
techniques in recent times, so the most appropriate method should be chosen corresponding to thetype of structure and the aim of performance veriﬁcation. Note that it is essential to appropriately
model action loading and structural type in order to obtain really accurate solutions, even if thismeans adopting a highly advanced structural analysis method. Furthermore, the results obtained
should be properly investigated and utilized.
(4) Where it proves diﬃcult to calculate response values using a numerical analysis method and/or
to establish suitable limit states, experimental conﬁrmation or veriﬁcation of compliance withregulations relating to the structure type, structural materials, etc. may be carried out insteadof a performance veriﬁcation.
(5) At the structural planning and design stages, it should be veriﬁed that the response value isless than or equal to the limit value of performance throughout the construction period and the14Standard Speciﬁcations for Steel and Composite Structures [General principles]

structure’s working life. That is, veriﬁcation includes not only safety, serviceability, restorability,
durability, and social and environmental compatibility but also the performance requirements
for the construction and maintenance stages. Workability is the construction stage performancerequirement relating to safety during construction, ease of fabrication and construction work,
etc. It is one of the most important aspects of performance that requires consideration at thestructural planning and design stages.
Maintainability, relating to the ease of maintenance of a structure, is also an important performance requirement that should be considered at the structural planning and design stages. In
Chapter 8 ”Maintenance” of the Structural Planning volume, considerations relating to the needfor and arrangement of maintenance systems and matters such as avoiding of structural details
that hinder maintenance, etc., are prescribed. In the Design volume, ”maintainability” is considered one of the performance items relating to performance requirement ”durability” because
the former is closely related to the latter. At the design stage, ease of inspection and repainting,ease of damage restoration, etc. are discussed.
Speciﬁc veriﬁcation methods are illustrated in the Structural Planning volume, the Designvolume, and the Seismic Design volume.)(6) At the construction stage, the performance requirement ”workability”, including such performance items as safety during construction, securing structural quality, etc. needs to be satisﬁed.
In particular, since the quality of construction can greatly inﬂuence the performances of a structure in service, it is important to satisfy the requirements for the initial soundness of the structure[JSCE (2003)]. Speciﬁc veriﬁcation methods are illustrated in the Construction volume.
(7) The performance required at the maintenance stage may be approximately the same as that
required at the structural planning and design stages. It should be ensured that the maintenancestage performance requirements are satisﬁed throughout the working life of the structure byimplementing appropriate measures such as periodical inspections, detailed investigations, andrepair and/or reinforcement according to demand. Speciﬁc veriﬁcation methods are illustrated
in the Maintenance volume.

2.3 Performance Level and Importance of Structure
Performance level shall be determined for each of required performances corresponding to safety,
serviceability, durability, repairability, societal and environmental compatibility. Performance level
shall be depend on the importance of structure.
【 commentary 】

Performance levels set one or more levels of performance that a steel or composite structure mustsatisfy. Performance levels may be set for any of the six performance requirements: safety, serviceability, restorability, durability, social and environmental compatibility, and workability. As an example,
Table C2.3.1 shows the performance levels relating to vehicle operating performance as described in
section 7.2.1 of the Design volume.
Performance levels depend on the importance of the steel or composite structure. Meanwhile, sincepartial safety factor design format is the basic method of performance veriﬁcation in these speciﬁcations, it is possible to change the structure factor instead of establishing various performance levels.
The structure factor also takes into account other speciﬁc conditions: social inﬂuence if the structure reaches the limit state, importance of the structure with regard to disaster prevention measures,
economic factors relating to reconstruction or repair costs, etc.

Chapter 2

Table C2.3.1

Basis for Structural Plan, Design, Construction and Maintenance

15

Example of performance levels relating to vehicle operating performance

Level

Action and weather conditions

Performance item

Details

Level 1

・Live-load acting during design

Vehicle operating performance under normal
conditions

Safety shall be secured and users
should suﬀer no unpleasant eﬀects.

Vehicle operating performance under abnormal conditions

Safety shall be secured although normal vehicle operating performance
may be degraded to some degree.

working life
・Weather condition 1 (low wind ve-

locity and little rainfall)
Level 2・Weather condition 2 (wind veloc-

ity and rainfall are greater than ana priori determined level)

References in Chapter 2
Japanese Society of Steel Construction (2001) ：Performance design guidelines for Civil Engineering Steel Structures, JSSC Technical Report No. 49.
Ministry of Land, Infrastructure, Transport and Tourism (2002) ：Design Basis for Civil and Architectural Engineering Structures ．
Japan Society of Civil Engineers (2003) ：Towards Establishment of Performance-based Design System for
Steel Structures ．

Volume II

Structural PlanningStandard Specifications for Steel and Composite Structures【 Structural Planning 】
Contents
Chapter 1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Scope of Structural Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Considerations in Structural Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.3 Supplementary considerations in structural planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Chapter 2 Constraints and Prerequisite Conditions in Structural Planning . . . . . . . . . . . 3
2.1 Constraints by Laws and Regulations of Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Prerequisite Conditions for Performance Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Chapter 3 Economic Eﬃciency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.1 General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5
3.2 Method of Consideration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Chapter 4 Safety. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6
4.1 General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6
4.2 Method of Consideration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Chapter 5 Serviceability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
5.1 General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8
5.2 Method of Consideration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Chapter 6 Durability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
6.1 General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
6.2 Consideration of Fatigue Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
6.3 Consideration of Corrosion Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
6.4 Consideration of Resistance to Material Deterioration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Chapter 7 Social and Environmental Compatibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
7.1 General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
7.2 Consideration of Landscape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
7.3 Consideration of Noise and Vibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
7.4 Consideration for Reduction of Environmental Impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Chapter 8 Maintenance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
8.1 General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
8.2 Consideration of Future Potential Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
8.3 Consideration of Maintenance Facilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Chapter 9 Consideration for Inﬂuence of Earthquakes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
9.1 General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
9.2 Selection of Type of Structure with High Seismic Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
9.3 Consideration for Safety during Earthquakes, and Restorability . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Chapter 10 Constructability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
10.1 General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
10.2 Consideration for Constructability during Shop Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
10.3 Consideration for Constructability during Erection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19

（ 1）

1

Chapter 1 General
1.1 Scope of Structural Planning
A structure shall comply with its intended purpose, satisfy conditions in applicable laws andregulations, and be economical. It shall also have adequate safety, serviceability, durability, safety
during earthquakes, serviceability and restorability after earthquakes, social and environmental
compatibility and maintainability. For those requirements, structural planning should be performed to select an appropriate form and type of structure, and to decide an outline of thestructure such as major dimensions.
【 Commetary 】

The structural planning phase of building a structure is the work of determining the form andstructural, the major dimensions, etc.; that is, the outline of the structure is deﬁned through thestructural planning process. This work is, in general, carried out after the basic investigation. It is
important work that aﬀects the overall project cost and construction period, as well as maintainability
after the structure opens for use. Careful study is required because the structural planning process isalmost the sole determinant of construction cost and construction period.
It is important through the structural planning process to select the form and type of structure
best able to meet the full range of requirements and required performances. That is, it is essential
to select the ideal form and type of structure that, while fulﬁlling its intended purpose and satisfying
the conditions set by applicable laws and regulations, is economically eﬃcient. The selected form
and type of structure must also exhibit adequate safety, serviceability, durability, safety during earthquakes, serviceability and restorability after earthquakes, social and environmental compatibility, andmaintainability against external action throughout its service life.

1.2 Considerations in Structural Planning
In structural planning, a structure should be conformed to its intended purpose and be ﬁtted
to conditions in applicable laws and regulations. Considerations for economic eﬃciency, safety,
serviceability, durability, social and environmental compatibility, maintenance, inﬂuence of earthquakes, and constructability of a structure should also be considered in structural planning. During
structural planning, adequate comparisons and considerations for each form and type of structure
should be performed.
【 Commentary 】(1) Considerations in Structural Planning
The structural planning process ensures that a structure fulﬁlls its intended purpose and conforms to applicable laws and regulations and is economically eﬃcient. At the same time, safety,
serviceability, durability, social and environmental compatibility, maintenance after construction,
earthquake inﬂuence, and workability, etc. should also be considered in structural planning. In
addition, as part of earthquake inﬂuence, restorability should be considered.
(2) Comparison of structural forms and types

2Standard Specifications for Steel and Composite Structures [Structural Planning]

In order to select the ideal form and type of structure, it is necessary to compare alternative
structural forms and types with respect to the considerations prescribed in (1) above. For example, in the structural planning of a bridge, it is necessary to compare and consider forms
and types including steel bridges, RC bridges, PC bridges, etc., taking into account their economic eﬃciency, social and environmental compatibility, workability as well as the required spanand existing ground conditions. Because construction cost is substantially determined throughthis selection process in many cases, it is essential to give it suﬃcient attention. In considering economic eﬃciency, it is desirable to consider the full life cycle cost, including the cost of
maintenance, as well as the initial construction cost.

1.3 Supplementary Considerations in Structural Planning
In addition to the considerations prescribed in 1.2, construction period and ground condition
should be taken into account.
【 Commentary 】

Further to the considerations prescribed in 1.2 above, construction period and ground conditions
should be taken into account through the process of structural planning.
(1) Construction Period
It is necessary to select a form and type of substructure in consideration of its consequent eﬀect
on construction period and economic eﬃciency (construction cost). For example, in the case ofa bridge crossing a river, the selected form and type of substructure and superstructure may
require construction to take place only in the dry season while the selected form and type of abridge over a railway or road may restrict the time available for construction.
(2) Ground Conditions
There are cases where detailed ground conditions, etc. are not examined at the structuralplanning stage. However, once the form and type of structure is selected, there are a great manycases when they cannot be changed afterwards. Consequently, it is necessary that structuralplanning be based on the most accurate possible information about special ground conditions,such as inclined ground, weak ground, etc.
References in Chapter 1
Japan Society of Civil Engineers (1989) ：Civil Engineering Handbook, Vol. 4
Japan Railway Construction Public Corporation (1998) ：Guidance for Structural Planning (Draft)
Japanese Society of Steel Construction (2001) ：Performance design guidelines for Civil Engineering Steel Structures, JSSC Technical Report No. 49
Japan Society of Civil Engineers, Steel Structure Committee (2003) ：Development of Performance-Based Design System for Steel Structures
East Nippon Expressway Company Limited, Central Nippon Expressway Company Limited, West Nippon
Expressway Company Limited (2006) ：Design Guide Vol. 2

3

Chapter 2 Constraints and Prerequisites
Conditions in Structural Planning
2.1

Constraints by Laws and Regulations of Structure

For construction of a structure, applicable laws and regulations should be well considered. If
there is some restriction by other structures, the structure should satisfy applicable laws andregulations, and adequate consultation with related organizations should be held.
【 Commentary 】

In the planning of a structure, laws and regulations may apply to the usage and/or function of thestructure, resource usage and/or waste disposal, environmental preservation, work safety, etc.
Further, in verifying each performance requirement, there are certain prerequisite conditions suchas actions to be supported, design working life, etc. In this specification, these are dealt with asconstraints and prerequisites to be considered, not as individual performance requirements. In thisclause, the minimum requirements to be satisfied are determined in consideration of the constraints
imposed by laws and regulations.
The form and type of a structure and its size may be restricted by laws and regulations related toother structures where other structures are intersecting or adjoining.
Further, in conferring with related organizations, various requirements may be lodged by withregard to the form and type of structure and its span, etc.
Accordingly, it is necessary to confer with related organizations about the plan as well as to carryout structural planning in full consideration of the content and spirit of related laws, ministerial
ordinances, etc.

2.2 Prerequisite Conditions for Performance Verification
For construction of a structure, prerequisite conditions such as actions to be supported anddesign working life should be considered at the stage of structural planning.
【 Commentary 】

It is necessary that a new structure satisfy the required performance given the assumed actions
that will occur over the design working life. Therefore, it is necessary to verify each performancerequirement in the round from the structural planning stage; that is, the range of actions and thedesign working life must be taken into account at the structural planning stage. In this specification,these performance requirements are treated as prerequisites to be considered in the construction of thestructure.
The type and characteristic values of actions to be taken into consideration are set as standard foreach type of structure and these can, in general, be used. In verifying the structural plan for a new
structure, it is necessary to determine adequately these characteristic values of actions and to assume
a worst-case combination of these actions on the structure in general.
Each structural type has a standard design working life and, in general, this can be used. It ispreferable to consider durability from the structural planning stage, including the method of mainte-

4Standard Specifications for Steel and Composite Structures [Structural Planning]

nance during the structure’s working life, and it is important to clarify the design working life of the
new structure.
References in Chapter 2
Tokyo Metropolitan Government (1987) ：Design Guide to Bridges ．
Japan Railway Construction Public Corporation (1998) ：Guidance for Structural Planning (Draft) ．
Editorial Supervisor: Railway Technical Research Institute (2000) ：Design Standards for Railway Structures
and Commentary (Steel and Composite Structures) ．
Japan Road Association (2002) ：Specifications for Road Bridges and Commentary, I: Common Reference
Volume ．
Japan Society of Civil Engineers, Steel Structure Committee (2003) ：Development of Performance-Based Design System for Steel Structures ．
East Nippon Expressway Company Limited, Central Nippon Expressway Company Limited, West Nippon
Expressway Company Limited (2006) : Design Guide Vol. 2

5Chapter 3 Economic Eﬃciency
3.1 General
Economic eﬃciency should be taken into account at the stage of selecting form of structure,
selecting type of structure and calculating major dimensions.
【 Commentary 】

In many cases, cost can be signiﬁcantly reduced by selecting an appropriate form and type ofstructure at the structural planning stage. Therefore, it is extremely important during structuralplanning to select a form and type of structure that oﬀers excellent economic eﬃciency. In thisconsideration, it is necessary to compare structural forms and types including not only steel andcomposite structures but also concrete structures and hybrid structures. Although economic eﬃciency
is an important consideration in structural planning and is prescribed in this chapter, it is also includedin the Design Part as a performance item (economical rationality), where it is considered part of thesocial and environmental compatibility of a structure.

3.2 Method of Consideration
Economic eﬃciency should be considered in terms of initial cost and life cycle cost.
【 Commentary 】

In considering the economic eﬃciency of a structure, it is necessary to look at life cycle cost, which
includes the cost of maintenance, the cost of replacement cost, etc., as well as the initial cost. Further,it should be optimized from the view point of wide-ranging asset management, so that not only is eachindividual structure optimized, but also, for example, the whole railway route or network.
Structures must be maintained regularly. Then they have to be replaced when they are no longer
able to meet the required performance. The cost of maintenance, replacement, etc. arising after
construction may greatly exceed the initial construction cost. Therefore, in structural planning, it isimportant to evaluate a structure not only in terms of initial construction cost but also according tofuture maintenance and replacement costs as estimated during the structural planning process. However, since the structure has not been given detailed consideration at this stage, the exact dimensions,etc. of each member of the structure may not be ﬁxed; in this case, it is necessary to use informationof construction cost and maintenance cost, etc, based on past experience with similar structures.
References in Chapter 3
Kazuhiro NISHIKAWA (1997) ：Proposal for minimum maintenance bridge that minimizes the life cycle costof a road bridge, Bridge and Foundation, Vol. 31, No.8 ．
Japan Railway Construction Public Corporation (1998) ：Guidance for Structural Planning (Draft) ．
Masaki YOKOYAMA, Nobuo SAITO, Osamu OMURA, Takayuki TSUZUKUISHI (1999) ：Study on the life
cycle cost of road bridge and its circumstances in the United States, Material collections of 1st symposium
concerning maintenance of steel structures ．
Japan Society of Civil Engineers, Steel Structure Committee (2003) ：Development of Performance-Based Design System for Steel Structures ．

6Standard Specifications for Steel and Composite Structures [Structural Planning]

Chapter 4 Safety
4.1 General
Safety should be considered at the stage of selecting form and type of structure and calculating
major dimensions.
【 Commentary 】

For any structure, it is necessary to secure safety at all times against various external actions over
the working life. Structural sections are often determined by satisfying safety requirements. A further
comparative consideration of economic eﬃciency, etc. is necessary to select the best structural form andtype, which is the purpose of structural planning, and it is necessary, in order to compare economic
eﬃciency, to decide on the main major dimensions of the structure and calculate the quantities ofwork and the construction cost. From this perspective, an examination of safety is necessary at thestructural planning stage.

4.2 Method of Consideration
Safety should be considered in accordance with the Design Part, Chapter6 ”Required performances and veriﬁcation for safety”.
【 Commentary 】

In the consideration of safety during the structural planning process, the required safety performance must be met in reference to the Design Part, Chapter 6 ”Required performances and veriﬁcationof safety”.
The Design Part includes sections on ”Structural safety” and ”Public safety”. The main consideration here is structural safety. Structural safety should usually be veriﬁed against dynamic phenomena
in consideration of strength, rigidity, deformation, stability, etc. At the structural planning stage,
not all items taken into account at the detailed design need be considered, but only those that arenecessary. Depending on the form and type of the structure, it may be diﬃcult to consider all safety
veriﬁcations beforehand. In such cases, it is acceptable to understand the problems by doing a roughcalculation, reﬂect the results in the structural plan, and decide on veriﬁcation items and values. It is
not the aim to optimize the section, shape and dimensions at the structural planning stage.
In general, the veriﬁcation of safety at the structural planning stage should be carried out as follows.
(1) In cases where an outline consideration is acceptable
1 Where there is experience with the form and type of structure and its scale, it is possibleto understand the major dimensions, materials, etc. without calculating actual sectional
forces (stresses) and cross-sectional dimensions.
2 Where a choice is made from among multiple alternative structural forms and types, thestress intensity of main members can be considered using a simple model (lattice analysis,
inﬁnitesimal deformation analysis, etc.) in general.

3 For a structure where the earthquake inﬂuence is predominant in the above-mentioned structural analysis, it is necessary to consider earthquake safety using a simple static veriﬁcation

Chapter 4

Safety7

according to ”Chapter 9 Earthquake Inﬂuence”.
(2) In cases where a comparatively detailed consideration is required
1 Where there is no experience with the form and type of structure or its scale, or wherethe various dimensions of the structural members are close to the applicable limit of thestructural form and type, it is necessary to consider detailed design.
2 Where a choice is made from among several alternatives, it is necessary to calculate thesectional forces (stresses) using an adequate model and to consider safety in the section
where the whole quantities of the structure ( the total steel weights, etc.) can be calculated.

3 For a structure where the earthquake inﬂuence is predominant, it is necessary to consider
the earthquake safety using a simple static veriﬁcation according to ”Chapter 9 Earthquake
Inﬂuence”, including dynamic analysis if necessary.
References in Chapter 4
Japan Railway Construction Public Corporation (1998) ：Guidance for Structural Planning (Draft) ．
Japan Society of Civil Engineers, Steel Structure Committee (2003) ：Development of Performance-Based Design System for Steel Structures ．
East Nippon Expressway Company Limited, Central Nippon Expressway Company Limited, West Nippon
Expressway Company Limited (2006) ：Design Guide Vol. 2 ．

8Standard Specifications for Steel and Composite Structures [Structural Planning]

Chapter 5 Serviceability
5.1 General
Serviceability should be taken into account at the stage of selecting form and type of structure
and calculating major dimensions.
【 Commentary 】

The meaning of serviceability is that structure’s functions are secured, that maintenance does
not require excessive cost and labor, that no feelings of anxiety are induced in users, and that nofunction-disrupting phenomena occur. The choice of structural form and type may be inﬂuenced
by serviceability considerations, while major dimensions may be determined on the basis of fulﬁlling
serviceability requirements. Serviceability should therefore be considered from the structural planningstage.

5.2 Method of Consideration
Serviceability should be considered in accordance with the Design Part, Chapter7 ”Required
performances and veriﬁcation for serviceability”.
【 Commentary 】

It is necessary to consider serviceability during the structural planning stage in order to avoid theneed for later corrections, such as changing the structure type, at the design stage. The required
serviceability is to be obtained in accordance with the Design Part, Chapter 7 ”Required performancesand veriﬁcation of serviceability”.
Taking a road bridge as an example of a steel or composite structure, suitable performance items to
be considered as relevant to serviceability are performance under moving vehicle loading and pedestrianloading, depending on the actual application of the bridge. That is to say, at the structural planningstage, it is necessary to consider certain questions directly linked to the structure form and dimensionsof the structure. These include such points as the location, intended purpose, and level of importanceof the structure, the planning of a road alignment that meets performance requirements, and theexamination, depending on the type of bridge, of deformations under moving vehicle loading andvibrations under pedestrian loading.
For structures other than bridges, there may be diﬀerent deﬁnitions of serviceability. For example,
in the case of port and harbor structures, serviceability may be deﬁned in terms of performance items
directly connected to the function of the structures. In the case of earthquake-reinforced structures
involved in the transportation of dangerous materials, it is necessary that the facility is still available
for normal operations after earthquake motion of level 2. Further, in the case of port and harbor
structures, there are many types of structure that require water-tightness, such as ﬂoating mooringsand submerged tunnels. In this way, the deﬁnition of serviceability in port and harbor structures
directly indicates the performance that the facility is not disabled in use and structural response of
the facility to envisaged action is required to control the damage in order that the structure is easily
restored to the original performance by small restoration work.

Chapter 5

Serviceability

9References in Chapter 5
Japan Road Association (2002) ：Specifications for Road Bridges and Commentary ．
Japan Society of Civil Engineers, Steel Structure Committee (2003) ：Development of Performance-Based Design System for Steel Structures ．
Japan Road Association (2004) ：Practical guide and implementation of Road Construction Ordinance ．
Japan Port and Harbor Association (1999) ：Technological Standard for Harbor Facilities and Commentary ．

10Standard Specifications for Steel and Composite Structures [Structural Planning]

Chapter 6 Durability
6.1 General
Durability should be taken into account at the stage of selecting form and type of structure andcalculating major dimensions.
【 Commentary 】

The performance of structure gradually deteriorates due to the action of loading and the environment. Therefore, to fulﬁll the durability requirement, the deterioration of performance level should beheld within certain limits such that adequate performance is maintained during the design working lifeof the structure. The durability should be considered from the structure planning stage. Durability isdeﬁned as the resistance of a structure or its members to performance deterioration under the actionof loading and the environment. It is extremely important that the necessary level of performance ismaintained throughout the design working life of the structure.
In considering the durability of steel and composite structures, it is generally adequate to review
fatigue resistance (that is, resistance to fatigue phenomena as caused by loading), corrosion resistance(that is, resistance to corrosion of steel materials under environmental action), and material deterioration resistance (that is, resistance to material deterioration phenomena that aﬀect concrete materials,etc.). That is to say, it is necessary to suppress these factors within deﬁned limits; further, it isrecommended that these factors relating to durability are checked from the structural planning stage
onward.

6.2 Consideration of Fatigue ResistanceIn principle, a type of structure that is concerned for fatigue resistance should be selected in theconsideration for durability.
【 Commentary 】

Fatigue resistance is usually checked by calculating the response to loading action. Then it is
conﬁrmed that the response is below a certain limit value, such as the allowable stress range forfatigue, for each respective member of a structure.
However, one of the worst scenarios with respect to fatigue damage is when fatigue cracks initiatedafter the structure enters service lead to an incident because inspections or countermeasures are impossible to implement. To avoid this kind of situation, it is recommended that a design in which stressconcentrations are very unlikely or one in which it is easy to identify fatigue cracking be consideredfrom the structural planning stage. Further, since some structural members, such as the hangers ofLanger bridges and the cables of cable-stayed bridges, are subjected to wind-induced vibration, it isadvisable to include relevant consideration of this from the structural planning stage.
In the case of bridge designs in which fatigue damage tends to occur, it is necessary to consider
avoiding the use of joints with lower fatigue strength at the structural planning stage, since the response
to loading action tends to be greater in the case of bridges with closely-spaced supports and bridges
subjected to frequent over-sized vehicle loading.

Chapter 6

Durability

11

It is also recommended that the fatigue resistance of not only steel-plate decks but also concrete
ﬂoor slabs such as those fabricated as RC slabs, PC slabs be considered, since these are exposed tosevere fatigue conditions because they directly support repeated wheel loading.

6.3 Consideration of Corrosion ResistanceIn principle, speciﬁc corrosion protections that have adequate corrosion resistance should beselected in the consideration for durability.
【 Commentary 】

The corrosion resistance of steel materials represents their performance with respect to inhibiting
corrosion caused by environmental action, etc. to below a deﬁned level during the design working life.
Anticorrosion design aimed at preserving the required performance, such as by developing speciﬁcations
that adequately counter corrosion, should be considered from the structural planning stage. Also,
concurrently with this assurance of corrosion resistance, anticorrosion speciﬁcations matched to theenvironmental action are required from the point of view of life-cycle cost.
There are various methods of inhibiting the corrosion of steel materials, such as by painting, application of weathering steel, hot-dip galvanizing, stainless steel or titanium covering, aluminum alloy
thermal spraying, and electrolytic protection. It is recommended that the most suitable method be
selected after a thorough comparative investigation of those methods applicable to the structure’s
in-service environment.
The factors that lead to the initiation and development of corrosion vary depending on the environment in the structure’s location. For example, if a steel structure in a coastal location subject toairborne salt remains underwater for long periods due to poor drainage, corrosion accelerates. It isparticularly important in the case of a complex structure consisting of many structural members tounderstand the increased exposure time to water resulting from rain and dew condensation as well as
the signiﬁcant eﬀect that can result from deposits of sand and anti-freezing agents.
In less severe corrosive environments, unpainted steel structures that use weathering steel generally
remain in good condition because a dense corroded layer forms. However, steel structures located on
the coast and steel bridges subjected to the spraying of anti-freeze agents (sodium chloride, calcium
chloride) do not form this kind of dense corrosion layer in some places and then extraordinary formsof corrosion, such as the imbricate form, are initiated and developed. In this kind of environment, ahigher level of anticorrosive speciﬁcations must be implemented.
In the case of concrete structural members such as ﬂoor decks, it is necessary to hold the neutralization thickness of the concrete cover and the concentration of chloride ions, etc. within deﬁned limits
throughout the design life so as to ensure the corrosion resistance of the reinforcing steel.

6.4 Consideration of Resistance to Material Deterioration
In principle, materials that have adequate resistance against material deterioration should beselected in the consideration for durability.
【 Commentary 】

Concrete’s resistance to material deterioration of concrete represents its performance with respect
to limiting aging deterioration resulting from environmental action, etc. to a deﬁned level during
the design working life of the structure. The anticipated material deteriorations of concrete are neu-12Standard Specifications for Steel and Composite Structures [Structural Planning]

tralization, freezing and thawing, chemical corrosion, and the alkali-aggregate reaction, etc. It is
recommended that, at the structural planning stage, materials with excellent resistance to material
deterioration are selected in consideration of environmental action. Also, it is important to pay attention to the initiation and development of corrosion of reinforcing steel within the concrete, which may
result from neutralization or salt damage.
In addition, it is not necessary to consider the aging deterioration of steel materials for typicalcivil engineering structures. However, in the case of tanks, water gates and water pressure steel pipes,
for example, the metallurgic aging deterioration may occur as a result of the graphitization or thehydrogen embrittlement. Therefore, in this kind of structure, it is necessary to select materials withexcellent resistance to material deterioration from the structural planning stage.
References in Chapter 6
Editorial Supervisor: Railway Technical Research Institute (2000) ：Design Standards for Railway Structures
and Commentary (Steel and Composite Structures) ．
Japan Society of Civil Engineers, Concrete Structure Committee (2002a) ：Standard Specifications for Concrete Structures (Structural Performance Check Volume) ．
Japan Society of Civil Engineers, Joint Sub-Committee of Steel Structures and Concrete Composite
Structures (2002b) ：Guidelines for Performance Check of Hybrid Structures ．
Japan Road Association (2002) ：Fatigue Design Guideline for Steel Road Bridges ．
Chitoshi Miki, Atsushi Ichikawa (2004) ：Modern Bridge Engineering - Leading-edge Technology in Paint-lessSteel and Bridges, Mathematical Engineering Company ．

13

Chapter 7 Social and Environmental
Compatibility
7.1 General
At the stage of selecting form and type of structure, social and environmental compatibility
should be taken into account in principle.
【 Commentary 】

Since civil engineering structures play an important role in their surrounding environments or
urban landscapes as a component of the social capital, it is necessary to consider these landscapes instructural planning. Further, structural forms or types that cause discomfort or stress among users
and residents should be avoided because civil engineering structures remain in use for a considerably
long period after entering service. Therefore, the structural form and type should be selected inconsideration of its environmental impact, including such eﬀects as noise, vibration, sunshine masking,and air pollution as well as its harmony with the local ecology. Furthermore, it is desirable to selectmaterials and structural forms and types taking into consideration their adaptability to recycling fromthe viewpoints of resource management and environmental damage reduction.
Social and environmental compatibility is a function of a structure that contributes to a soundsocial, economic, and cultural community and minimizes negative impacts on the social and naturalenvironment. Accordingly, taking into account of social and environmental compatibility in principle, necessitates study of landscape, noise, vibration, and other environmental factors that must be
considered at the structural planning stage.

7.2 Consideration of LandscapeLandscape should be concerned in the consideration for social and environmental compatibility.
【 Commentary 】

Consideration of the landscape is necessary because civil engineering structures are likely exposed tothe public eye. In general, there are various ways of understanding landscape issues, but the point here
is how to coordinate a structure with the surrounding environments or urban environment and how
to create a contrast with it. It is an important aspect of gaining favorable acceptance from users andnearby residents. It is diﬃcult to evaluate landscape using a quantitative approach because landscapeis a concept strongly depending on subjective and sensory judgment. However, it is generally necessary
to take into consideration the following in selecting a structural form and type:
1 The structural form and type should exhibit a balance of structural forces.

2 The structural form and type should be able to cope with the demands on it.

3 The unity of structural form and type should be considered as much as possible.
4 Methods of linking parts of the structure should be carefully considered so as not to spoil the
look of the structure.

14Standard Specifications for Steel and Composite Structures [Structural Planning]

7.3 Consideration of Noise and Vibration
Noise and vibration should be concerned in the consideration for social and environmental
compatibility.
【 Commentary 】(1) Noise: For structural planning, noise abatement measures should be taken into account if necessary. In this case, any environment standard applicable to the location of the structure is referredto.
(2) Vibration: There are an increasing number of cases in which structure-induced vibrations are
causing environmental problems. Often, these cases arise where a bridge section is located on
weak ground or on excavated soil.
(3) Sunshine masking: For a structure in an urban area, due consideration should be given to themasking eﬀect it will have on sunshine.
(4) Others: It is also necessary to adequately consider the possible inﬂuence of noise, vibration, andwater contamination during the construction period.

7.4 Consideration for Reduction of Environmental Impact
Reduction of environmental impact by eﬀective utilization of resources should be concerned in
the consideration for social and environmental compatibility.
【 Commentary 】

It is desirable to consider reducing environmental impact through the eﬀective use of resources atthe structural planning stage. The eﬀective use of resources depends on controlling waste generation(reduce), reusing construction components (reuse), and reusing construction materials as raw materials(recycle). Since it is relatively easy to increase the working life of a steel structure through partial
repair or reinforcement, it has been pointed out that it is relatively easy to reuse the main parts
or components, and furthermore to reuse the material (steel). This implies that steel structuresoﬀer excellent characteristics with respect to ”reduce,” ”reuse,” and ”recycle”. In particular, steel
has excellent recycling properties. In practice, when a bridge is replaced, the steel can be reused after
processing at a steelworks after scrapping. As for ”reuse,” temporary structures such as marine staging
are often made of leased material which is reused.
References in Chapter 7
Railway Construction Public Corporation, Study Group on Landscape Design (1977) ：Handbook of landscapedesign for railway structures (draft) ．
Railway Construction Public Corporation (1998) ：Handbook for Structural Planning (draft) ．
Japan Road Association (2002) ：Specifications for Highway Bridges and Commentary, I Common Specifications Volume ．
East Nippon Expressway Company Limited, Central Nippon Expressway Company Limited, and West
Nippon Expressway Company Limited (2006) ：Design Guide Vol.2 ．

15

Chapter 8 Maintenance
8.1 General
At the stage of selecting form and type of structure, maintenance should be taken into accountto ensure initially intended performance after the start of service.
【 Commentary 】

Maintenance is essential for all structures once they enter service. Since the physical life of astructure largely depends on the maintenance work carried out, its physical life can be extended totwo or three times the design working life. In this regard, it is necessary to consider the ease withwhich steady maintenance can be carried out at the structural planning stage in order to satisfy the
structure’s performance requirements throughout its design working life.

8.2 Consideration for Future Potential Problems
Future potential problems with maintenance of structure should be considered at the stage ofstructural planning.
【 Commentary 】

Potential future issues related to structure maintenance should be adequately reﬂected in the structural planning, with reference to the following examples which have arisen in the past.
(1) Settlement, tilting, and displacement of the structure
If, for example, a structure is planned without suﬃcient consideration of ground deformation
where the land is reclaimed or consists of weak soil, unexpected lateral movement/diﬀerential
settlement of the stratum may take place, as has been experienced a number of times. Countermeasure against such movement are very expensive. Therefore, during structural planning,
suﬃcient investigations should be carried out to verify if any structural problems had have been
experienced by other structures under similar conditions.
(2) Vibration, noise, and abnormal deﬂection
Cases have been noted where, since a steel structure generally consists of thin components,
unexpected vibration, noise, or abnormal deﬂection has resulted. This is particularly likely if thestructure consists of thin plate elements or a girder structure with low rigidity.
(3) Damage due to lack of recognition of the environment at the structure’s location
Many examples of failure to properly understand the environment a structure is exposed tohave led to diﬃculty in maintenance work and a signiﬁcantly reduced service life as a resultof failure to select suitable materials/structures. Therefore, it is important to select the mostsuitable materials and structural type based on a careful investigation of the environment at thelocation of the structure when it enters service and in the future.

16Standard Specifications for Steel and Composite Structures [Structural Planning]

8.3 Consideration of Maintenance Facilities
Maintenance facilities for a structure should be considered at the stage of structural planning.
【 Commentary 】

While a structure needs maintenance work during its service period, the structural type or form
sometimes presents diﬃculties with respect to making inspections/examinations for maintenance. In
selecting a structural type and form, it is necessary to consider how maintenance working space will
be secured and what maintenance facilities are required for inspection and repainting, together withconsideration of the ease of maintenance work, at the structural planning stage. Further, if partial
repair or replacement of the structure is anticipated in the future, it is better to consider what facilities
are required to allow such work.
References in Chapter 8
Nobuyuki Narita (1998) ：Future of Steel Bridges, Gihodo publishing co. ．
Tokyo Metropolitan Government (2002) ：Inspection Manual of Bridges ．
Japan Society of Civil Engineers (2003) ：Towards Establishment of Performance-based Design System for
Steel Structures ．

17

Chapter 9 Consideration for Influence ofEarthquakes
9.1 General
If the inﬂuence of earthquakes is dominant in a structure, inﬂuence of earthquakes should beconsidered at the stage of selecting form and type of structure and calculating major dimensions.
【 Commentary 】

A structure should possess suﬃcient seismic resistance (seismic safety and post-earthquake serviceability and restorability) to earthquakes. The cross-sectional dimensions of structural members arelikely to be determined from the viewpoint of conformity with this performance requirement. For thisreason, it is necessary to review earthquake scenarios from the structural planning stage. In particular, where the response of a structure by earthquake motion is large, a structural form and type withgood seismic resistance is to be selected and conformity with the required seismic performance is tobe checked.

9.2 Selection of Type of Structure with High Seismic Performance
Topography, geology, ground condition and locational condition should be considered at thestage of selecting form and type of structure. Then the type of structure that has adequate safety
during earthquakes, serviceability and restorability after earthquakes should be selected.
【 Commentary 】

In choosing the form and type of a structure where the response will be largely dominated byearthquake motion, it is important to select a structure that excels in seismic resistance and oﬀers a highdegree of seismic safety and post-earthquake serviceability and restorability, taking into consideration
topographical, geological, ground, and locational conditions. Here, it is important to select not only
individual structure members with excellent seismic resistance but also a structure that has excellent
seismic resistance as a whole system.

9.3 Consideration for Safety during Earthquakes, and Restorability(1) Prospective earthquake motion and importance of structure should be determined in the consideration for safety during earthquakes, serviceability and restorability after earthquakes.
(2) Appropriate seismic performance should be determined in accordance with the prospective
earthquake motion and the importance of structure, which are determined in (1).
(3) A structure should satisfy the seismic performance, which are required in (2), in the consideration for safety during earthquakes, serviceability and restorability after earthquakes.

【 Commentary 】(1) In reviewing the inﬂuence of earthquakes on a structure, it is necessary to deﬁne the anticipated18Standard Specifications for Steel and Composite Structures [Structural Planning]

earthquake motions and the importance of the structure.
The seismic intensity acting on a structure as a result of an earthquake depends on the characteristics of seismic event, seismic wave transmission characteristics, and ground conditions.
Further, the response of a structure to an earthquake can vary depending not only on the amplitude of the input earthquake motion but also on its periodic component. Accordingly, it isrecommended, in reviewing the inﬂuence of earthquakes on a structure, to deﬁne the anticipatedearthquake motion as a result of a thorough understanding of these characteristics. However, it
is diﬃcult to develop deﬁnitions individually for every form and type of structure. Therefore, it isusually acceptable to deﬁne the anticipated earthquake motion according to the design standardsof the intended structure.
Further, it is necessary to deﬁne the importance of the structure appropriately according to
the design standards of the intended structure in consideration of its social role.
(2) and (3) It is necessary to deﬁne the structure’s seismic resistance in accordance with the anticipated earthquake motion and the importance of structure as deﬁned in (1) above. Then, in
reviewing the seismic resistance of the structure, this deﬁned seismic resistance must be achieved.
Meanwhile, in reviewing the inﬂuence of earthquakes at the structural planning stage, it isunnecessary to use a more complex design method than called for. A simple method is acceptableas long as the necessary data can be obtained. For example, in a case where the structuralform and type or data needed to determine the major dimensions can be obtained from pastexamples and where there is no problem with estimating the response characteristics of theplanned structure to the earthquake, it is acceptable to carry out this review of the inﬂuence ofearthquakes through a static analysis instead of a dynamic analysis.
References in Chapter 9
Railway Technical Research Institute (1999) ：Design Standards for Railway Structures and Commentary,
Earthquake-resistant Design ．
Japan Society of Civil Engineers (2001) ：Guideline of Earthquake-resistant Design for Civil Structures (Draft),
Handbook for Preparation of Earthquake-resistance Design Standards ．
Japan Road Association (2002) ：Specifications for Highway Bridges and Commentary, V Earthquake-resistant
Desin Volume ．
Tsutomu Usami (2006) ：Guideline for Earthquake-resistance and Vibration Control in Steel Bridges, Editorial
Supervisor: Japanese Society of Steel Construction, Gihodo ．

19

Chapter 10 Constructability
10.1 General
At the stage of selecting form and type of structure, constructability should be taken into
account.
【 Commentary 】

Since various restrictions related to factory fabrication, transportation, and erection steel may
aﬀect the design of composite structures, it may be that a certain structural form and type is renderedunworkable. For example, in bridges that cross rivers, roads, or railroads, it is not unusual for thetype of structure to be constrained by the selected erection method. Further, if the working spaceis constrained, such as where ground conditions are very diﬃcult, the urban location restricts space,or the environment has to be preserved, choosing the appropriate erection method may have a large
inﬂuence on economic eﬃciency and margin of safety.
Thus, it is necessary at the structural planning stage to select the type of structure taking into
consideration not only the completed structural system but also its workability. Here, it is acceptableto review the workability of shop fabrication, transportation, and erection methods as well as theerection conditions of steel structures.

10.2 Consideration for Constructability during Shop Fabrication
In the consideration for constructability, constructability during shop fabrication should beconsidered in principle.
【 Commentary 】

Steel and composite structures should be of easily fabricated structure to the degree possible.
For example, it is considered that fabrication is simpliﬁed by the adoption of structural members of
simple design and by reducing the number of structural members as a consequence of simplifying thestructure. Similarly, the number of man-hours required is reduced by the adoption of available shaped
steel (I-beams, H-section steel, steel pipes, etc.).

10.3 Consideration for Constructability during Erection
In the consideration for constructability, constructability during erection should be c in principle.
【 Commentary 】

The method used to erect a structure (e.g. bent erection, erection by cable, etc. in the caseof a bridge) is generally determined in consideration of topographical conditions at the erection site(narrow intermontane valley, river zone, marine straits, railroad grade crossing, road, or urban zone,etc.), with constraints applied according to ﬁeldwork (consultation with local residents, work during

20Standard Specifications for Steel and Composite Structures [Structural Planning]the dry season in a river zone, erection in an environmental preservation area, erection in limited spacein an urban zone, and erection process in the ﬁeld, etc.) and the limitations of erection equipment,
etc.
References in Chapter 10
Construction Industry Research Company (1990) ：Handbook for Design and Construction of Bridges ．
Japan Society of Civil Engineers, Steel Structure Committee (2003) ：Development of Performance-Based Design System for Steel Structures ．

Volume III

DesignStandard Specifications for Steel and Composite Structures【 Deisgn 】
Contents
Chapter 1 General Provisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Scope. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
1.2 Terms and Deﬁnitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2.1 Commonly used terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2.2 Terms used in this Design volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5
1.3 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5
1.4 Basis of Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4.1 Purpose of design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7
1.4.2 Veriﬁcation of performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4.3 Veriﬁcation method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.4.4 Partial factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.4.5 Modiﬁcation factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.5 Structural Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Chapter 2 Actions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.1 General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 Kinds of Actions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3 Combinations of Actions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.4 Action Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4.1 General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22
2.4.2 Dead load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23
2.4.3 Earth pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.4.4 Prestressing force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.4.5 Live load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25
2.4.6 Impact load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.4.7 Flowing water pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.4.8 Hydrostatic pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26
2.4.9 Buoyancy or uplift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.4.10 Wind load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.4.11 Snow load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.4.12 Braking force and acceleration force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.4.13 Centrifugal force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.4.14 Longitudinal load imposed by long welded rail . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.4.15 Lateral train load and transverse wheel thrust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.4.16 Wave pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.4.17 Erection-related force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.4.18 Collision force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.4.19 Concrete shrinkage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.4.20 Eﬀect of concrete creep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.4.21 Eﬀect of temperature changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.4.22 Eﬀects of displacement of supports and diﬀerential settlement . . . . . . . . . . . . . . . . . . . . . . 34
2.4.23 Eﬀect of earthquake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.4.24 Eﬀect of airborne salinity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37
2.4.25 Eﬀect of exhaust gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

（ 1）

2.4.26 Eﬀect of carbon dioxide concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.4.27 Eﬀect of acid concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38
2.4.28 Eﬀect of drying and wetting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.4.29 Eﬀect of sunshine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.4.30 Eﬀect of freezing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.4.31 Eﬀect of ﬁre . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.5 Action Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Chapter 3 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.1 General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.1.1 Fundamentals of material physical properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.1.2 Required properties of materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.2 Structural Steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.2.1 Required steel properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.2.2 Selection of steel type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.3 Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.4 Value of Material Properties for Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.4.1 General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .50
3.4.2 Structural steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.4.3 Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54
3.5 Partial Factors for Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54
Chapter 4 Structural Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.1 General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.2 Structural Analysis Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .62
Chapter 5 Structural Member Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.1 General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.2 Partial Factor for Uncertainty in Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.3 Steel Member Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.3.1 Tensile resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.3.2 Compressive resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.3.3 Bending resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .68
5.3.4 Shear resistance of web . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.3.5 Local buckling resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.4 Resistance of Steel Pipes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.5 Resistance of Cables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .85
Chapter 6 Demand for Safety and Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6.1 General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6.2 Performance Requirement for Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6.2.1 Structural Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6.2.2 Public Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
6.3 Veriﬁcation of Structural Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
6.3.1 Veriﬁcation of load-carrying capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
6.3.2 Veriﬁcation of Displacement/Deformation Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.3.3 Veriﬁcation of Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.4 Veriﬁcation of Structural Safety by Nonlinear Structural Analysis . . . . . . . . . . . . . . . . . . . . . . .105
6.5 Veriﬁcation of Structural Safety through Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
Chapter 7 Required Serviceability Performance and Verification . . . . . . . . . . . . . . . . . . . . . 107
7.1 General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
7.2 Required Performance for Serviceability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107（ 2）

7.2.1 Vehicle operating performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
7.2.2 Train operating performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
7.2.3 Pedestrian comfort . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
7.2.4 Other Considerations for Users . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
7.3 Veriﬁcation of Serviceability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
7.3.1 Veriﬁcation of vehicle operating performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
7.3.2 Veriﬁcation of train operating performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
7.3.3 Veriﬁcation of pedestrian comfort . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
7.3.4 Veriﬁcation for other considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
Chapter 8 Required Durability Performance and Verification . . . . . . . . . . . . . . . . . . . . . . . . 120
8.1 General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
8.2 Required Durability Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
8.2.1 Fatigue resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
8.2.2 Corrosion resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
8.2.3 Resistance to material deterioration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
8.2.4 Maintainability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
8.3 Veriﬁcation of Durability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
8.3.1 Veriﬁcation of fatigue resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
8.3.2 Veriﬁcation of resistance to steel corrosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
8.3.3 Veriﬁcation of resistance to material deterioration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
8.3.4 Veriﬁcation of maintainability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
Chapter 9 Required Social and Environmental Compatibility Performance andVerification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
9.1 General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
9.2 Required Social and Environmental Compatibility Performance . . . . . . . . . . . . . . . . . . . . . . . . . 134
9.3 Veriﬁcation of Social and Environmental Compatibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
9.3.1 Veriﬁcation of social compatibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
9.3.2 Veriﬁcation of economic rationality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
9.3.3 Veriﬁcation of environmental compatibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
Chapter 10 Structural Members in General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
10.1 Structural Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
10.2 General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
10.2.1 Secondary stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
10.2.2 Stress concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
10.2.3 Members with alternate stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
10.2.4 Minimum plate thickness and corrosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .140
10.2.5 Curved members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
10.2.6 Dynamic wind-resistant design of structural members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .141
10.3 Frame Members with Axial Tensile Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
10.3.1 Slenderness ratio of members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
10.4 Frame Members with Axial Compression Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
10.4.1 Width-thickness ratio of plate subjected to compressive stress and stiﬀened plate . . 142
10.4.2 Perforated plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
10.4.3 Inﬂuence of eccentric bending moment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
10.4.4 Slenderness ratio of structural members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
10.5 Frame Members with Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .147
10.5.1 Width-thickness ratio of plate subjected to compressive stress and stiﬀened plate . . 147
10.5.2 Eﬀective section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147（ 3）

10.5.3 Overlapping ﬂange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
10.5.4 Eﬀective section for shear forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
10.6 Steel Pipes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
10.6.1 Radial thickness ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
10.6.2 Stiﬀened member . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
10.6.3 Node structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
10.6.4 Curved tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
10.6.5 Steel pipe connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
Chapter 11 Joints. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
11.1 General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
11.2 Joint Safety Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
11.3 Veriﬁcation of Joint Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
11.4 General Principles for Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
11.4.1 Member joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
11.4.2 Mixed welded, high-strength bolted, and bolted connections . . . . . . . . . . . . . . . . . . . . . . . 156
11.5 Welded Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
11.5.1 Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
11.5.2 Safety veriﬁcation of welded connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .158
11.5.3 Size of ﬁllet welds and geometry and dimensions of welded connections . . . . . . . . . . . . 162
11.6 High-Strength Bolted Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
11.6.1 Requirements for safety of high-strength bolted connections . . . . . . . . . . . . . . . . . . . . . . . 165
11.6.2 Safety veriﬁcation of high-strength bolted connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
11.6.3 Design characteristic values for veriﬁcation of connection safety . . . . . . . . . . . . . . . . . . . . 172
11.7 Structural Details of High-Strength Bolted Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
11.7.1 Bolts, nuts, and washers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .176
11.7.2 Holes for bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
11.7.3 Bolt length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
11.7.4 Bolt spacing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
11.7.5 End and edge distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
11.7.6 Minimum number of bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
11.7.7 Filler plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
11.7.8 Angled and circular washers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
11.8 Bolted Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
11.8.1 General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
11.8.2 Bolts, nuts, and washers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .182
11.8.3 Structural details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
11.9 Pin Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
Chapter 12 General Considerations for Framed Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
12.1 Scope. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
12.2 Member Section Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
12.2.1 General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
12.2.2 Design of truss members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
12.2.3 Design of rigid frame members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
12.2.4 Design of arch members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
12.2.5 Calculation of eﬀective buckling length by eigenvalue analysis . . . . . . . . . . . . . . . . . . . . . 204
12.3 Checking of Entire Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
12.4 Constraint in the Transverse Direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
12.5 Camber. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207（ 4）

12.6 Members Considered as Substructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .207
12.7 Considerations of Torsion Acting on Steel Towers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
Chapter 13 Plate Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
13.1 General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
13.2 Eﬀective Width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
13.3 Steel Girder Web . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
13.4 Plate Structure Subjected to Out-of-Plane Loading or Combined Out-of-Plane and InPlane Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
13.5 Other Plate Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
13.6 Load Concentrate Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
13.7 Beam-to-Column Connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
13.8 Panel Connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
13.9 Cross Beam, Cross Frame, Lateral Bracing, and Diaphragm . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
13.9.1 General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
13.9.2 Cross beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
13.9.3 Cross frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
13.9.4 Lateral bracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .216
13.9.5 Diaphragms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
Chapter 14 Slab Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
14.1 General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
14.1.1 Structural scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .219
14.1.2 Design action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
14.1.3 Analytical procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
14.2 Safety. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
14.2.1 Safety of slab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
14.2.2 Out-of-plane shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
14.2.3 Out-of-plane bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .222
14.2.4 In-plane forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
14.2.5 Safety veriﬁcation of slab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
14.3 Serviceability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
14.3.1 Serviceability of slab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
14.3.2 Serviceability veriﬁcation of slab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
14.4 Fatigue Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
14.4.1 Fatigue resistance of slab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
14.4.2 Fatigue due to out-of-plane shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
14.4.3 Fatigue due to out-of-plane bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
14.4.4 Inﬂuence of water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
14.5 Corrosion Resistance and Resistance to Material Deterioration . . . . . . . . . . . . . . . . . . . . . . . . 230
14.5.1 Resistance to steel corrosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
14.5.2 Resistance to concrete deterioration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
14.6 Slabs of Various Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
14.6.1 Reinforced concrete slab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .232
14.6.2 Pre-stressed concrete slab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
14.6.3 Steel-concrete composite slab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
14.6.4 Orthotropic steel deck . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
Chapter 15 Design of Composite Girders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
15.1 General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
15.2 Strength of Composite Girder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241（ 5）

15.2.1 Classiﬁcation of cross sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
15.2.2 Design bending resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
15.2.3 Veriﬁcation of bending moment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
15.2.4 Shear strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
15.2.5 Veriﬁcation of shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
15.2.6 Veriﬁcation of combined bending and shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
15.3 Structural Analysis and Resultant Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .249
15.4 Shear Connectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250
15.4.1 General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250
15.4.2 Type of shear connectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250
15.4.3 Ultimate limit state for shear connectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
15.4.4 Veriﬁcation at safety limit state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252
15.4.5 Veriﬁcation at fatigue limit state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
15.4.6 Design strength of shear connectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
15.4.7 Inﬂuence of steel girder plasticity on horizontal shear force . . . . . . . . . . . . . . . . . . . . . . . . 258
15.5 Detailing of Shear Connectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
15.5.1 Headed stud connectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
15.5.2 Perforated-plate dowels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .260
15.5.3 Block connectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
15.6 Veriﬁcation of Crack Width in Composite Girders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
15.7 Eﬀective Width of Concrete Deck for Composite Girders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263

（ 6）

1

Chapter 1 General Provisions
1.1 ScopeThis Design volume of the Standard Speciﬁcations for Steel and Composite Structures (”Speciﬁcations”) describes the standard procedure for performance veriﬁcation in the design of steel
structures and composite girders (”steel and composite structures”). The Speciﬁcations also describe the structural details of the structure to be veriﬁed. The design step of verifying the eﬀects
of a large-scale earthquake (L2 earthquake) is described separately in the Seismic Design volume.

【 Commentary 】

These ”Standard Speciﬁcations for Steel and Composite Structures” (”these speciﬁcations” hereafter) comprise six volumes: General Principles, Structural Planning, Design, Seismic Design, Construction, and Maintenance. This Design volume applies to the design of steel structures and composite
girders (”steel and composite structures”). The structures considered in this volume are general steel
structures, in which the structural material used for the main members is steel, and composite girders
and columns comprising both steel and concrete. In the design of composite girders, the speciﬁcations[JSCE 2002a] and [JSCE 2002b] may be referred to instead of this volume.
In cases where the speciﬁcations given in this Design volume are insuﬃcient and/or inappropriate
for the structural design of a particular speciﬁc structure, it may be unnecessary to apply this volume
if the required performance is veriﬁed through a full-scale experiment or model experiment that takes
full account of the design actions, a numerical analysis method of certiﬁed accuracy and applicability,
or a similar approach. In this case, however, the substance of this Design volume might be taken
into account in the design of the structure while clarifying the accuracy and applicable scope of theperformance veriﬁcation method with respect to required performance at the design stage.
One of the design steps is verifying the eﬀects of a large-scale earthquake, such as an earthquake
producing Level 2 earthquake motion. This is described separately in the Seismic Design volume. If
medium earthquakes, such as those producing Level 1 earthquake motion, are to be taken into accountat the design stage, this Design volume may be used for performance veriﬁcation because the relevant
veriﬁcation methods introduced here are applicable to such cases.

1.2 Terms and Definitions
1.2.1 Commonly used terms(1) General terms relating to design
1) Performance-based design method: a design method in which there is no restriction
on structural type and materials, design method, or construction method. The only
requirement is that the designed structure meets the performance requirements. Speciﬁcally, it is a design method in which the speciﬁed performance of the structure is assured
at each of the structural planning, design, construction, and maintenance stages oncethe objectives and functions of the structure have been clearly deﬁned. That is, theperformance of the structure is speciﬁed so as to fulﬁll its function.
2) Regulation-based design: a design method in which the structure or structural members

2Standard Specifications for Steel and Composite Structures [Design]

are designed based on speciﬁc design codes that specify suitable procedures, such as
design calculations, structural materials, and their sizes.
3) Deemed to satisfy regulations: regulations in which one or more solutions that are
deemed to satisfy the performance requirements are illustrated. These regulations may
be adopted in cases where the method of verifying structural performance is not necessarily speciﬁed. These regulations specify structural materials and their sizes, procedures such as design calculations that are empirically regarded as correct, and otherfactors.
4) Reliability-based design method: a design method in which the possibility of a structure/structural member reaching the limit state is estimated based on probabilistic
theory.
5) Limit-state design method: a design method in which a limit state to be veriﬁed isclearly speciﬁed and partial-factor design is adopted as the veriﬁcation format. The
partial-factor design format is classiﬁed as a Level 1 veriﬁcation format from thereliability-based design viewpoint. Strictly speaking, partial-factor design is not equivalent to limit-state design, although the two are sometimes regarded as equivalent inJapan.
6) Partial-factor design format: a design format incorporating certain partial factors inorder to take into account uncertainties or scatter relating to actions??, geotechnicalparameters, structural member size, structural analysis method, etc.
7) Life-cycle cost: the total cost of structural planning, design, construction, maintenance,and demolition of a structure; in other words, the total amount invested over thecomplete life cycle of the structure.
8) Design working life: the assumed period for which a structure fulﬁls its intended purpose
without major repair and within the scope of the initially established maintenanceplan. Design working life is determined at the design stage. Initially planned regularinspections and repairs are continued throughout the design working life.
9) Durable lifetime: the period between entering service and the point in time at which
the performance of the structure falls below requirements due to fatigue, corrosion,material deterioration, or other factors and the structure reaches its limit state.
10) Objective: a common expression of the reason for building the structure. It is often
desirable for the objective to be expressed with the word ’client’ or ’user’ as the subjectof the sentence.
11) Function: the role that a structure has to play in accordance with the objective.
12) Review: a process carried out by an authorized third-party institution in order to determine whether the design process, from determination of the objective to veriﬁcation,is proper or not.
13) Authorization: the ﬁnal determination by the third party brought in to perform areview.
14) Certiﬁcation: the act of the third party institution issuing a certiﬁcate once the structural design is determined to be proper.
(2) Terms relating to performance
1) Performance: the behavior that the structure has to demonstrate in order to meet theobjective or requirements.
2) Required performance: the performance that the structure has to demonstrate in order
to meet the objective.
3) Performance item: itemization of required performance. For each item, a veriﬁcationindex is set. The index, generally, includes a speciﬁed limit state.

Chapter 1 General Provisions

4) Performance level: the level of performance that is required of each structure. Performance level is determined for each required performance depending on its necessity.
5) Safety: ability of a structure to protect the lives and assets of users and third parties.
6) Serviceability: ability of a structure to perform such that allowed degrees of userexperienced displeasure or unease are not exceeded.
7) Durability: ability of a structure or structural element to resist deterioration causedby repeated variable action and/or environmental action. In the case of steel and composite structures, corrosion of steel members caused by environmental action, fatigue
phenomena caused by repeated variable action, and deterioration of concrete member
materials and strength are considered.
8) Restorability: ease with which a structure can be restored to its originally speciﬁed
performance level after undergoing assumed actions that lead to deterioration of its
performance level.
9) Social and environmental compatibility: a measure of how a structure not only contributes to sound social, economic, and cultural activities but also minimizes stress on
the surrounding social and natural environment.
10) Constructability: a measure of how safe and assured construction work is during fabrication and erection.
11) Initial soundness: the requirement that a structure performs, upon completion, in linewith the level intended at the design stage.
12) Maintainability: the ease of maintenance of a structure.
(3) Terms relating to limit state
1) Limit state: a state in which the structure or structural element no longer meets therequired performance.
2) Safety limit state: a state resulting in collapse or other similar form of structural failure
due to excessive deformation, displacement, vibration, or similar. The safety limit stateis used as the limit state associated with structure safety. The term is often referred toas the ”ultimate limit state” and so is used in the Seismic Design volume.
3) Serviceability limit state: a state that corresponds to conditions beyond which thespeciﬁed service requirements for the structure or a structural element are no longer met.
The serviceability limit state is used as the limit state associated with the serviceabilityof a structure.
4) Repair limit state: a state in which continued use of a structure damaged by expectedaction is possible after repairs using currently available repair methods, carried out atreasonable cost, and carried out within a reasonable period. The repair limit state isused as the limit state associated with ease of repair. In the Seismic Design volume,the term ”damage limit state” is used in place of ”repair limit state”.
5) Fatigue limit state: a state in which a structure or structural member suﬀers fatigue or
failure as a result of repeating variable action. Fatigue limit state is used as the limit
state corresponding to the fatigue durability of a structure.
(4) Terms relating to veriﬁcation
1) Performance veriﬁcation: activities performed in order to verify that the designed structure satisﬁes all of the performance requirements. When the limit-state design method
is adopted, the judgment entails comparing response values with the limit values of
performance.
2) Veriﬁcation index: index used to express a performance item as a physical quantity.
Veriﬁcation indices are used in performance veriﬁcation.
3) Response value (Demand) S: physical quantity representing the response of the struc-34Standard Specifications for Steel and Composite Structures [Design]

ture to an action.
4) Limit value of performance (Capacity) R: allowable limit of physical response to acorresponding structural response. This value is determined based on the required
performance level.
5) Statistical characteristic value: a value corresponding to the a priori speciﬁed fractile ofthe statistical distribution of a random variable such as a material property or action.
The expected value and the mode of a random variable are regarded as statisticalcharacteristic values.
6) Optimization: the process of obtaining an optimal solution such that the objective function, including required performance, performance item, etc. as subordinate variables,
becomes a minimum or maximum under restraint conditions.
7) Partial factor: a factor assigned to each design value in order to consider its uncertainty.
Five partial factors are generally used: an action factor, a material factor, a structural
analysis factor, a structural member factor, and a structure factor.
8) Structure factor: a factor that takes into account the importance of the structural,social, and economic eﬀects that failure of the structure would have.
(5) Terms relating to actions
1) Action: any eﬀect that leads to deformation, displacement, constraint, or deteriorationof a structure or structural element.
2) Load: an assembly of mechanical forces directly acting on a structure. The forces areconverted from actions through the analytical model. A load is used as an input datumfor design calculations of the stress resultant, stress, displacement, and so on.
3) Design value of action: a value obtained by multiplying the action factor by the characteristic value of the corresponding action.
4) Direct action: an assembly of concentrated or distributed mechanical forces acting ona structure.
5) Indirect action: the cause of deformations imposed on the structure or constrained init.
6) Environmental action: mechanical, physical, chemical, or biological action that may
cause deterioration of the materials constituting a structure.
7) Permanent action: action which is likely to act continuously throughout the design
working life and for which variations in magnitude with time are small compared withthe mean value.
8) Variable action: action for which the variation during the design working life is not
negligible in relation to the mean magnitude and is not monotonous.
9) Primary variable action: one or one set of variable actions considered as the primaryinﬂuences when load combinations are taken into account in performance veriﬁcation
work.
10) Secondary variable action: an action considered secondary among the variable actions
and that is additive to the combination of primary variable action and accidental action.
11) Accidental action: action that rarely occurs on a structure over the design working life
but which may cause serious damage if it does happen to occur.
12) Action modifying factor: a factor for converting the standard or nominal value of action
into a characteristic value.
13) Action factor: a factor that takes into account the unfavorable deviation of statisticalcharacteristic values of action, uncertainty relating to the action model, changes in action characteristics during the design working life, the inﬂuence of action characteristics
on the relevant limit state of the structure, variations in environmental action, and soChapter 1 General Provisions

5on.
(6) Terms relating to structural materials
1) Characteristic value of material strength: a value corresponding to an a priori speciﬁed
fractile of the statistical distribution of material strength. The statistical distribution
is determined based on statistical data obtained from standardized material strength
tests.
2) Standard value of material strength: a value of material strength adopted in structural design speciﬁcations/standards other than ”Standard Speciﬁcations for Steel andComposite Structures”.
3) Material strength modifying factor: a factor for converting the standard value of material strength into a characteristic value.
4) Material factor: a factor that takes into account unfavorable deviation of statisticalcharacteristic values of material strength, diﬀerences in material properties between
experimental specimens and the real structure, the inﬂuence of material properties on
the relevant limit state of the structure, changes in material properties over a givenreference period, and so on.
5) Design value of material strength: a value obtained by dividing the characteristic valueof material strength by the corresponding material factor.
(7) Terms relating to calculation of response value
1) Factor for structural analysis: a factor used to take into account the accuracy of structural analysis methods applied in the calculation of the stress resultant and similar,
uncertainties relating to the modeling procedure used for the structure, and so on.
(8) Terms relating to capacity of structural member
1) Structural member factor: a factor that takes into account the accuracy of structuralresistance analysis methods applied in the calculation of load-carrying capacity, variations in structural member size, the importance of the role of the structural member,and so on.
2) Design capacity of structural member: a value obtained by dividing the capacity by the
structural member factor. Capacity is calculated by using the design values of strength
materials.
1.2.2 Terms used in this Design volume(1) Primary member: a member whose failure would directly lead to loss of stability and/or
function and failure of the whole structure.
(2) Secondary member: a member that fulﬁlls a secondary function and whose failure would not
directly lead to loss of stability and/or function nor failure of the whole structure.
(3) Structural detail: a design method agreed in response to a part that cannot be designed byapplying a design calculation method and/or to a request made regarding construction to beconsidered at the design stage. A structural detail is a necessary condition for guaranteeing
appropriate prior conditions for the design calculations.S【 Commentary 】

The terms commonly used in these speciﬁcations and principal ones used in the Design volume aredeﬁned here.

1.3 Notation
The following notation is deﬁned for this speciﬁcation. Only general notation is given.

6Standard Specifications for Steel and Composite Structures [Design](1) Action, sectional force, capacity and stress
Fk
Characteristic value of action
Design action
Fd
M
Bending moment
Design bending moment
Msd
M1 , M2
End moment
ME
Lateral torsional buckling moment
Flexural capacity
Mu
Mrd
Design ﬂexural capacity
Yield moment
My
Mp
Full plastic moment
N, P
Axial force
Axial capacity
Nu , Pu
Design axial force
Nsd
Nrd , Prd
Design axial capacity
NY , Ny
Yield axial force
V
Shear force
Design shear capacity
Vrd
T
Torsional moment
Tsd
Trd
PE , Pe
fk
fd
fyk
fyd
fuk
fud

fyk

fyd
fvyk
fvyd
σ
τ
σrd
τrd
σcr
τcr
σE , σeσrσu
σY , σy(2) Displacement and strainu, v, wεεyγDesign torsional moment
Design torsion capacity
Euler buckling load
Characteristic value of material strength
Design material strength
Characteristic value of tensile yield strength
Design yield strength
Characteristic value of tensile strength
Design tensile strength
Characteristic value of compressive strength
Design compressive strength
Characteristic value of shear yield strength
Design shear strength
Normal stress
Shear stress
Design local buckling strength
Design shear strength
Buckling stress
Shear buckling stress
Euler buckling stress
Residual stress
Ultimate stress
Yield stress
Displacement in x, y, z direction
Axial strain
Yield strain
Shear strain

Chapter 1 General Provisions

εst
E
G
Est
ν
(3) Geometrical values
A
Ae
Et3
D=
12(1 − ν 2 )L, IIωω , CωJb σY 12(1 − ν 2 )
R=
t
E
π2 k
W
Z
r
e
e /r
be
t
α = a/bkγe 1 σYλ=r πE(4) Veriﬁcation
S, R
Sd , Rd
γi
γa
γf
γb
γm

7

Starting hardening strain
Modulus of direct elasticity
Modulus of rigidity
Initial strain hardening coeﬃcient
Poisson’s ratio
Cross-sectional area
Eﬀective cross-sectional area
Bending stiﬀness of plate
Member length
Geometrical moment of inertia
Bending torsional constant
St.Venant’s torsional constant
Width-thickness ratio parameter
Sectional modulus
Plastic sectional modulus
Radius of rotation (radius of gyration of area)
Eﬀective buckling length
Slenderness ratio
Eﬀective width of plate
Plate thickness
Aspect ratio of plate (ratio of long side to short side)
Buckling coeﬃcient
Relative stiﬀness of stiﬀener
Slenderness ratio parameter
Response value, Limit value (Resistance)
Design response value,Design limit value (Design resistance)
Structural factor
Structural analysis factor
Action factor (load factor)
Structural member factor
Material factor【 Commentary 】

This is the principal notation used in these speciﬁcations. The SI system of units is adopted,
although other practical systems may be used where values are quoted from other standards, papers,
etc.

1.4 Basis of Design
1.4.1 Purpose of design
Steel and composite structures shall be designed so that they satisfy the required performancein all areas such as safety, serviceability, restorability, durability, and social and environmental

8Standard Specifications for Steel and Composite Structures [Design]compatibility throughout their design working life.
【 Commentary 】

Steel and composite structures should conform to their purpose of use and should be both safe andalso functional. To meet these requirements, steel and composite structures or structural members must
be designed such that they meet the required performance in all areas such as safety, serviceability,
restorability, durability, and social and environmental compatibility under the various actions thataﬀect them during their construction and service periods. As stated in the General Principles volume,the design working life of a bridge is generally established at 100 years at present.

1.4.2 Verification of performance(1) During design, the performance required for steel and composite structures shall be deﬁned
clearly. Generally, required performance shall be established in the areas of safety, serviceability, restorability, durability, and social and environmental compatibility .
(2) During design, a performance level shall be speciﬁed for each performance item and theperformance level shall be veriﬁed for each performance item.
(3) In general, veriﬁcation indexes and limit states for the indexes shall be established. The performance of the structure shall be veriﬁed such that the response calculated by appropriate
numerical analysis does not exceed the limit states.
(4) For any veriﬁcation not carried out by the method in (3) above, veriﬁcation through experimental methods or adherence to speciﬁcations relating to structure details and materials
can be considered a suitable means of performance veriﬁcation.
(5) In verifying performance, it shall be veriﬁed that the response value does not exceed thelimit value at any time during the construction period and the design life.
【 Commentary 】(1) The ﬁrst step at the structural planning and design stages is to determine the required performance of the steel or composite structure. However, there remain at present various opinions
and arguments regarding the deﬁnition and classiﬁcation of required performance; as yet, noconsensus on these matters has been reached.
In [Ministry of Land, Infrastructure, Transport and Tourism (2002)], three performance requirements - that is, safety, serviceability, and restorability - are deﬁned as the fundamental
required performance of a structure. These three are subdivided according to the function of
the structure Social and environmental compatibility is a recent requirement associated withchanging social and economic circumstances. This new fundamental performance requirement
may become crucial from now on, although techniques for deﬁning and estimating the relevant
limit state are inadequate at present.
A commonly used veriﬁcation method is to check that a response value is no greater than thelimit value, but this may not be applicable where it proves impossible to deﬁne the limit state.
In such cases, performance veriﬁcation is carried out by optimizing the objective function, which
is a function of the design variables [JSCE (2003a)].
The performance items corresponding to each of the basic performance requirements - safety,
serviceability, restorability, and social and environmental compatibility - are listed in Table
C1.4.1. In this table, the performance item ”durability” is incorporated into the safety, serviceability, and restorability requirements as it is commonly related to these three basic performancerequirements. These basic performance requirements are applicable not only to the structuraldesign stage but also to the maintenance stage when the structure is in service.

9

Chapter 1 General Provisions

In light of the current situation regarding the availability of veriﬁcation techniques at thedesign stage as well as convenience for the design engineer, it may be more appropriate to use
performance classiﬁcations that reﬂect the actual process of design speciﬁcation, since structuraldesign is not necessarily carried out according to classiﬁcations of required performance. Thus,
the performance items corresponding to each basic performance requirement in Table C1.4.1 iscovered in the volume indicated in the third column. The performance requirements listed inTable C1.4.2 are the ones established in this Design volume.
This classiﬁcation relating to required performance is determined based on the following consideration.
1 SafetyAs safety performance items, the safety of the whole structure (structural safety) andsafety with respect to members of the public in the vicinity of the structure (public safety)
are established in these speciﬁcations. Structural safety includes action resistance performance, displacement and deformation performance, stability performance, etc. Structuralsafety is in fact the requirement to ensure overall safety of the structure under the severest
expected action. Although it is desirable to verify the safety of the structure as a whole, theTable C1.4.1
items
Basic
performancerequirement

SafetyBasic performance requirements and examples of related performance
Performance item examples

Coverage in these specifications

Structural safety (resistance, stability, etc.)
Public safety (damage to third party such as
falling objects)
Safety during earthquake (resistance, deformation capacity, stability)
Safety during construction (resistance, stability, initial soundness)

Design volume: safety
Design volume: safety

Durability

Serviceability

Serviceability for users (vehicle operating
performance, pedestrian comfort)
Serviceability after earthquake (vehicle operating performance, pedestrian comfort)(fatigue,corrosion,and material deterioration)

Serviceability for maintenance (ease ofmaintenance (inspection, painting, etc.))

Restorability

Restorability after earthquake (restorationof damage caused by earthquake)
Maintainability(ease of repair after degradation with thepassage of time and inspection)
Social compatibility (consideration of social importanceof structure)
Economic rationality (LCC, LCU)

(Other volume: Seismic Design volume)
Design volume: Constructability(Other volume: Construction volume)
Design volume: serviceability(Other volume: Seismic Design volume)
Design volume: durability
Designvolume:restorability(Other volume: Seismic Design volume)

Design volume: durability
Design volume: social and environmental compatibility
Design volume: social and environmental compatibility
Design volume: social and environmental compatibility (Other
volume: Construction volume)

Environmental compatibility (noise, vibration, negativeenvironmental impact (LCA), aesthetics, etc.) Environmental compatibility during construction (noise, vibration, and negative environmental impact)Note) LCC: Life cycle cost LCU: Life cycle utility (social, economic utility during life cycle) ，
LCA: Life cycle assessment
Social and environmental
compatibility

designvolumedurability
volume10Standard Specifications for Steel and Composite Structures [Design]

Table C1.4.2

Classification of performance requirements in this Design volume

Performance requirement

Performance item

SafetyStructural safety
Public safety
Vehicle operating performanceserviceability

Restorability∗

Durability

Pedestrian comfort
Restorability after earthquake
Fatigue
resistanceCorrosion resistanceResistancetomaterial deterioration
Maintainability

SocialbilitySocial and environmental
compatibility

compati-Economic rationality
Environmental
compatibility

Example of check item
resistance of structural member, resistance of whole structure, resistance of joint, stability, etc.
injury to users and third parties(falling object etc.)
vehicle operating performance under usual conditions (soundness andrigidity of road)train operating performance andride comfort under usual conditions
pedestrian comfort under usual conditions (walking-induced vibration)level of damage (ease of restoration)
fatigue durability against variableactionsrust prevention and corrosion protection performance of steel material
concrete deteriorationease of maintenance (inspection,
painting, etc.) and ease of restoration
appropriateness of partial factor(consideration of social importanceof structure)social utility during life cycle ofstructurenoise, vibration, environmental impact (CO2 emissions), aesthetics,
etc.

Example of verification index
Stress resultant, stress−

Road surface flatness, deformation of
main girder
Natural frequency of main girder
Response value (damage level)/limit
value of performance (damage level)
Equivalent stress range/allowablestress range
Corrosion environment and painting
specification, LCC
Water-content ratio, cover of concrete–

Partial factor (structural factor), etc.

LCC ，LCU
Noise and vibration levels for surrounding residents, life-cycle CO2 ,aesthetic reaction to structural shapeand color, monumental aspect, etc.
Stress resultant, stress, deformation

Constructability∗ Safety
duringsafety during construction
construction
Ease of construcease of fabrication and construction worktion
∗ Note: Actual verification methods for restorability and Constructability are prescribed in the Seismic
Design and Construction volumes, respectively, although the required performance is established here in
the form of these performance requirements.

conventional method generally used for veriﬁcation is to determine whether the structuralmember(s) and their connections reach the required level of resistance. Public safety is therequirement to avoid injury or damage to any public third party as a result of the existence of the structure, such as through the collapse of ancillary equipment (e.g., highway orrailway signs), the dropping out of high-tension bolts that have suﬀered delayed fracture,
the stripping away of concrete fragments from slabs, and so on. This performance item isestablished in consideration of the environment around the structure according to demand,so no veriﬁcation method is speciﬁed in this Design volume.
2 ServiceabilityServiceability is the ability of a structure to perform such that users suﬀer no problems or
discomfort. Performance items relating to serviceability should be established according to
the utilization pattern of the structure. In this Design volume, vehicle and train operating

Chapter 1 General Provisions

11

performance (performance relating to vehicular traﬃc) and pedestrian comfort (performance
relating to walking) are considered as performance items with respect to bridges. Vehicle
operating performance is speciﬁed for highway bridges and train operating performance forrailway bridges. However, the former is meant in this Design volume when the term ”vehicle
operating performance” is used.
Some structural engineers might consider that the performance item representing theease of structure maintenance should be included as part of ”serviceability”, as shown in
Table-commentary 1.4.1. However, this performance item is not treated as part of serviceability in this Design volume; only the performance items relating to users are included.
Maintainability, representing the ease of maintenance of a structure, is regarded here as oneof the performance items relating to ”durability”, with which it is closely related. Furthermore, the inﬂuence of the structure on the surrounding social and natural environment istreated as one of the performance items relating to ”social and environmental compatibility” in this Design volume, although this performance item is sometimes classiﬁed as partof ”serviceability”.
In addition to the vehicle operating performance, train operating performance, and pedestrian comfort, ”serviceability” also includes the requirement to prevent excessive deformation and/or appearance degradation of the structure (or its structural members), to securewater-tightness, and other performance items, so as to ensure that no unpleasant and/or
harmful eﬀects are caused for users. As described above, the performance requirement ”serviceability” is deﬁned here in terms of bridge structures. However, the deﬁnition sometimes
diﬀers for structures other than bridges. For example, in the case of port and harbor structures, serviceability is established as a performance requirement directly connected to thefunctioning of the structure and ”serviceability” is then deﬁned as the requirement thatusers can utilize the structure without any inconvenience. In this case, the requirement
is that any damage to functionality caused by expected actions should be limited to thatwhich can be restored by small and rapid repairs. Therefore, ”serviceability” has to bedeﬁned according to the conditions of use and utilization patterns of a particular structure.
3 Restorability
”Restorability” represents the ease with which a structure can be restored to its originallyspeciﬁed performance level after undergoing assumed actions that lead to performance deterioration. This performance requirement is generally assumed to be relevant in the case of
exceptional actions such as earthquakes. Restorability of damage caused by normal actions
is treated as one of the performance items in ”durability,” because it is closely related tothe ease of maintenance of a structure.
Performance in earthquakes is essentially part of required performance relating to structural design. However, the design philosophy and veriﬁcation techniques for earthquake
performance are generally recognized as special. And it is also recognized that separation of
the Design volume and the Seismic Design volume is more convenient for structural engineers
in practice. Consequently, the volumes are in fact separated and performance veriﬁcation
against performance items such as safety under earthquake motion, serviceability after anearthquake, and restorability after an earthquake - especially Level 2 earthquake motion-is carried out using the Seismic Design volume, as shown in Table C1.4.1. Where a performance veriﬁcation is carried out against Level 1 earthquake motion, the Design volume
may be used because applicable veriﬁcation methods are described in this volume.
In this Design volume, ”restorability after an earthquake” does not need to be taken into
consideration because no earthquake damage will result if the structure is designed suchthat the stress resultant remains less than the yield value. It is, however, established as one

12Standard Specifications for Steel and Composite Structures [Design]of the performance items relating to ”restorability”. In cases where slight damage is allowed
to be caused by Level 1 earthquake motion, however, veriﬁcation of ”restorability after anearthquake” is essential. For this purpose, ”restorability” is prescribed in this volume asshown in Table C1.4.2. An actual veriﬁcation method for restorability is given in the Seismic
Design volume.
4 Durability”Durability” is established as a performance requirement in this Design volume though
it is not included in Table C1.4.1 as a basic performance requirement. The reasons for thisare as follows.
Properly speaking, it may be reasonable to take account of performance deterioration
over time in verifying the basic performance requirements such as safety, serviceability, andrestorability throughout the design working life. There exists an assertion that the durabilityof structure has to be ensured by satisfying these three fundamental required performances
during its design working life and thus durability must be treated diﬀerently from thesafety, serviceability and restorability [JSCE (2002b), JSSC (2001)]. However, securing of
durability is extremely important for the steel and composite structures as the control of
performance degradation as a function of time elapsed caused by variable action which acts
on a structure repeatedly and/or environmental one may seriously inﬂuence on the physicalworking life of structure. Therefore, ”the control of performance degradation as a functionof time elapsed caused by variable action which acts on a structure repeatedly and/or
environmental one” is regarded as being equal to the veriﬁcation of durability and durability
is established as on of the important required performances in this Design volume. Thoughdegradation of performance over time is closely related to all of the basic performancerequirements, a general approach is to verify durability separately from other performancerequirements from the viewpoint of performance veriﬁcation methodology. In other words,
in practice, if the veriﬁcation entails controlling the performance degradation over timesuch that it is less than an a priori prescribed level, the veriﬁcation of safety, serviceability,
etc. can generally be carried out without any consideration of degradation. This former
veriﬁcation that degradation does not exceed a certain level is regarded as a veriﬁcation ofdurability.
”Durability” is deﬁned as the ability of a structure or structural element to resist deterioration caused by repeated variable actions and/or environmental action [JSCE (2003a)].
The veriﬁcation of durability entails ensuring that deterioration of safety, serviceability,
etc. over time is held to less than an a priori prescribed level. Actual performance items
relating to ”durability” in these speciﬁcations are fatigue resistance, corrosion resistance,and resistance to material deterioration. Although the veriﬁcation of fatigue resistancecan be regarded as part of the veriﬁcation of safety, because fatigue failure of a structuralmember is checked as part of the durability veriﬁcation, fatigue resistance is treated as aperformance item relating to durability in this Design volume. Furthermore, the ease of inspecting and repainting a structure, the ease of repairing damage, and so on are consideredas part of a structure’s maintainability, which is included among performance items relatingto ”durability” because these items greatly inﬂuence the durability of a structure.
5 Social and environmental compatibility”Social and environmental compatibility”, as shown in Table C1.4.1, has come to beconsidered important as changes in social and economic circumstances have taken place.
Performance items relating to this performance requirement have been established: social
compatibility, economic rationality, and environmental compatibility. Social compatibility
is the performance item used for veriﬁcation of the structure in consideration of its social

13

Chapter 1 General Provisions

importance. This performance item is required if the importance of the structure is considered in selecting the veriﬁcation method or setting the partial factors. Economic rationality
is the performance item used to verify which structure is the best from the viewpoint oflife-cycle cost. At present, it is impossible to estimate the eﬀect that the existence of astructure will have on people’s social and economic life using a measure such as ”utility”.
However, if a method of estimating ”utility” is fully developed, it may be desirable to design
a structure so that its life-cycle utility is maximal.
”Social and environmental compatibility” is veriﬁed by optimizing an objective functionthat is a function of several performance requirements based on economic and technicalviewpoints.

6 Constructability”Constructability” represents performance during fabrication and erection of a structure,such as safety, ease of fabrication and erection, ease of construction quality control, andso on. This is one of the important performance requirements that must be taken into
account at the design stage, so it is established as one of the performance requirementsin this Design volume. An actual veriﬁcation method for Constructability is given in theConstruction volume. Consideration of initial soundness, which is one of the important
performance items relating to ”Constructability” [JSCE (2003a)], is also described in theConstruction volume and not the Design volume because it must be taken into account at
the construction stage.
Among the six performance requirements 
1 ∼
6 above, there are some performance items
for which relevant limit states have been clearly determined, such as structural safety in thesafety performance requirement, vehicle operating performance and pedestrian comfort in
the serviceability performance requirement, etc. On the other hand, it is diﬃcult to determine a relevant limit state for social and environmental compatibility, for example. Where
limit states have been determined, performance veriﬁcation is carried out quantitatively. In
other cases, the quantitative performance veriﬁcation is replaced by an attempt to optimize
the objective function.
(2) Where a veriﬁcation as to whether a designed steel or composite structure satisﬁes the perfor-

Table C1.4.3
Required
formanceper-

SafetyServiceability
Restorability

Durability

Social andenvironmental
compatibility
Constructability

Limit states for each performance item

Performance item
structural safety
public safetyvehicle operating performancepedestrian comfort
restorability after earthquake
fatigue resistancecorrosion resistanceresistance to material deterioration
maintainabilitysocial compatibility
economic rationality
environmental compatibility
safety during constructionease of fabrication

Limit state
Safety limit state or ultimate limit state;(public safety is not established in this Designvolume.)Serviceability limit state(restorability limit state or damage limit state[in Seismic Design volume])
fatigue limit state
A certain state which may threaten to damage
the other limit states
Corresponding limit state is not established inthis Design volume
Corresponding limit states are not establishedin this Design volume
Corresponding limit states are not establishedin this Design volume

14Standard Specifications for Steel and Composite Structures [Design]

mance requirements is carried out, the general procedure is to verify whether the limit statecorresponding to the a priori required performance level is reached or not. The term ”limit
state” as used here means the itemized limit state established with respect to each performance
item for an individual performance requirement. If this limit state is speciﬁcally deﬁned, veriﬁcation based on the limit state design method is possible. Each performance item and its
respective limit state as adopted in this Design volume is shown in Table C1.4.3. Although theideal would be to establish a limit state for every performance item, it is currently only possible
to establish limit states for structural safety, serviceability, restorability, and fatigue resistance;
there are no methods at present for setting the others. As noted in the commentary to ”1.2
Terms and Deﬁnitions”, the limit state for safety is deﬁned so that it includes not only structuralsafety but also public safety. However, it is not possible at present to determine a limit statefor public safety. Only ultimate limit states that are conventionally adopted are considered here.
Corrosion resistance and resistance to material deterioration, which are part of the durability
performance requirement, are regarded as having limit states because degradation of performance
may threaten to damage other limit states.
As the basis for veriﬁcation in performance-based design, the design response value must be no
more than the design limit value of performance under the assumption that these two values arecalculated using partial factors for each performance item. Fig.C1.4.1 illustrates the frameworkof performance veriﬁcation. In cases where the establishment of a limit state is impossible,
performance veriﬁcation is carried out by optimizing an objective function such as cost, utility,
etc., which is a function of the design variables.

Verification for each performanceverification

Level of action
Death and live-load
Environmental
action etc.

index
Response Performan limit
value
value

Structurallevel
Load-proof and levelof the lesion
Use period etc.
Calculation of demand

Fig.C1.4.1

Sectional force, stress, anddisplacement and transformation
Cost and environmental impact, etc.

Power-proofof section
Rigidity
Generation
cost etc.

Calculation of capacity

Framework of performance verification(3) In calculating response values, it is necessary to select a structural model and a structural analysis method capable of appropriately estimating the performance of the designed structure. With
respect to structural analysis, linear methods such as beam theory, grid theory, and so on have
conventionally been adopted because they oﬀer convenience in considering load combinations
by simply summing the eﬀect of dead load, live load, etc. With recent remarkable developments in computer techniques, advanced methods such as ﬁnite element analysis (in which athree-dimensional arrangement of many structural members including the ﬂoor slab is taken into
account), ﬁnite displacement analysis (where the eﬀect of geometric nonlinearity is considered),
dynamic analysis, and others have come into frequent use. The most suitable analysis methodshould be selected according to the type of structure and the purpose of the veriﬁcation. Itshould be noted that a fully accurate solution can not be obtained, even when using advanced
computer-based structural analysis methods, if the modeling of loads applied by actions andstructural shapes is not appropriate. Further, note that careful estimation and in-depth discussion of the stress results obtained by, for example, ﬁnite element analysis, using shell or solid
elements is essential to obtaining reasonable results.

15

Chapter 1 General Provisions

In this Design volume, a practical veriﬁcation method corresponding to each performancerequirement is prescribed in the chapters noted below.
・ Veriﬁcation for safety: Chapter 6 Demand for Safety and Veriﬁcation
・ Veriﬁcation for serviceability: Chapter 7 Required Serviceability Performance and Veriﬁcation
・ Veriﬁcation for durability: Chapter 8 Required Durability Performance and Veriﬁcation
・ Veriﬁcation for social and environmental compatibility: Chapter 9 Required Social andEnvironmental Compatibility Performance and Veriﬁcation.
As for joints, ﬂoor slabs, and composite structures, all design-related provisions such as veriﬁcation method, structural details, etc. are speciﬁed in the relevant chapter, because giving theprovisions from the viewpoint of the veriﬁcation method for the performance requirements maylead to confusion. Veriﬁcation methods for restorability and Constructability are not given in thisDesign volume; instead they are prescribed in the Seismic Design volume and the Construction
volume, respectively.
(4) Where it is not possible to calculate a response value using a numerical analysis method orwhere the deﬁnition of a limit state is not possible, veriﬁcation through experimental methods
or adherence to speciﬁcations relating to structural details and materials can be considered asuitable means of performance veriﬁcation.

1.4.3 Verification method(1) Veriﬁcation shall be based on the partial factor method on the basis of reliability theory
and, as a standard design procedure, it shall be based on the limit-state design method.
(2) In general, veriﬁcation shall be based on design responses to design actions, design limits asdetermined by design material strengths, and individual partial factors. The performance ofthe structure shall, in general, be veriﬁed using Equations (1.4.1) and (1.4.2):
Sd
≤ 1.0
Rd

γa · S(γf · Fk )≤ 1.0
γi
R(fk /γm )/γb

γi

Rd
fk
γm
γb
R(· · · )
Sd
Fk
γa
γf
S(· · · )γiwhere ，

(1.4.1)(1.4.2)：design resistance：characteristic value of material strength：material factor：structural member factor：function for calculating limit value of structure from material strength：design response：individual characteristic value of action：structural analysis factor：action factor corresponding to each action (load factor)：function for calculating response value of structure from action：structural factor(3) During design, a veriﬁcation shall be carried out for every limit state that can be considered.

【 Commentary 】(1) Veriﬁcation shall be based on the partial factor method according to reliability theory. The safety
and serviceability limit states are a basic consideration and both fatigue and deterioration limit

16Standard Specifications for Steel and Composite Structures [Design]

states must be considered with respect to durability.
In general, reliability-based veriﬁcation formats are classiﬁed into three categories from the pointof view of the accuracy of the relationship between failure probability and the reliability measureused in each [e.g. JSSC (2001)]. In this Design volume, the Level-1 veriﬁcation format is
adopted. This format is based on the partial factor method and has commonly been used ingeneral structural design.
(2) The performance of a structure should, in principle, be veriﬁed using Equation (1.1.1), which
includes one factor (structural factor γ i) determined in consideration of the structural, social,and economic eﬀects that failure of the structure would have. Regardless of the structural analysis
method used, the load eﬀect, stress resultant, stress, deformation, etc. can be adopted as thedesign values of Rd and Sd corresponding to the relevant performance items when this equation
is used. However, given present practice whereby design calculations are generally carried out
using linear analysis methods and the performance veriﬁcations are carried out not for the whole
structure but for each of its structural members, the rather more convenient Equation (1.4.2)
can be used. This is a performance veriﬁcation format based on multiple partial factors and iseasier to implement than Equation (1.4.1) when calculating design values Rd and Sd.
In Equation (1.4.2), partial factors γf , γm , γa , and γb correspond to the action factor, material
factor, structural analysis factor, and structural member factor, respectively. These factors must
be determined in consideration of unfavorable deviations from characteristic values, uncertainties
in computational accuracy, discrepancies between design and practice with respect to actions or
structures and structural material strengths, etc.
Design resistance R

Design action eﬀect S

characteristic value ofmaterial strength： fk

Characteristic value of action： Fk

γm

γf

?
?

?

Resistance： R(fd )γbAction eﬀect： S(Fd )γa?

Design resistance： Rd = R(fd )/γbγi?

Design action eﬀect： Sd =

γa S(Fd )?

Veriﬁcation： γi
Fig.C1.4.2?

Design value of action： Fd = γf Fk

Design value ofmaterial strength： fd = fk /γm

Sd
≤ 1.0
Rd

Concept of verification of safety relating to structural resistanceIn the design of steel and composite structures, the ideal would be for the type, shape, and size ofthe structure to be determined such that the probability of demand exceeding capacity is below an apriori prescribed value. At present, however, the calculation of such a probability remains extremely
diﬃcult and is recognized as impossible in practice. Therefore, this Design volume prescribes Equation(1.4.2) as the veriﬁcation format to check whether the required performance of a structure or its
structural members is met or not.
As an example of the process, Fig.C1.4.2 outlines the veriﬁcation of safety relating to structuralresistance based on Equation (1.4.2) [Steel and concrete common structural design standards Subcommittee (1992)].

17

Chapter 1 General Provisions

In carrying out a veriﬁcation based on Equation (1.4.1) or (1.4.2), the precision of the values givenon the left side of each equation should be two signiﬁcant digits. Thus, the design response value,
design limit value, etc., are obtained to three signiﬁcant digits.

1.4.4 Partial factors(1) Partial factors in a veriﬁcation shall be determined based on the concept given in (2) and(3).
(2) The material factor, structural member factor, structural analysis factor, and action factor
shall be determined in consideration of 1) unfavorable deviations from characteristic values,2) uncertainties in computational accuracy, and 3) discrepancies between design and practicewith respect to actions or structures and materials.
(3) The structural factor shall be determined as per the provisions of Section 1.5 below.

【 Commentary 】

In this Design volume, the required partial factors are speciﬁed in the chapters listed below. Standard values of these partial factors used in the veriﬁcation of safety, serviceability, and durability arelisted in Table C1.4.4. Values of the structural factor are given in Table C1.5.1.
Structural factor: Chapter 1 General Provisions, 1.5 Structural Factor
Action factor: Chapter 2 Actions
Material factor: Chapter 3 Materials
Structural analysis factor: Chapter 4 Structural Analysis
Structural member factor: Chapter 5 Structural Member Resistance
Table C1.4.4

Standard values of partial factors

Performance requirement (performance item)

Action factor
γfStructural analysis
factor γaMaterial factor
γm

Structural member
factor γb

Safety (structural safety)
Serviceability(vehicle operating performanceand pedestrian comfort)
Durability (fatigue resistance)

1.0 ∼ 1.7

1.0 ∼ 1.1

1.0 ∼ 1.05

1.0 ∼ 1.3

1.0

1.0

1.0 ∼ 1.05

1.0

1.0 ∼ 1.1

1.0

1.0

1.0 ∼ 1.1

When the partial factor design method is used as the veriﬁcation format, reliance is placed onrational decision making by the design engineer as to whether each partial factor should be further
subdivided or whether some partial factors can be lumped together. Note that in some other design
standards, various views about this decision process have been proposed and/or adopted.

1.4.5 Modification factors(1) The speciﬁcation provides for two modiﬁcation factors, namely a material modiﬁcation factor
and an action modiﬁcation factor.
(2) The action modiﬁcation factor shall be deﬁned for converting a speciﬁed or nominal action
value into a characteristic action value.
(3) The material modiﬁcation factor shall be deﬁned for converting a speciﬁed value of material
strength into a characteristic value of material strength.

【 Commentary 】

In the case that a speciﬁed or nominal value is used besides characteristic values relating to action

18Standard Specifications for Steel and Composite Structures [Design]

and/or material strength at present, the relevant characteristic value should be determined by adjusting
the speciﬁed or nominal value with a modiﬁcation factor.

1.5 Structural Factor
Structural factor γi shall be determined according to structural importance and also the socialand economical impact of the structure reaching its limit state.
【 Commentary 】

The structural factor, which is used to take into account the importance of the structure, includes
the social impact of the structure reaching its limit state, the structure’s relevance to disaster prevention, and economic factors such as the cost of rebuilding or repairing the structure if it reaches its
limit state. Basically, the value of the structural factor should be determined according to the wishesof the owner of the structure, because it is impossible to determine it theoretically based on reliability
theory. Once the structural factor has been determined, social compatibility as prescribed in ”Chapter
9 Required Social and Environmental Compatibility Performance and Veriﬁcation” must be considered
carefully.
The standard values given in Table C1.5.1 are generally adopted for the structural factor.
Table C1.5.1

Standard values of structural factor

Performance requirement (performance item)

Structural factor γi

Safety (structural safety)
Serviceability (vehicle operating performanceand pedestrian comfort)
Durability (fatigue resistance)

1.0∼1.2
1.0
1.0

References in Chapter 1
Railway Technical Research Institute (1992) ：Design Standards for Railway Structures and Commentary,
Steel and Composite Structures ．
Japan Society of Civil Engineers(1992) ：General principles for the limit state design of steel and concrete
structures, Journal of Structural Mechanics and Earthquake Engineering, JSCE, No.450/I-20, pp.13-20.
Japan Society of Civil Engineers (1997a) ：Design Code for Steel Structures, PART A; Structures in General.
Japan Society of Civil Engineers (1997b) ：Design Code for Steel Structures, PART B; Composite Structures.
Japanese Society of Steel Construction (2001) ：Guidelines for Performance-based Design of Civil Engineering
Steel Structures, JSSC Technical Report No. 49.
Japan Road Association (2002) ：Speciﬁcations for Highway Bridges and Commentary I Common Speciﬁcations, II Steel Highway Bridges.
Ministry of Land, Infrastructure, Transport and Tourism (2002) ：Design basis for civil and architectural engineering structures.
Japan Society of Civil Engineers (2002a) ：Standard Speciﬁcation for Concrete Structures, Structural Performance Veriﬁcation Volume.
Japan Society of Civil Engineers (2002b) ：Guidelines for Performance Veriﬁcation of Hybrid Structures (tentative).
Japan Society of Civil Engineers (2003a) ：Towards establishment of performance-based design system for steel
structures.
Japan Society of Civil Engineers (2003b) ：Comprehensive design codes (tentative) code PLATFORM ver.1.
ISO(1998) ：ISO2394 International Standard, General Principles on Reliability for Structures ．

19

Chapter 2 Actions
2.1 General(1) In the design of steel and composite structures, actions expected to act on a structure during
the construction period and during the design working life shall be determined according to
the required performance.
(2) Actions are all causes of deformation, displacement, constraint, and deterioration of a structure or structural member, as indicated below.
• Direct action: an assembly of concentrated or distributed mechanical forces acting ona structure.
• Indirect action: the cause of deformations imposed on the structure or constrained init.
• Environmental action: mechanical, physical, chemical, or biological action that may
cause deterioration of the materials constituting a structure.
(3) A load is deﬁned as an assembly of mechanical forces acting directly on a structure. These
forces are converted from actions through the analytical model. A load acts as an input
datum for design calculations yielding the stress resultant, stress, displacement, and so on.

【 Commentary 】(2) Actions are categorized as direct, indirect, or environmental according to the way in which
they inﬂuence a structure, as prescribed in Article 2.1 (2). But they may also be classed aspermanent, variable, or accidental according to their frequency of occurrence, duration, andpattern of ﬂuctuations and as static, dynamic, or repeating based on how the structure responds
to them. In this clause, actions are considered as direct, indirect, and environmental so as toclarify the diﬀerence between actions and loads. Other classiﬁcations of actions are consideredin Article 2.2 ”Kinds of Actions”.
(3) A load is deﬁned as an action in the form of forces acting directly on the structure. The relationship between action and load is explained in Fig.C2.1.1.

【 load 】
dead (fixed) load
live-load
impactwind loadsnow load
braking force andacceleration force
centrifugal force,【 action 】
effect of concrete creep and shrinkage
effect of temperature changes
effect of displacement of supports anddifferential settlement
effect of earthquake
effect of airborne salinity
effect of exhaust gases

Fig.C2.1.1 Conceptual diagram of relationship between action and load

20Standard Speciﬁcations for Steel and Composite Structures [Design]

2.2 Kinds of Actions(1) In the design of steel and composite structures, actions shall be properly determined incorrespondence with the veriﬁcation items and the relevant structural members.
(2) Actions are classiﬁed into three classes according to their characteristic occurrence frequency,
duration, and ﬂuctuation, as deﬁned below.
• Permanent action: action that is likely to act continuously throughout a given reference
period and for which variations in magnitude with time are small compared with themean value.
• Variable action: action for which the variation in magnitude with time is neither negligible in relation to the mean value nor monotonic.
• Accidental action: action that is unlikely to occur with a signiﬁcant value on a structure
over a given reference period and which may cause a serious damage to a structure if
it does happen to occur.
(3) Actions are classiﬁed into three classes according to the characteristics response of a structure
to them, as deﬁned below.
• Static action: action that does not cause signiﬁcant acceleration of the structure or
structural members.
• Dynamic action: action that may cause impulse acceleration or other signiﬁcant acceleration of the structure or structural members.
• Repeating action: action that may result in fatigue damage.

【 Commentary 】

The relationships between actions prescribed in Articles 2.2 (2) and (3) are shown in Table C2.2.1.
These relationships may be reconsidered if suﬃcient investigation is carried out, because an action’s
frequency of occurrence and duration might be expected to depend on the type of structure, conditions
at the location of the structure, and the structure’s surroundings. Action values are prescribed in
Article 2.4. Environmental actions that may lead to deterioration of materials constituting a structure
are summarized in list form in Table C2.2.2.

2.3 Combinations of Actions
In a typical case of structural design, the combinations of actions shown in Table 2.3.1 shallbe considered. In a case where an unusual combination of actions might be anticipated, action
combinations aside from those listed in Table 2.3.1 may be taken into consideration according to
the judgment of the responsible chief engineer.
Table 2.3.1
Required performance
SafetyServiceability
Durability【 Commentary 】

Combinations of actions

Combination of actions
Permanent actions+Primary variable actions+Subsidiary variable actions
Permanent actions+Accidental actions+Subsidiary variable actions
Permanent actions+Variable actions
Permanent actions+Variable actions

21

Chapter 2 Actions

Table C2.2.1 Kinds of action

permanent
actionvariable
actionaccidental
actiondirect action(1) dead load(2) earth pressure(3) prestressing force

indirect action(18) eﬀect of concreteshrinkage(19) eﬀect of concrete creep(4) live load (static, dynamic,
repeating)a) moving load of vehiclesb) railway loadingc) crowd loading(5) impact load (static, dynamic)(6) ﬂowing water pressure(static, dynamic)(7) hydrostatic pressure(8) buoyancy or uplift (static)(9) wind load (static, dynamic)(10) snow load (static)(11) braking force, acceleration
force (static, dynamic)(12) centrifugal force (static)(13) longitudinal load imposedby long welded rail (static)(14) lateral train load andtransverse wheel thrust (static)(15) wave pressure (static, dynamic)(16) erection-related force(17) collision force(20) eﬀect of temperaturechanges (static)(21) eﬀect of displacementof supports and diﬀerential
settlement (static)(22) eﬀect of earthquake

environmental action(23) eﬀect of airborne salinity(24) eﬀect of exhaust gases(25) eﬀect of carbon dioxide concentration(26) eﬀect of acid concentration(27) eﬀect of drying and wetting(28) eﬀect of sunshine(29) eﬀect of freezing(30) eﬀect of ﬁreTable C2.2.2 Environmental actions that may cause deteriorationof materials constituting a structure
deterioration phenomenon

corrosion
corrosionmaterial deterioration

corrosion of reinforcement bars
caused by percolating salinity
alkali-aggregate
reaction∗1

weather
conditions
temperature,humidity,
rainfall, windtemperature,humidity,
rainfall, windtemperature,humiditysalinity supply
airborne salinity,
seawater splashing,de-icing agentsairborne salinity,
seawater splashing,de-icing agentsairborne salinity,
seawater splashing,de-icing agents

moisture
supplyrainfall,seawatersplashingrainfallotherssulfur oxide
supplyalkali supply

excesstemperature,moisture,temperarainfall
ture change,sunshine*1：As environmental action cannot be controlled, it is usual to control the total alkali content
of the materials used in construction.
freezing

22Standard Speciﬁcations for Steel and Composite Structures [Design]

The value of each of the actions described in Table 2.3.1, consisting of permanent actions, primaryvariable actions, subsidiary variable actions, and accidental actions, is speciﬁed in Article 2.4.
A primary variable action is one or a set of variable actions considered the primary inﬂuencewhen combined loading is taken into account during performance veriﬁcation work. A subsidiary(secondary) variable action is an action considered secondary among the variable actions; it is added
to the combination of primary variable actions and accidental actions. Accordingly, the probabilityof a subsidiary variable action of the design value occurring should be greater than that of a primaryvariable action of the design value occurring, considering the probability of both variable actions
occurring simultaneously with their extreme values.
Under certain circumstances, particularly large design values have to be given to multiple variableactions or combined variable and accidental actions when combinations of actions are considered. In
this case, the engineer(s) in charge must determine the kind of actions to be combined and their design
values.
In structural analysis, combinations of actions are generally treated by summing up the loads
resulting from all actions, the design values of which are set suﬃciently on the safe side. This approach
may not give rise to problems, because the calculation gives a result that is safer than the actuallydesigned structure. However, care must be taken not to accept this as a universal truth [JSCE (1998)].
Rather, where combinations of actions are considered, the inherent characteristics of each action must
be carefully considered. In a case where static and dynamic actions are combined, for example, careful
discussion is necessary as to whether any structural deformation caused by the combined action isaccurately simulated or not. It is important to recognize that the stress resultant and deformation
caused by the combination of a static action with a dynamic one are not simple sums but in fact
nonlinear functions of the stress resultant and deformation caused by each action.

2.4 Action Values
2.4.1 General(1) The values of permanent actions and primary variable actions that are considered whenverifying safety against structural failure or collapse may be statistical characteristic values
obtained as an a priori speciﬁed fractile of construction period and design lifetime largest or
smallest value probability distribution. The accidental action value may be taken to be thepreviously occurring largest value. The value of subsidiary variable action shall depend on
which action combination is taken into account.
(2) The action value considered when verifying serviceability shall be the value expected tobe observed frequently during the construction period and the design working life. Thisvalue shall be determined depending on the required performance and the relevant action
combination.
(3) The value of action considered when verifying durability shall be determined by taking into
account the variability of action during the design lifetime.
【 Commentary 】(1) In considering the limit state of a structure relating to safety against failure or collapse, thestructural state of interest is one where functionality and stability have been seriously damagedby failure, deformation, displacement, etc. Therefore, the action values to be adopted in verifying safety against failure or collapse must be those that are likely to have the most serious
inﬂuence on the structure during its construction and over its design working life. In general,the design values of permanent actions and primary variable actions are set at the maximal orChapter 2 Actions

23

minimal values for an action return period longer than the design working life. A statisticalcharacteristic value obtained from the lifetime maximal or minimal distribution of actions should
be adopted as the action value, although current statistical data are not necessarily adequate fordetermining the probability distribution. Here, the decision as to what percentage fractile value
is appropriate as the statistical characteristic value is left to the judgment of the design engineer. In general, 5∼10% excess probability (in the case of a distribution of maximal values) or
non-excess probability (in the case of minimal values) is considered appropriate. However, where
it is not reasonable to calculate this fractile because the available statistical data are insuﬃcientor data measurement accuracy is low, or where adoption of this fractile value is not desirable
because action variability is extreme (for example, action values relating to earth pressure), theexpected value of the lifetime maximal or minimal action distribution may be adopted instead.
As for accidental action values, the concept of the largest past value - as commonly used in theseismic design standards of Japan and the United States of America - is introduced here becausea usable and understandable determination method is required in situations where a statisticalestimation is impossible.
In general, it is rare to consider only one variable action in design. That is, the simultaneous
occurrence of multiple variable actions is commonly considered at the design stage. When thisis the case, the likelihood of all the variable actions taking their maximal or minimal values
simultaneously may not be high, so it is rational to make some adjustment for the combinedcase. Accordingly, variable actions are classiﬁed into primary and subsidiary ones, with thedesign value of the former taking their expected maximal or minimal values and the latter taking
values determined appropriately according to which action (primary variable or accidental) they
are combined with. The design value of a variable action treated as a subsidiary variable action
may be lower than one adopted as a primary action.
(2) An action with a value that is expected to be observed frequently, as is to be considered whenverifying serviceability, is one for which no limit state (such as yielding of a steel member,excessive cracking of concrete, harmful deformation of structure, etc.) is expected to be reachedas long as the action does not exceed this value. Such values should be determined mainly forpermanent and variable actions depending on the characteristics of the structure, the type ofaction, and the limit state under consideration.
(3) All of the permanent actions, variable actions, and accidental actions must be considered whenverifying durability. Steel corrosion and material deterioration of concrete members under environmental action and the loss of resistance caused by fatigue should be taken into account whenassessing durability. Action values are to be determined according to changes and ﬂuctuations
in environmental action over the design working life.

2.4.2 Dead load
(1) The dead load shall be the action caused by the weight of the structural elements andancillary facilities themselves.
(2) The characteristic value of dead load shall be calculated by reading oﬀ the dimensions ofstructural members precisely and by evaluating the unit weight of the structural materials
properly.
【 Commentary 】(1) The dead load is subdivided into two components: the ﬁxed dead load and the additional deadload.
(2) The characteristic value of the dead load is to be determined in consideration of the actual

24Standard Speciﬁcations for Steel and Composite Structures [Design]

weight of the structure and any variations in this weight. Table-commentary 2.4.1, which lists
the standard unit weight values for various structural materials, may be used to determine theaction value of the ﬁxed dead load. The action value for the additional dead load is to be
determined by taking account of any variations.
Table C2.4.1 Standard unit weight values for various structural materials
structural material

steel, cast steel, and steel
forging
cast ironaluminum
reinforced concrete
prestressed concrete
reinforced lightweight aggregate concrete(all aggregates are lightweight aggregates)

unit
weight(kN/m3 )
77.0
71.0
27.5
24.0∼24.5
24.5
18.0

structural material

concrete
cement mortar
wood
bitumen material
asphalt concrete pavement
lightweight aggregate concrete（ all aggregates are lightweight aggregates）

unit
weight(kN/m3 )22.5〜23.0
21.0
8.00
11.0
22.5
16.5

2.4.3 Earth pressure
Earth pressure shall be determined according to the required performance by considering thetype of structure, structural rigidity, and type of subsoil.
【 Commentary 】

Several formulas have been proposed for calculating earth pressure. It is important to select themost suitable of these in consideration of the behavior of the designed structure.

2.4.4 Prestressing force(1) In a case where prestress is to be introduced into the structure, both the prestressing force
immediately after the prestress is applied as well as the eﬀective prestressing force after
losses shall be considered in design and these values shall be determined according to therequired performance.
(2) If a statically indeterminate force is caused by prestress, it shall also be considered properly.
【 Commentary 】(1) The prestressing force immediately after the introduction of prestress should be calculated inconsideration of the tensile force acting at the end of the prestressing steel, the elastic deformationof the concrete, the friction between prestressing steel and sheath, and the total amount of set
at the anchorage.
The eﬀective prestressing force should be obtained taking account of the prestressing force
immediately after prestress introduction, concrete creep, concrete shrinkage, relaxation of prestressing steel, and the reinforcing bar restraint eﬀect.
(2) Redundant force generally arises because deformation of the structural member is restricted
during prestressing, but this is avoidable if a proper arrangement of prestressing steel is developed. The possibility of redundant force must be taken into consideration when calculating theChapter 2 Actions

25

distribution of stress over area.
If the timing of prestress introduction is staggered or if the degree of statical indeterminacychanges between the start and end of prestressing, the redundant force will vary as concrete creep
increases. This point must be taken into consideration at the design stage.
The tensile force of the prestressing steel varies as a result of concrete creep, concrete shrinkage, and relaxation of the prestressing steel. Each cross section may have a diﬀerent degree ofvariation. In general, the redundant force arising from the eﬀective prestressing force may be
calculated by multiplying the redundant force immediately after prestressing by the value obtained by averaging the tensile force eﬀectiveness coeﬃcient of each prestressing cable for eachcross section over the whole of the structural member.

2.4.5 Live load
The live load shall consist of the moving load of vehicles, railway loading, and sidewalk loading (including crowd loading). It shall be determined according to the required performance byconsidering the load variations.
【 Commentary 】

The characteristic value of live load may be determined by referring the design standards such as the
highway bridge speciﬁcations [Japan Road Association (2002a)] or the railway structure speciﬁcations[Railway Technical Research Institute (2000)], where the nominal value based on the legal authority
is adopted. When designing a structure for a highway where restrictions may be placed on vehicles
whose total weight or axle weight exceeds an a priori speciﬁed value, the speciﬁed value may be
reduced if necessary. Also available is a method of determining the characteristic value of live loadusing computer simulation results, where traﬃc ﬂow is modeled based on research into actual live loadconditions [Fujiwara, et al (1988) and (1989)], as long as the characteristic value can be estimated, forexample, in the case that the load-carrying capacity of an existing highway bridge is veriﬁed. However,loading methods in which the live load is a function of the number of lanes, as adopted in foreign
standards such as [BS5400 (1978)], [OHBC (1983)], and [AASHTO (1996)], are more suitable thanthose where the live load is given according to the eﬀective road width regardless of the number oflanes such as the ”L load” speciﬁed in [JHA (2002a)].
When verifying fatigue resistance, all of the variable actions acting on a structure over the design
working life must be considered and they must be determined taking account of an appropriate action
value and the corresponding equivalent repetition value. In verifying fatigue resistance for a highway
bridge, reference [JHA (2002c)] may be used.

2.4.6 Impact load
The stress imposed by the live load shall be incremented to account for impact eﬀects. The
dynamic inﬂuence of vehicles moving over the structure shall be considered as one kind of impact. The value of the impact load shall be determined according to the required performance inconsideration of the structure’s span, design characteristics, etc.
【 Commentary 】

The characteristic value of the impact load may be determined based on relevant standards, suchas [JHA (2002a)] in the case of a highway bridge design or [RTRI (2000)] in the case of a railway
bridge, that specify a standard value. In the case of highway bridges, for example, the impact load ismodeled by replacing its dynamic eﬀect with a static load obtained by multiplying the live load by an
impact coeﬃcient. On the other hand, in the case of railway bridges, impact load is determined taking

26Standard Speciﬁcations for Steel and Composite Structures [Design]account of the maximum train speed, the axle arrangement, the number of cars or wagons, the spanof the structural member, any non-linear behavior, the fundamental natural frequency, the damping
constant, the kind of response value required, the track and vehicle maintenance level, etc. using anappropriate numerical analysis method such as dynamic response analysis.

2.4.7 Flowing water pressure(1) The value of ﬂowing water pressure acting on a structure shall be determined according
to the required performance in consideration of the type of structure and the shape of thestructural members.
(2) When designing structures on which ﬂowing water may act, the dynamic inﬂuence of the
ﬂow water shall be taken into consideration.
【 Commentary 】(1) The characteristic value of ﬂowing water pressure, pw , can be deﬁned by Eq.(C2.4.1).
pw =where ，

pw
Cv
ρ
v
A

1
ρ Cv A v 2
2(C2.4.1)：characteristic value of ﬂowing water pressure：coeﬃcient of resistance depending on the cross-sectional shape of the structure：density of water ，1000 kg/m3：ﬂow velocity (m/s) determined in correspondence with the relevant limit state：projected area of structure in direction of ﬂow(m2 )The value of coeﬃcient of resistance (Cv ) can be set referring to [JSCE (2002a)], [JHA (2002a)],and [RTRI (2004)].
(2) In large sluices, such as a long sluice across a wide river or a Tainter gate used for the emergency
release of water from a dam, it has been reported that vibrations can be caused during discharge.
If such a phenomenon might be expected, the dynamic eﬀect of the ﬂowing water must be
considered.

2.4.8 Hydrostatic pressure
The value of hydrostatic pressure shall be determined according to the required performance byproperly taking into consideration ﬂuctuations in water level and the size of the structure.
【 Commentary 】

The characteristic value of hydrostatic pressure can be calculated using Eq.(C2.4.2). However, if
the hydraulic pressure acting on the below-ground part of the structure does not have a triangular
distribution as a result of the particular ground conditions, the this value may be reduced to a level
estimated from evidence such as ﬁeld measurements of pore water pressure, etc.
ph = w0 h(C2.4.2)
where ，

phw0h：characteristic value of hydrostatic pressure：unit weight of water (kN/m3 )：depth below surface of water (m)Where a bridge abutment is planned for a location where water level ﬂuctuations are particularly
large, a diﬀerence in water level may arise between the upstream and downstream sides of the abutment.
In such cases, the residual water pressure resulting from the diﬀerence in water level must be considered.

27

Chapter 2 Actions

2.4.9 Buoyancy or uplift(1) The value of buoyancy or uplift shall be determined according to the required performanceby properly taking into consideration the pore water and ﬂuctuations in water level.
(2) Buoyancy or uplift shall be assumed to act in the vertical direction and the severest case of
uplift shall be assumed.
【 Commentary 】(1) Buoyancy is the load caused by an upward hydrostatic pressure on the bottom of a structure asa result of pore water in the ground or between the ground and the structure. Uplift is the loadcaused by a water level diﬀerence between the upstream and downstream sides of a structure orby a temporary increase in water level around a structure caused by wind, waves, etc.
(2) Reference [JRA (2002a)] gives example cases in which buoyancy and uplift should and should
not be taken into consideration. Also provided in this reference is a methodology for considering
the buoyancy or uplift expected to act on a structure according to water seepage over time andthe placement conditions of the structure. For example, the application methodology where thebuoyancy or uplift shall be determined on the safer side in the structural design and this action
shall be considered in case of falling down and sliding and not considered in case of settlement
when verifying the stability of a structure is explained.

2.4.10 Wind load
(1) The value of wind load shall be determined according to the required performance by properly taking into consideration the wind characteristics of the construction site, the type ofstructure, the shape of structural members, etc.
(2) Flexible structures or structural members, in particular, shall be designed in considerationof dynamic deformation or stress resulting from wind because they may be considerably
inﬂuenced by wind vibration.
【 Commentary 】(1) The possible eﬀects of wind on a structure are the static wind load, gust response, divergent
vibration, vortex-excited vibration, etc. These wind eﬀects must be evaluated appropriately at
the design stage because they may result in deformation and/or vibration of a structure.
The characteristic value of wind load is to be determined by estimating the wind velocity foreach relevant limit state in consideration of measured wind speed data, the design working lifeof the structure, and the return period of speciﬁc wind velocity levels. In general, wind velocity
is calculated from the mean value of wind speed over a period of ten minutes at a height of ten
meters from the ground or sea surface; this ﬁgure is modiﬁed for altitude, horizontal and verticallength of structure, eﬀect of ground surface roughness, eﬀects of surrounding topography andgeographical features on intercept and convergence, eﬀect of temporal and spatial ﬂuctuations
in wind speed, etc. The value of drag coeﬃcient is determined according to the cross-sectional
shape of the structural member.
The characteristic value, W, of wind load can be obtained using Eq.(C2.4.3).
W =where ，WCρ1
ρ C A v2 G
2

(C2.4.3)：characteristic value of wind load：drag coeﬃcient depending on cross-sectional shape of structural member：density of air, taken as 1.23kg/m3

28Standard Speciﬁcations for Steel and Composite Structures [Design]v
AG：design wind speed determined (m/s) for each limit state：projected cross-sectional area of structural member (m2 )：gust response coeﬃcient.

The handling of structural members on the windward and leeward with respect to determining
projected cross-sectional area, A, and drag coeﬃcient, C, is provided in [JSCE (2002a)], [JRA(2002a)], and [RTRI (2004)]. Further, a suitable increment ratio, known as the gust response,
is introduced to take account of deformation and/or vibration caused by ﬂuctuating drag whencalculating the characteristic value of wind load in [JRA (2002a)] and [JRA (2005)]. The valueof the gust response coeﬃcient, G, depends on only the intensity of wind turbulence in the caseof normal structures; it increases with decreasing altitude and with increasing ground surface
roughness. A suitable value of gust response coeﬃcient may be obtained by referring to [JRA(2002a)] and [JRA (2005)].
References [JSCE (2002a)], [JRA (2002a)], and [RTRI (2004)] also provide for the wind load
acting on bridges with noise barriers, existing bridges in parallel, and under-structures. Also given
is a loading method for wind load. It should be noted that the change in cross-sectional shapecaused by accumulated snow can sometimes inﬂuence the behavior of a structure signiﬁcantly.
(2) Occasionally, a structure may suﬀer from amplitude-limited vibration caused by light-windinduced vortexes (vortex-induced vibration) or from vibration of rapidly rising amplitude caused
by aerodynamic forces resulting from the vibration itself at high wind speeds and excites thevibration of structure (divergent vibration). Dynamic wind eﬀects arising from vortex-induced
vibration, divergent vibration, etc. must be considered in the design of ﬂexural bridges such assuspension and cable-stayed bridges and of low-rigidity members such as the hangars in an archbridge.
The wind velocity at which vortex-induced vibration, divergent vibration, and so on will
occur and the likely vibration amplitude must be estimated appropriately in consideration ofcharacteristics of winds at the construction site and the structural characteristics of the designed
structure. The structure can be judged as satisfying the performance requirements if the windvelocity at which such vibrations occur is considerably higher than the maximum wind expectedduring the design working life or if the resulting vibration does not critically aﬀect the safety andserviceability of the structure. The determination of the characteristic value of dynamic windload for medium- and short-span bridges may be according to reference [JRA (2005)], while thatfor long-span bridges may be carried out as in [HSBA (2001)].
Reference [JRA (2005)], which gives the speciﬁcations for short and medium-span bridges, isalso recommended for its presentation of recent research results relating to the following areas:
1) design concepts, actual examples of vibration control countermeasures, application examples, and matters for attention with respect to wind-induced cable vibrations;2) estimation formula for the dynamic response of steel bridges with few (mainly two) I-shaped
plate girders, based on actual examples, from the viewpoint of reducing erection work andconstruction costs, where particular care is needed because, as the span of such bridges
increases and the natural frequency for torsional vibration falls below that of steel boxgirder bridges, tortional vortex-induced vibration can arise;3) estimation formula for the structural damping of bridges with rubber bearings.

2.4.11 Snow load
In the design of structures that are constructed in areas that receive snowfall, the value of snow
load shall be determined according to the required performance by taking into consideration the29

Chapter 2 Actions

snowfall characteristics and maintenance procedures.
【 Commentary 】

The depth of snow on a structure depends not only on its location but also on whether snow removal
is carried out, the characteristic value of snow load should preferably be determined in considerationof local snowfall characteristics, maintenance procedures, and the design working life of the structureusing actual records of snowfall.
There are two main categories of method for calculating the value of snow load. One assumes
that vehicles continue to pass over the fully compacted snow, while the other takes account only of
the snowfall because passage of vehicles becomes impossible. In the former, a value of 1 kN/m2 forcompacted snow up to 150 mm in thickness is speciﬁed in, for example, reference [JRA (2002a)]. In
the latter case, the characteristic value of snow load is given by Eq.(C2.4.4) where the design unit
weight of snow, (ws ), is determined referring [JRA (2002a)] or [RTRI (2004)].
SW = ws z I
where ，

SW
wsz
I

(C2.4.4)：characteristic value of snow load：design unit weight of snow (N/m3 )：design snowfall depth on surface(m)：coeﬃcient due to inclination of surface

I = 1 + (30 − θ)/30
where ，I = 1.0 for θ ≤ 30 ° and I = 0 for θ ≥ 60 °θ：inclination of surface subjected to snowfall（ °）2.4.12 Braking force and acceleration force
Braking forces and acceleration forces act on a structure when vehicles and trains slow downor accelerate. The values of these forces are determined according to the required performanceby properly taking into consideration the types of vehicles or trains and the characteristics of thestructure.
【 Commentary 】

In the case of structures that carry trains, braking and acceleration forces must be considered in
the design. Particularly careful investigation of these forces is necessary in the case of extremely light
structures that carry trains. Speciﬁcations such as [JRA (2002a)] and [RTRI (2000)], where standard
values for these two forces are prescribed, should preferably be referred to in the design of highway
bridges and railway bridges.

2.4.13 Centrifugal force
A structure carrying curved tracks shall be designed to withstand centrifugal force. The valueof centrifugal force shall be determined according to the required performance by properly taking
into consideration the type of train and the characteristics of the structure.
【 Commentary 】

Speciﬁcations such as [JRA (2002a)] and [RTRI (2000)] give standard values for centrifugal force
which should be used in the design of highway bridges or combined railway-highway bridges.

30Standard Speciﬁcations for Steel and Composite Structures [Design]

2.4.14 Longitudinal load imposed by long welded rail
Where long welded rails are laid on a railway bridge, the mutual force resulting from diﬀerences
between the behavior of the rails and the bridge under temperature changes shall be treated as alongitudinal load imposed by the long rails. The value of this longitudinal load shall be determinedaccording to the required performance by considering the type of bridge, its length, the track type,the arrangement of bearings, etc.
【 Commentary 】

Where a railway bridge carries long continuously welded rails, a force arises from the diﬀerential
expansion of rails and the bridge under temperature changes. This force acts on both rail and bridge
through the rail fastenings. In general, this force is treated as a longitudinal load in the design ofrailway bridges. The characteristic value of longitudinal load imposed by continuously welded rail may
be determined with reference to the speciﬁcations for railway bridges [RTRI (2000)], where values areprovided.

2.4.15 Lateral train load and transverse wheel thrust
A train crossing a bridge imposes a lateral load while the wheels cause a transverse thrust. The
values of these forces shall be determined properly according to the required performance.
【 Commentary 】

The lateral train load is the transverse force resulting from oscillations of railway vehicles, suchas yawing, etc. Transverse wheel thrust is the force produced by the wheels if a railway vehicle carenters a section of track with an angle of incidence. The characteristic values of these two loads may
be determined by reference to the speciﬁcations for railway bridges [RTRI (2000)], where static values
determined based on available experimental evidence are provided. In theory, however, the dynamic
eﬀects of these two loads should be taken into account.
2.4.16 Wave pressure
The value of wave pressure shall be properly determined according to the required performanceby considering the type of structure, its shape, the water depth, and the wave characteristics.
【 Commentary 】

The characteristics of wave pressure depend on the type of structure they are acting on. For
example, the wave pressure is diﬀerent on a continuous vertical wall structure, such as a breakwater,
than on an isolated vertical structure, such as a bridge pier. The characteristics also depend on water
depth and the wave properties. These factors must be properly considered at the design stage.

2.4.17 Erection-related force
Structures are generally designed in consideration of the structural system in place at completion, but this may diﬀer from the system of load support during erection. The forces arisingduring erection shall be properly taken into consideration according to structural conditions during
erection and erection procedure used.
【 Commentary 】

Suﬃcient safety must be ensured at all erection steps used during construction. Structures areChapter 2 Actions

31

generally designed in consideration of the structural system in place at completion. However, this may
diﬀer from the system of load support and the loading conditions during erection, and the directionof loading may even be reversed in certain cases. Accordingly, in the design of structures as alreadydescribed, it is necessary to verify and conﬁrm structural safety for each erection step.
The vertical force (self weight of structural members), wind load, eﬀect of earthquake, snow load,
eﬀect of temperature changes, horizontal force, impulsive load, frictional force, disproportional load,
expected special load, and so on are among the erection-related forces that must be considered. The
actual selection of loads to be considered as erection-related forces should preferably be made inconsideration of the type of structure, the erection procedure, the season during which erection takes
place, the erection period, etc. Earth pressure, wave pressure, buoyancy, collision forces, and otherspecial loads should be considered as required.

2.4.18 Collision force
A collision force might be imposed by a user of the structure, as in the case of a vehicle collision,
by a third party as in the case of a ship impact, or through a natural phenomenon such as impact
by driftwood, etc. The anticipated value of the collision force shall be determined according to
the required performance in consideration of the location of the structure.
【 Commentary 】

Collision forces may be imposed on the structure by vehicles, ships and other water craft, airplanes,
driftwood, falling rocks, and others. Whether each type of collision force is considered in the design andthe selection of a suitable value should be determined in consideration of the location of the structure
and the likelihood of each type of collision. If the collision force is expected to be considerably large,
consideration might be given to the construction of a secondary protective structure.
There are two methods of determining the characteristic value of collision force. One is to deﬁne
the velocity, mass, size, and incidence angle of the body that is in collision with the structure, taking
account of any special modes at the time of collision. The other is to replace the dynamic collisionenergy with a static force based on consideration of the mechanical equivalence property. Characteristic
values of collision forces acting against the guard rail and ﬂoor slab may be determined with reference
to the speciﬁcations [JRA (2002a)] and [JRA (2004)].

2.4.19 Concrete shrinkage(1) The characteristic value of concrete shrinkage shall be determined in consideration of thematerials used, environmental conditions, the size of structural members, etc.
(2) In the design of statically indeterminate structures such as rigid frames and arches, concreteshrinkage may have a uniform eﬀect on the cross section of the structure.
【 Commentary 】(1) Total concrete shrinkage comprises drying shrinkage, self shrinkage, and carbonation shrinkage.
It is inﬂuenced by the temperature and humidity to which the structure is exposed, the shapeand size of structural members, the concrete mix proportion, the properties of the aggregates, thetype of cement, the degree of concrete compaction, the concrete curing conditions, and various
other factors. Therefore, the value of shrinkage strain used in the veriﬁcation must be determinedin consideration of these factors.
Where the total shrinkage strain and the rate of shrinkage progress in normal concrete with acompression strength of less than 55 N/mm2 2 (or 70 N/mm2 2 in the case of high-strength concrete32Standard Speciﬁcations for Steel and Composite Structures [Design]with a low water-cement ratio) are obtained from the surrounding temperature and member size,
which are the factors that have a strong eﬀect on shrinkage, reference [JSCE (2002a)] may be
used.
The actual concrete mix proportion is generally not yet known at the design stage, so thevalues of shrinkage strain for normal concrete and lightweight aggregate concrete given in Tablecommentary 2.4.2 may be applied in general.
Table C2.4.2 Shrinkage strain of concrete (×10−6 )environmental
age of concrete∗conditions
up to 3 days 4×7 days 28 days 3 months
indoor
400
350
230
200
outdoor
730
620
380
260
* age from start of drying as considered in design

1 year120
130(2) The value of concrete shrinkage strain used when calculating the redundant force based on elastic
theory may be taken as 150×10 −6 in general, although the eﬀect of concrete creep should beconsidered.

2.4.20 Eﬀect of concrete creep(1) The characteristic value of concrete creep shall be determined in consideration of the materials used, environmental conditions, structural member size, concrete age at application ofstress, etc.
(2) In the design of statically indeterminate structures such as rigid frames and archs, concrete
creep may have a uniform eﬀect on the cross section of the structure.
【 Commentary 】(1) The creep strain of concrete may be calculated using Eq.(C2.4.5) under the assumption that itis proportional to the elastic strain by the stress arising.
εcc =
where ，

εcc
φ

σct
Ect


φ σct
Ect

(2.4.5)： compressive creep strain of concrete：creep coeﬃcient：compressive stress arising：Young’s modulus at age of loading

However, the application of Equation (commentary 2.4.5) is limited to cases where the compressive stress of the concrete is no more than about 40% of its compressive strength. Where thisis not so, it is not suitable to consider creep strain as proportional to the elastic strain causedby the stress arising. The creep coeﬃcient depends on the temperature and humidity to which
the structure is exposed, the shape and size of structural members, the concrete mix proportion,
the age of the concrete at loading, the properties of the aggregates, the type of cement, theconcrete compaction, the concrete curing conditions, and various other factors. Therefore, thedesign value of creep coeﬃcient should be determined by referring to experimental results, ﬁeld
measurements of existing structures, etc. In a case where the creep coeﬃcient of normal concretewith a compression strength of up to 55 N/mm2 (70 N/mm2 in the case of high-strength concretewith a low water-cement ratio) is to be obtained without experiment, reference [JSCE (2002a)]
may be used.
The values of creep coeﬃcient for prestressed concrete shown in Table C2.4.3 or Table C2.4.4

Chapter 2 Actions

33

may be applied in general. If the creep strain is obtained using Table C2.4.3 or Table C2.4.4 andEq.(C2.4.5), the value of Ect should be that at the age of loading.
Table C2.4.3 Creep coeﬃcient for normal concrete
environmental
conditions
indooroutdoorage of concrete at prestressing or loading
4×7 days 14 days 28 days 3 months 1 year
2.7
1.7
1.5
1.3
1.1
2.4
1.7
1.5
1.3
1.1

Table C2.4.4 Creep coeﬃcient for lightweight aggregate concrete
environmental
conditions
indooroutdoorage of concrete at prestressing or loading
4×7 days 14 days 28 days 3 months
1 year
2.0
1.3
1.1
1.0
0.8
1.8
1.3
1.1
1.0
0.8

2.4.21 Eﬀect of temperature changes(1) The eﬀect of temperature changes shall be determined according to the required performanceby taking into consideration the type of structure, environmental conditions, the size ofstructural members, etc.
(2) The characteristic value of temperature change shall be determined as a rise and fall intemperature from an a priori speciﬁed temperature. In the design of statically indeterminate structures, temperature change may have a uniform eﬀect on the cross section of thestructure.
(3) In the case of a structure in which the temperature diﬀerence between structural members
or between portions of the structure is not negligible, such diﬀerences shall be taken into
account.
(4) In order to ensure a safe-side design, the characteristic value of temperature change whencalculating the structure’s stress resultant shall preferably be diﬀerent from that used indetermining the deformation of the structure.
【 Commentary 】】(1) Changes in temperature cause structural deformations such as shrinkage, expansion, warping,etc. Because the total amount of deformation depends on how much the temperature changes,
a reference temperature and temperature variation range should be determined in considerationof the type of structure, environmental conditions at the construction site, the properties ofthe materials used, the size of members, and so on. Design values relating to the temperature
variation range and temperature distribution may be determined from the actual situation if
good estimates are available for these two values. These values depend on the many factors
noted above as well as on which actions are considered as load combinations.
(2) In the design of statically indeterminate structures such as rigid frames and arches, it may
be assumed that temperature changes occur uniformly over the cross section of the structure.
The design value of reference temperature should preferably be +20 ℃ in general or +10 ℃ in
cold regions. The design value of temperature variation range, under the assumption that thevariations occur uniformly over the whole of the structure, may be determined as follows:
1) the range of temperature variations for steel structures is from –10 ℃ to +50 ℃, or from
–30 ℃ to +50 ℃ in cold regions;2) the range of temperature variations for concrete structures must be determined in consideration of the diﬀerence between the reference temperature and the average air temperature

34Standard Speciﬁcations for Steel and Composite Structures [Design]at the construction site. In general, the value should be 15 ℃ while it should be ±10 ℃ if
the minimal size of the cross section is greater than or equal to 700 [mm] because in thiscase the eﬀect of temperature variations is not serious;
3) the eﬀect of temperature variations for a structure in the water or under the ground may
be negligible.
(3) If temperature changes give rise to variations in temperature, and resulting diﬀerential expansion
or shrinkage, between two structural members or between diﬀerent two parts of one member, theeﬀect of this must be considered. The design value of temperature diﬀerential may be determined
as follows:
1) the relative temperature diﬀerential for steel structures is 15 ℃ ;2) the relative temperature diﬀerential between a concrete ﬂoor slab and a steel girder in thedesign of a steel girder bridge with a concrete ﬂoor slab is 10 ℃, with the temperature
distribution over each member assumed to be uniform;3) the relative temperature diﬀerential for concrete structures at the point of the maximal valueof redundant force is 15 ℃ in the Chubu region of Japan (inland areas and the Hokuriku
district) and in the northern part of the Tohoku district, while it is ±12.5 ℃ in other districts.
In this case, the minimal size of a hollow cross section, such as a box-shape section, should bedetermined without any deduction of the size of the portion completely shut down from theoutside air; the relative temperature diﬀerential between the ﬂoor slab and other structuralmembers is 5 ℃ and the temperature distribution in each is considered uniform;4) because the cracks caused by annual temperature changes open and close, the characteristic
value of temperature change for estimating cracks in assessing durability may be reduced
from the value speciﬁed in 3) above where the maximal redundant force is considered; ingeneral, a 20% reduction is allowed;
5) structures such as ﬂoor slabs subject to high temperatures, chimneys, and tanks storing
liquids at high or low temperatures have large temperature diﬀerentials between surfaces.
In such cases, the internal stress resulting from temperature changes must be taken into
account because the assumption of uniform temperature change over the cross section is notrealistic.
(4) the range of temperature variation used to calculate movements of bearings and expansion joints
in the design of bridge may in general be taken from Table C2.4.5.
Table C2.4.5 Range of temperature variation for the calculationof bearing and expansion joint movement in bridge design
type of bridge
reinforced concrete bridge
prestressed concrete bridge
steel bridge (deck bridge)
steel bridge (through bridgeand steel plate deck bridge )temperature change
normal temperaturescold regions–5 ℃ ∼+35 ℃–15 ℃ ∼+35 ℃–10 ℃ ∼+40 ℃–10 ℃ ∼+50 ℃–20 ℃ ∼+40 ℃–20 ℃ ∼+40 ℃

2.4.22 Eﬀects of displacement of supports and diﬀerential settlement(1) Where displacement of a structure’s supports and/or diﬀerential settlement is anticipatedand if the eﬀects of such movement on the structure might be signiﬁcant, their eﬀects shall be
determined according to the required performance in consideration of the type of structureand subsoil conditions.

Chapter 2 Actions

35(2) The characteristic values of displacement of a structure’s supports and/or diﬀerential settlement shall be determined carefully as they may have a considerable eﬀect on the size andshape of structural members.
【 Commentary 】(1) During the Kojaeri earthquake in Turkey and the Cheche earthquake in Taiwan in 1999, bridge
girders collapsed and a dam body failed after displacements of 5-10 meters occurred at faults.
Where a fault is thought to be present under a designed structure, the probability of a displacement occurring during the design working life and its magnitude should preferably be estimatedat the design stage. In the design of a bridge, however, it is very diﬃcult to cope well withlarge fault displacements, so it is important to secure good redundancy in the road network, toestablish an early recovery plan, and to develop earthquake-prooﬁng techniques as well as toclarify the performance requirements.

2.4.23 Eﬀect of earthquake(1) Earthquake motion and all actions resulting from earthquake motion shall be considered in
the seismic design of a structure.
(2) In taking account of the direction of earthquake motion, it is preferable that two perpendicular directions on the horizontal plane be considered not independently rather than simultaneously. If necessary, earthquake motion in the vertical direction shall be consideredaccording to the dynamic characteristics of the structure.
(3) Two classes of earthquake motion shall be used in veriﬁcation, as follows.

1 Level 1 earthquake motion that has a relatively high probability of occurring during
the working life of the structure.

2 Level 2 earthquake motion that is strong and has a relatively low probability of occurring
during the working life of the structure.
(4) The worst-case eﬀect of earthquake motion on the structure shall be determined by considering seismicity around the site of construction, characteristics of the hypocenter andpropagation of earthquake motion, ampliﬁcation characteristics depending on subsoil conditions at the site, etc.
(5) Generally, a time-history acceleration wave of earthquake motion shall be used for veriﬁcation.
【 Commentary 】(1) The eﬀects of earthquake on a structure are generally considered to be the following:
1 inertial forces caused by structural masses and attached masses
2 dynamic interaction between structure and soil
3 hydrodynamic pressure during earthquake
4 earthquake-induced ground deformation, such as liquefaction of soil and resulting ground
ﬂows
In considering the eﬀects of earthquake at the design stage, the type of structure and its
loading conditions, the surrounding environment, and other factors determine which of theseeﬀects should be taken into account.
Both the mass of the structure itself and the mass of any attached structures should beconsidered as contributing to the inertial force under earthquake motion. In general, the massesof permanent actions and subsidiary actions may be considered under the assumption that themass of attachment bodies causes the inertia force along with the earthquake.

36Standard Speciﬁcations for Steel and Composite Structures [Design]

Dynamic interactions between structure and soil arise because of a relative diﬀerence in dynamic response characteristics between the two. These dynamic interactions need to be taken into
account in the case of abutments, retaining walls, underground structures, foundation structures
such as piles and caissons, and similar.
In the design of structures that hold liquids, such as storage tanks, and those that standin water, such as bridge piers, the hydrodynamic pressures arising from both the added massof the stored liquid and its vibration must be taken into account, as these act on a structureduring earthquake. o Countermeasures against soil liquefaction are the basis of the seismic
design process of a structure. However, the eﬀect of soil liquefaction on the seismic resistance ofa structure must also be fully considered at the design stage if countermeasures are expected to
be technically diﬃcult or particularly uneconomical. Where the ground surface is sloping or if
the pressure on the structure is always unsymmetrical, then ground ﬂows caused by liquefaction
must be considered as they might occur during an earthquake.
(2) Horizontal earthquake motion alone may, in general, be taken into account in verifying seismic
performance because it is the dominant earthquake eﬀect on a structure. Although horizontal
earthquake motion can act on the structure in any random direction, veriﬁcation may be carriedout in two independent orthogonal directions. However, in the design of curved-in-plane bridges,
structures in which torsion arises, and columns on which largely eccentric axial forces act, theinﬂuence of earthquake motion from multiple directions should ideally be considered, as the
structure might show multi-axial response even for earthquake motion from one direction.
Veriﬁcation against vertical earthquake motion must be carried out if the eﬀect of verticalmotion on the seismic resistance of the structure, which depends on the type, shape, and rigidity
distribution of the structure, is not negligible.
(3) Two classes of earthquake motion must be used to verify seismic performance, preferably considering the characteristics of earthquake motions, as follows:
Level 1 earthquake motion, which has a relatively high probability of occurring during theworking life of the structure.
Level 2 earthquake motion, which is a strong motion with a relatively low probability ofoccurring during the working life of the structure [JSCE Research Subcommittee for Level 2
earthquake motion (2000)].
The intensity of each of these motions may be determined by specifying a return period basedon the working life of the structure. In references [JSCE (2001)] and [JSCE (2002a)], the return
period for Level 1 earthquake motion is speciﬁed as 50 years. On the other hand, the return
periods of Level 2 earthquake motion, deﬁned as Typeor Type II as below, may be speciﬁed
as 100 years and 1000 years, respectively. The latter is speciﬁed in order to consider extremely
strong earthquakes.
1 Type I earthquake motion: earthquake motion caused by a large-scale interplate earthquakejust oﬀshore
2 Type II earthquake motion: earthquake motion caused by the shifting of an active fault inthe epicentral area or nearby(4) The actual earthquake motion used for veriﬁcation should take into account the seismicity inthe vicinity of the construction site, the characteristics of the hypocenter, the propagation of theearthquake motion, the ampliﬁcation characteristics, etc. However, it is very diﬃcult to estimate
all of these factors accurately and in fact some of them are at present still very uncertain, so
earthquake motion for veriﬁcation may in general be established by taking into account measured
earthquake motions and the failure mechanism of the earth’s crust in the epicentral area.
(5) Generally, a time-history acceleration wave should be used to represent earthquake motion in
the veriﬁcation, because the dynamic response of a structure to Level 2 earthquake motion isChapter 2 Actions

37

analyzed using nonlinear time-history analysis. The eﬀects of earthquake on the structure must
be expressed in suitable form according to the analysis method adopted, such as the static
structural analysis method, the response spectrum method, etc.

2.4.24 Eﬀect of airborne salinity
If required performance is determined in consideration of airborne salinity, the worst-case eﬀectover the structure’s working life shall be assumed by considering the site location, the materials
used, etc.
【 Commentary 】

The amount of salt in the air determines the selection of steel products and rust protection methods
as well as the cover thickness for a ﬂoor slab and felloe guard concrete and the method of protecting reinforcing bars from rust. Airborne salinity should preferably be determined from ﬁeld measurements atthe construction site because it depends on region, topography, distance from the shore, etc. Reference[PWRI, SPC and JBCA (1993)] may be used to obtain a value if ﬁeld measurements are impossible.

2.4.25 Eﬀect of exhaust gases
In designing a structure located where traﬃc jams are common, the eﬀect of exhaust gases shallbe considered by taking into account traﬃc ﬂow volumes and transportation system management.
【 Commentary 】

Concrete structures such as those that form the Metropolitan Expressway in Tokyo are exposed tosevere environmental conditions because of the presence of exhaust gases. Test surveys and chemical
testing on concrete bridge components exposed to exhaust gases for more than 30 years have shownthat the concrete neutralization depth relates to the amount of carbon adhered to the surface. It has
been also been revealed that nitrogen and sulfur oxides contained in exhaust gases further promote
concrete deterioration. This poses a particular problem for poured concrete expressway walls, forwhich it is diﬃcult to guarantee compaction quality during construction because of their large height
to breadth ratio.
In designing road structures for locations where traﬃc jams are common, the cover thickness ofconcrete members expected to suﬀer deterioration because of exhaust gases should ideally be ensured
by taking into account the design working life and maintenance procedures.

2.4.26 Eﬀect of carbon dioxide concentration
If necessary, the eﬀect of carbon dioxide (CO2 ) concentration shall be considered as it might
aﬀect the neutralization of concrete.
【 Commentary 】

It is known that carbon dioxide (CO2 ) inﬂuences the neutralization of a concrete structure. The
progress of neutralization has been generally assumed, on the basis of experiments and observations,√to follow the t law with elapsed time (t); that is, a parabolic law. Accelerated tests with a high set
value of CO2 concentration have also shown adherence to this parabolic law. What this means is that,
if CO2 diﬀusion into concrete follows Fuck’s ﬁrst law, the neutralization depth remains proportional
to the square root of elapsed time and is also proportional to the square root of the diﬀerence in CO2
density between the surface and the interior of the concrete.
Since the latter half of the 20th century, the CO2 concentration of the air has tended to increase38Standard Speciﬁcations for Steel and Composite Structures [Design]annually, although seasonal changes are also observed. Further, it is expected that the synergistic
eﬀect of this trend and air temperature rises driven by global warming might result in accelerating
CO2 concentrations in the latter half of the 21st century. The value of carbon dioxide concentration
used to estimate and evaluate durability should be determined by considering recent research thatshows the neutralization rate of concrete increasing step-wise if the CO2 concentration does so.
According to the current speciﬁcations [JSCE (2002b)], no concrete neutralization problems are
expected to occur for 100 years or more if concrete is suitably mixed with normal portland cement
and a water-to-cement ratio of less than 50% as long as the cover thickness is greater than 30mm.
However, this example assumes current CO2 concentrations.

2.4.27 Eﬀect of acid concentration
The worst-case eﬀect of acid concentration on the structure over its design working life shall be
determined by considering the site location, materials used, etc.

【 Commentary 】

Acid-induced chemical corrosion is rarely a problem for steel structures in a normal environment.
However, the eﬀect of acid concentration should be considered as required if ﬁeld measurements of acidconcentration indicate a need, particularly if the structure is situated in an unusual environment suchas in a hot spring area or in the drainage basin of an acid river.

2.4.28 Eﬀect of drying and wetting
The eﬀect of repeated drying and wetting shall be considered in the case that a structure is
subject to extremely frequent dry-wet cycles, since cracks leading to deterioration of concrete
members may result.

【 Commentary 】

According to the literature [Kato, et al. (1987)], water absorption and dehydration in the range
of 6% and expansion and contraction of ±300×10 −6 can result from repeated drying and wetting of aconcrete member. Therefore, the eﬀect of repeated drying and wetting should be considered in cases
where a structure is subject to extremely frequent dry-wet cycles. If a waterprooﬁng method such as
coating with a waterproof agent is to be used, its eﬀectiveness should be considered after adequate
discussion based on experimental data.

2.4.29 Eﬀect of sunshine
In the case that a steel structure has a required performance relating to painting for which theeﬀect of sunlight is considered, the worst-case eﬀect of sunshine over the design working life shallbe determined by considering the site location, materials used, etc.

【 Commentary 】

The durability of a steel structure may be reduced because of a phenomena by which the pigment
included in the paint ﬁlm discolors under ultraviolet radiation from the sun. The surface of thepaint ﬁlm is resolved into a powder (through a process known as the ”chalking phenomenon”). The
performance requirements for the paint ﬁlm should be satisﬁed, taking account of the weather resistanceof the structure over its design working life.

Chapter 2 Actions

39

2.4.30 Eﬀect of freezing
In a case where repeated freezing and thawing might cause severe cracking in concrete members,
the eﬀect of freezing shall be considered properly.
【 Commentary 】

The factors determining concrete’s susceptibility to freezing damage are divided into three categories: factors relating to the environment, factors relating to the supply of water, and factors relating
to the quality of the concrete. The ﬁrst category corresponds to environmental conditions, such as
meteorological eﬀects like the minimum temperature and the amount of sunshine received by the structure. The second corresponds to rainfall, snowfall, and splashing, where freezing might occur if water
is supplied to the surface of a concrete member. The third corresponds to the type and quality ofmaterials used, the quality of the concrete (depending on its mix proportion), and the construction
quality, including placement, compaction, curing method, curing period, etc.
Countermeasures against freezing should preferably be applied after considering these three types
of factors.
2.4.31 Eﬀect of ﬁre
In a case where there is a possibility of the structure being exposed to high temperatures suchas in a ﬁre, their eﬀects shall be considered properly.
【 Commentary 】

In a case where there is a possibility of the structure being exposed to high temperatures, suchas in a ﬁre, their eﬀects must be properly considered according to both the level of damage caused
and the performance required of the structure after the disaster. In other words, it must be conﬁrmed
whether the material properties of the steel and concrete members will change under the anticipatedhigh temperatures or not, and the possibility of continuing to use the members must be judged. In
the speciﬁcations for building structures, it is prescribed that the upper limit of elevated temperature
is 350 ℃ and that, after cooling, concrete which has experienced a temperature up to 500 ℃ should
remain usable. Reference [JCI (2002)] may also be consulted.

2.5 Action Factors(1) An action factor is used to take into account any unfavorable deviation of the statisticalcharacteristic value of an action, uncertainties relating to action modeling, changes in action
characteristics over a given reference period, inﬂuence of action characteristics on the relevant
limit state of structure, variations in environmental action, and so on. The actual design
value of each action shall be obtained by multiplying the action value as deﬁned in 2.4 by
its corresponding action factor.
(2) Where combinations of actions are taken into consideration, the action factors described in(1) above shall be modiﬁed by a reduction factor in consideration of the probability of thesimultaneous occurrence of multiple actions according to the judgment of the responsible
chief engineer.

【 Commentary 】(1) The action factors that might be introduced when actions speciﬁed in Article 2.4 are used in the40Standard Speciﬁcations for Steel and Composite Structures [Design]design of steel and composite structures are given here. The following deﬁnitions are assumed:2• ”Unfavorable deviation of the statistical characteristic value of an action” means there is apossibility that an extremely serious outcome (negative convenience) might arise if larger(or smaller) actions than expected act on the steel or composite structure, leading to thestructure reaching its limit state.
• ”Uncertainties relating to calculation of action value” corresponds to inadequacy in thestatistical data used in the calculation of the statistical characteristic value of the relevant
action.
• ”Changes in action characteristics over a given reference period” means an expectationof changes in the characteristics of the relevant action itself. An example would be theexpectation that average air temperatures will rise as a result of global warming.
• ”Inﬂuence of action characteristics on the relevant limit state of structure” means there isa possibility that, for instance, an impulsive action might cause a sudden failure such as abrittle fracture.
• ”Variations in environmental action” means the expectation of changes in the corrosion
environment surrounding a steel member as a function of time elapsed, for example.
If an action factor is adopted in consideration of the factor(s) described above, the engineer incharge of design is expected, in principle, to determine the value of the action factor. Here, thevalues of action factors corresponding to ”unfavorable deviation of the statistical characteristic
value of an action” and ”inﬂuence of action characteristics on the relevant limit state of structure”
should be determined subjectively based on the experience and instincts of the engineer in charge.
The value of an action factor relating to ”uncertainties relating to calculation of action value”
should be determined by applying statistics. The values of action factors related to ”changes
in action characteristics over a given reference period” and ”variations in environmental action”
should be determined through the application of both the experience and instincts of the engineer
in charge and statistics.
Table C2.5.1 Load combination factors and load modifying factors proposed by [JRA (1986)]
combinationof loadsload modiﬁcation factor
S

P
D

L+I
T-20
L-20
3.1
1.7
1.6
0.9
–
–
–
–
1.6
0.9

HP

U

W

T

EQ

SW1

SW2

PP
GD

PA
SD

WP

CF

BK

CO

P+PP
1.0
1.0
1.0
–
–
–
1.0
1.0
1.0
1.0
P+PP+T
1.0
1.0
1.0
–
1.0
–
1.0
–
1.0
1.0
P+PP+W
1.0
1.0
1.0
1.0
–
–
1.0
–
1.0
1.0
P+PP+EQ
1.0
–
–
–
–
1.0
–
–
–
–
P+PP+CO
1.0
1.0
1.0
–
–
–
1.0
–
1.0
1.0
ER
to be considered according to erection conditions–： means the load is not included in the load combination

1.0
1.0
1.0
–
1.0

1.0
1.0
1.0
–
1.0

–
–
–
–
–

–
–
–
–
1.0

(Load modiﬁcation factors relating to PS, CR, SH, and E have been omitted because they are as yet undecided.)
P
S
PP
PA
D
L
I
HP
U

：primary load：subsidiary load
：partial primary load
：partial subsidiary load
：dead load
：live load
：impact：hydrostatic pressure：buoyancy or uplift

W
T
EQ
SW1
SW2

：wind load
：eﬀect of temperature changes：eﬀect of earthquake：snow load considering compacted snow
：snow load considering only snowfall depth

GD
SD
WP

：eﬀect of ground displacement：eﬀect of support displacement：wave pressure

CF
CO
ER
PS
CR
SH
E
BK

： centrifugal force： collision force： erection-related force： prestressing force： eﬀect of concrete creep： eﬀect of concrete shrinkage： earth pressure： braking force including

acceleration force

Values speciﬁed in other standards may, as explained below, be adopted if the determination ofa suitable value is diﬃcult. It should be noted, however, that there is also an opinion that there
is no need to adopt action factors in the design of steel and composite structures judging frompast design achievements and from the way they are speciﬁed in the current standards [JSCE41

Chapter 2 Actions

Table C2.5.2 Combinations of actions and action factors speciﬁed in [RTRI (2000)](a) steel bridge (steel girder)
limit state

veriﬁcation ofultimate limit
state

veriﬁcation ofserviceability
limit state
veriﬁcation of
fatigue
limit
state

combination of action and action factor

・1.0D + 1.1L + 1.1I + 1.1C + {LR } + {T }・1.0D + 1.1L + 1.1I + 1.1C + {LR } + {LF } + {W }・1.0D + 1.1L + {LR } + {B} + {W }・{LR } + 1.1B or 1.1LR + {B}・1.1LF + {W }・1.1B + {W }・1.0D + 1.1L∗2 + 1.1C ∗2 + 1.0W
・1.0D + 1.2W
・ D + L + C + EQ

performanceitem
prescribed in thisDesign volume

veriﬁcation of safety(load-carrying capacity)

veriﬁcation of safety(load-carrying capacity)

・[D] + L + [C] · · · deﬂection by train load

veriﬁcation of serviceability(train operating performance)

・1.0D + 1.1L + 1.1I + 1.1C · · · veriﬁcation of fatigue limit
・D + L + I + C · · · veriﬁcation considering repetition number

veriﬁcation of durability(fatigue resistance)(b) composite girder
limit state

combination of action and action factors
・1.1∗1 D1 + 1.0D2 + 1.1L + 1.1I + 1.1C + 1.0SH + 1.0CR +{LR } + {T }veriﬁcation ofultimate limitstate・1.1∗1 D1 + 1.0D2 + 1.1L + 1.0SH + 1.0CR + {LR } + {B} + {T }・1.1∗1 D1 + 1.0D2 + 1.1L∗2 + 1.1C ∗2 + 1.0W
・1.1∗1 D1 + 1.0D2 + 1.2W
・D1 + D2 + L + C + EQ

veriﬁcation ofserviceability
limit state
veriﬁcation of
fatigue limitstate・[D] + L + [C] · · · deﬂection under train load

performance item prescribed inthis Design volume
veriﬁcation of safety (loadcarrying capacity)

veriﬁcation of serviceability(train operating performance)

・1.1∗1 D1 + 1.0D2 + 1.1L + 1.1I + 1.1C

veriﬁcation of durability· · · veriﬁcation of fatigue limit(fatigue resistance)
・D1 + D2 + L + I + C · · · veriﬁcation considering repetition
number・Actions in ｛ ｝are subsidiary variable actions.
・Actions in [ ] are combined with other actions as required.
・*1 Action factor 1.0 is used for the dead load of a concrete ﬂoor slab and action factor 1.1 is used
for a steel girder.
・*2 When the inﬂuence of empty train vehicles is greater, 1.0 is used.
Action symbols used in the table are as follows:D：Dead load
D1
：Fixed dead load
：Train load
I
：Impact
L：Longitudinal load imposed
LF：Lateral train load and transverseLR
by long welded rail
wheel thrust：Wind loadT：Eﬀect of temperature changes
W：eﬀect of concrete shrinkage
EQ：earth pressure
SH

D2
C
B

：Additional dead load
：Centrifugal load
：Braking force andCR：eﬀect of concrete creep

acceleration force(1998)].
As an example of the values adopted in other standards, the following are given in Common
Principles in Limit State Design Methods for Steel and Concrete Structures [SCCSDSS (1992)]:
1.0∼1.2 for permanent actions (1.0∼0.8 in cases where a smaller value is critical)
1.1∼11.2 for primary variable actions
Regarding action factors for use in the design of highway bridges, [JRA (1986)] proposes thevalues shown in Table C2.5.1, which incorporate the concept of load combinations. The values
given in this table may be used in the design of highway bridges or similar steel and composite
structures.
Similarly, action factors for use in the design of railway bridges can be taken from Table
C2.5.2, as speciﬁed in the Standard Speciﬁcations for Railway Structures and its commentary(Steel and Composite Structures) [RTRI (2000)]. Here, detailed values are listed according to42Standard Speciﬁcations for Steel and Composite Structures [Design]

the limit state considered at the design stage and to load combinations. The third column inTable C2.5.2 indicates the applicable performance items prescribed in this Design volume.
(2) With regard to combinations of actions, a coeﬃcient that increases the allowable stress is introduced in the current Standard Speciﬁcations for Highway Bridges [JRA (2002)], for example.
In these speciﬁcations, the probability that multiple actions will occur simultaneously is taken
into account by reducing the action level against combinations in which frequently occurring
action(s) coincide with rarely occurring action(s). Combinations of actions that are extremelyrare are disregarded. Table C2.5.3 lists the prescribed reduction factors for various combinationsof actions. These reduction factors correspond to the inverse of the coeﬃcient that increases
allowable stress in the Standard Speciﬁcations for Highway Bridges, which were obtained frompast investigations [Sugiyama, et al. (1990)].
Table C2.5.3 Reduction factors for combinations of actions
load combination
1.
2.
3.
4.
5.
6.

reduction
factor
1.00
0.90
0.80
0.75
0.80

primary load(P)+particular primary load(PP)primary load(P)+particular primary load(PP)+ eﬀect of temperature changes(T)primary load(P)+particular primary load(PP)+wind load(W)primary load(P)+particular primary load(PP)+ eﬀect of temperature changes(T)+wind load(W)primary load(P)+particular primary load(PP)+ braking force(BK)
primary load(P)+particular primary load(PP)+collision force(CO)for steel member
0.60
for reinforced concrete member
0.70
7.
primary load(P) except live load and impact + eﬀect of earthquake(EQ)0.708.
wind load(W) only
0.85
9.
braking force (BK) only
0.85
10.
erection-related force(ER)0.80
It is necessary to classify P, PP, and other loads described in the Standard Speciﬁcations for Highway Bridges
into the categories permanent action, primary variable action, and subsidiary variable action as deﬁned inthis Design volume.

Action factors proposed in other standards for the load combinations shown in Table C2.5.1
and 2.5.2 may be used if their application is judged to be preferable.
As for action combinations that include multiple variable actions acting on the designed structure or structural member, Turkstra’s method should be adopted; the value of the primaryvariable action is equal to the characteristic value given in Article 2.4 while values of the othervariable actions are the expected design working life maximum (or minimum) value distributions
and then these values are then summed up [Turkstra, et al. (1980)].
With the capabilities of personal computers advancing so rapidly in recent times, it is now
possible to adopt the Monte Carlo simulation method if suﬃcient information has been collected
to determine the probability distributions of occurrence frequency (or the interval between two
consecutive occurrences), duration, and intensity of the variable action and its ﬂuctuations. If
such a simulation method is adopted, the maximal value of combined load or the 5-10
It is necessary to classify P, PP, and other loads described in the Standard Speciﬁcations for
Highway Bridges into the categories permanent action, primary variable action, and subsidiaryvariable action as deﬁned in this Design volume.
References in Chapter 2
Sugiyama et al.(1985) ： Determination of distribution model and characteristic value from statistical data,
Journal of Structural Engineering, Vol.31A, pp.287-300.
Japan Road Association - Bridge committee - Subcommittee for limit state design method (1986,1989) ：First
report by subcommittee for limit state design method - working group for loads and second report byChapter 2 Actions

43

Subcommittee for limit state design method - working group for loads.
Ishii, et al.(1987) ：Vibration of long span water sluice caused by ﬂuid motion, Proc. of JSME-Part B ，53-495 ，pp.3267-3273 ．
Kato, et al.(1987) ：Deterioration of durability of concrete member caused by drying and wetting and countermeasures, Journal of JSCE Annual meeting No. 24, V-216, pp.470-471 ．
Fujiwara, et al.(1988) ：Estimation of design live load in limit state design method, Public Works ResearchInstitute Material, No.2539 ．
Fujiwara, et al.(1989) ：Estimation of design live load in limit state design method, Public Works ResearchInstitute Material, No. 2700.
Sugiyama, et al.(1990) ：Probabilistic consideration of load combination factors, Journal of Structural Engineering, Vol.36A, pp.479-490 ．
Steel and concrete common structural design standards subcommittee(1992) ：Common principles in limit state
design methods for steel and concrete structures, Proc. of JSCE, No.450/I-20 ，pp.13-20 ．
Okada, et al.(1993) ：Maintenance of highway bridges (foundations), Hanshin Expressway Management Technology Center ，pp.175-178 ．
Kiichiro Muta(1993) ：Fire, repair, and reinforcement, Concrete technology, Vol.31, pp.83-86 ．
Ministry of Const. Pubic Works Research Institute, Steel Products club, Japan Bridge Const. Society(1993) ：Joint research report (XX) on application of atmospheric corrosion resisting steel to bridges - Course ofdesign and erection of bridges constructed from unpainted atmospheric corrosion resisting steel (revised
version), Joint research report, No.88.
Ishii, et al.(1994) ：Various problems relating to hydraulic structures (Vibration of long span shell-type watersluice caused by ﬂuid motion), Journal of Japanese Wind Engineering Association, 59 ，pp75-79.
Tsuda, et al.(1995) ：Experiment on characteristics of concrete exposed to exhaust gases for more than 30
years, Journal of JSCE Annual meeting, No. 50 ，pp258-259.
Tsuda, et al.(1996) ：Chemical analysis of reinforced concrete of age more than 30 years, Journal of JSCE
annual meeting No. 51 ，pp322-323.
Japan Society of Civil Engineers(1998) ：Design Code for Steel Structures, PART A; Structures in General.
JSCE Earthquake Engineering Committee - Research subcommittee for Level 2 earthquake motion(1993) ：Research activity report of Research subcommittee for Level 2 earthquake motion.
Railway Technical Research Institute(2000) ：Standard Speciﬁcations for Railway Structures and Commentary,
Steel and Composite structures.
Japan Highway Public Corporation(2000) ：Design Guide Vol. 2, Bridge Design Volume.
Nippon Expressway Company Limited (2006) ：Japan Society of Civil Engineers (2001) ：Guideline of earthquake-resistant design for civil structures (Draft)- Handbook for Preparation of Earthquake-resistance Design Standards - ．
Toshio Fukushima(2001) ：Trend of atmospheric CO2 concentration and new prediction and estimation methods for neutralization progress of concrete, Journal of Global Environment Symposium, No.9 ，pp.151-156 ．
Honshu-Shikoku Bridge Authority(2001) ：Wind-resistant Design Standards for Honshu-Shikoku Bridge andCommentary.
Railway Technical Research Institute(2002) ：Standard Speciﬁcations for Railway Structures and Commentary,
Composite Structures with Steel and Concrete.
Shirase, et al.(2002) ：Estimation of eﬀect of adhering nitrogen oxides on the durability of RC highway bridges,
Journal of JSCE annual meeting, No. 57,pp.1075-1076．
Japan Society of Civil Engineers(2002a) ：Standard Speciﬁcation for Concrete Structures, Structural Performance Veriﬁcation Volume.
Japan Society of Civil Engineers(2002b) ：Standard Speciﬁcation for Concrete Structures, Construction Volume.
Japan Concrete Engineering Association(2002) ： Report of research committee on safety of concrete structures
against ﬁre.
Japan Road Association(2002a) ：Speciﬁcations for Highway Bridges and Commentary, I General Volume.
Japan Road Association(2002b) ：Speciﬁcations for Highway Bridges and Commentary, III Concrete Volume.
Japan Road Association(2002c) ：Fatigue Design Recommendations for Steel Highway Bridge.

44Standard Speciﬁcations for Steel and Composite Structures [Design]

Railway Technical Research Institute(1992) ：Design Standards for Railway Structures and Commentary, Steeland Composite Structures ．
Japan Road Association(2005) ：Wind-resistant Design Manual for Highway Bridges.
BS5400(1978) ：BS5400 Part 1 ，British Standards Institution ．
OHBD(1983) ：Ontario Highway Bridge Design Code ，Ministry of Transportation and Communications ，Ontario ．
AASHTO(1996) ：AASHTO Standard Speciﬁcation for Highway Bridges ，16th Edition ．

45

Chapter 3 Materials
3.1 General
3.1.1 Fundamentals of material physical properties
Regarding basic physical properties, the materials used in steel and composite structures mustsatisfy the following requirements:(1) Adequate strength and deformability, or toughness(2) Resistance to change or deterioration in quality during the working life(3) Minimum impact on the environment(4) Minimum impact on human beings and animals/plants【 Commentary 】

This article describes the fundamental properties required of the materials used in steel and composite structures. These include materials used for structural members (e.g. steel and concrete), forattachments and pavements (e.g. rubber, plastic and asphalt), for welding and painting, for improvement of service and for maintenance.
(a) The fundamental performance requirement of materials forming the structure is that they shouldbe able to resist actions such as the various loadings to which the structure is exposed.
(b) Materials forming the structure should not reach unexpected limit states as a result of deterioration phenomena during the working life of the structure.
(c) Materials-related energy consumption and CO2 discharges should be minimized, while recyclability should be high.
(d) Any materials that escape into the surrounding environment during construction and service
should not have a strong impact on human beings, animals and plants.

3.1.2 Required properties of materials(1) The materials used in steel and composite structures must have properties that are suﬃcient
to meet the required performance.
(2) Material properties must be described using measurable physical quantities and be consistent
with the calculation model.
【 Commentary 】(1) Any materials that escape into the surrounding environment during construction and service
should not have a strong impact on human beings, animals and plants.
(2) Corresponding to design requirements, the materials should be evaluated to ensure that theirproperties are suitable with respect to strength (tensile, compressive and shear), deformation(e.g. elastic modulus), heat-resistance and water-tightness.
Material properties and their characteristic values should be determined by tests speciﬁed in thestandards, such as ISO and JIS, or by other widely accepted methods. These tests should be carriedout on the basis of random samples representing the overall population. The characteristic values
obtained from tests on such specimens should be converted to suit the design calculation models using
appropriate conversion factors or functions. However, since details of materials are generally not yet

46Standard Specifications for Steel and Composite Structures [Design]identiﬁed a the design stage, it is also rational to determine characteristic values from statistical values
rather than actual experiment [ISO, 1998]. Values speciﬁed in standards such as ISO and JIS should
then be used as characteristic values; alternatively, characteristic values should be determined suchthat the probability of actual values being less than those values is a deﬁned small value [JSCE, 1992].

3.2 Structural Steel
3.2.1 Required steel properties(1) The mechanical properties, chemical composition, shape, and dimensions of structural steel
must satisfy the structure’s required performance.
(2) Structural steel conforming to standards such as ISO and JIS and that has a long history ofuse in past projects is deemed to satisfy requirement (1). Such material can be used once
conformity with the standards is conﬁrmed through inspection certiﬁcates.
【 Commentary 】(1) The required performance of the steel materials used in steel and composite structures is prescribed. These steel materials should possess the required properties and qualities in order thatthe structure or structural member that these steel materials are used meets the required performance such as safety, durability, fabricability, etc.［ Japan Road Association, 2002a ］.
Also, the properties and qualities of the steel materials should satisfy the performance requirements throughout the planning, design, construction, and maintenance stages.
(2) In general, steel and composite structures are designed based on assumptions about the properties
and qualities of the materials to be used. Therefore, a precondition for the use of all materials isthat stable quality can be assured. Since there is some variability in the properties of industrial
products, the average or the distribution of each property should meet the requirement. Quality iscommonly controlled using standards such as ISO and JIS. Structural steel materials conforming
to standards such as ISO and JIS and that have been used in many structures in the past
are deemed to satisfy the requirements of (1) above. Thus, such steel materials can be used
after conﬁrming conformance with the standards by inspecting the certiﬁcates［ Japan Road
Association, 2002a; JSSC, 2004 ］.
Recently, new steel materials with improved properties and qualities have come into use forthe purpose of rationalizing fabrication and improving durability (3.2.2 (2)). Most of these newmaterials are produced by improving the chemical composition or rolling method for standard
materials, such as speciﬁed by ISO and JIS. These new steel materials can be used in structures
after conﬁrming the inﬂuence of any changes from the standards on structural performancethrough experiments or other means. Also, since the qualities of these steel materials are deemed
to meet the same ISO and JIS standards, they can be used after conﬁrming their conformity withthe standards by inspecting the certiﬁcates. Any steel materials with properties that deviate fromthe standards can be used in the same way.

3.2.2 Selection of steel type(1) The type of steel used for a steel or composite structure must be selected according to therequired material properties, which depend on the stress state where used, environmental
conditions at the site, corrosion protection method, construction method, and so on. The
properties of interest include strength, ductility, toughness, chemical composition, shape,size, and surface characteristics.

Chapter 3 Materials

47(2) A variety of types of steel is available depending on the requirements of quality control, workability, labor-saving, etc.. The selected material shall be demonstrated to have properties
that satisfy the objective through an appropriate procedure such as testing.
【 Commentary 】(1) The fundamental principles for the selection of steel type are prescribed［ Japan Road Association,
2002b ］. Particular consideration should be given to the selection of steel type in the following
cases.
1) For seismic energy and deformation absorbing members
In the Design Speciﬁcations for Highway Bridges Part V［ Japan Road Association, 2002c ］,
damage tolerance design is adopted on condition that there should be no bridge collapses orrepairable after Level 2 ground motions. For example, there is one design in which the steel
bridge piers have no concrete ﬁlling, allowing the structural members to yield and absorb theseismic energy in Level 2 ground motions. In this case, the premise is that there should be
no damage such as fractures to the structural members or the joints. Thus, the stress-strain
curves after yielding［ JSCE, 2000; Tominaga et. al, 1994 ］, fracture toughness［ Sasaki,
2000 ］, and z-tension test results［ Japan Road Association, 2002b ］should be considered inselected energy and deformation absorbing members.
2) For use in regions with low temperatures
Brittle fractures at low temperature should be considered. Adequate toughness taking
into account the lowest temperatures experienced in the region should be ensured for steel
materials used in important welded structural members in tension. Certain special regulations for the selection of steel types for cold regions may be useful［ Japan Road Association,
1985 ］. In the regulations of the Hokkaido Development Bureau, there are three categories
of cold according to the lowest temperature (lowest temperature≤ − 35 ℃, -35 ℃＜ lowest
temperature ＜− 25 ℃, − 25 ℃ ≤lowest temperature) and corresponding usable steel types
are decided accordingly.
3) For structural members subjected to signiﬁcant welding restraint or tensile force in the
thickness direction
Where there are welds such as cruciform joints, T-shaped joints, or corner joints, or where
structural members are subjected to tensile force in the thickness direction, a fracture in the
thickness direction known as a lamellar tear may occur. Lamellar tearing is a phenomenon
in which sulﬁde inclusions (MnS) in the steel become elongated through rolling; tearing thenhappens because of tensile force in the thickness direction acting between the inclusions andthe steel. Consequently, the concentration of sulﬁde inclusions is related to the evaluationof susceptibility to lamellar tearing.
To avoid lamellar tearing, consideration should be given to selecting a suitable joint type(weld design), reducing the force or strain in the thickness direction (welding procedure),or adoption of lamellar tear resistant steel［ JSCE, 1985 ］.
4) For structural members bent to a small radius
For the purpose of landscape design or rationalized structural design, structural members
worked to a small radius are increasingly being used. Steel hardens with bending due tostrain aging. To minimize the inﬂuence of strain aging embrittlement, it is important not to
introduce large local strains. In general, the inside bending radius should be greater than
15 times the steel thickness so that surface strain does not exceed about 3%. However, thisrule does not apply to steel materials with enhanced toughness prescribed later or if it has
been conﬁrmed that strain aging embrittlement does not occur.
5) In the case of welding with low preheating temperature

48

Standard Specifications for Steel and Composite Structures [Design]

Welds may crack because of the presence of hydrogen in cases where there are a lot ofalloying elements in the steel and where they are subjected to signiﬁcant welding restraint.
In general, the steel is preheated to prevent weld cracking. Lower preheating temperature
are desired because preheating leads to much work in fabrication and work conditions are
not good.
To prevent weld cracking it is eﬀective to reduce PCM which is an indicator of thesusceptibility to weld cracking. Further, the type of welding materials (diﬀusible hydrogen)and shape of joints (thickness, degree of restraint) should be considered in deciding thepreheating temperature.
6) In the case of large heat input welding
Large heat input welding with reduced welding passes realizes a rationalization of workwhen ﬁeld welding the full cross section of the I-girders in a twin I-girder bridge. The heat
input has to be restricted according to the type of steel because, in general, the heat-aﬀectedzone becomes weaker in proportion to the heat input. Recently, new types of steel that allow
for large heat input welding have been developed. These steel materials can be used after
conﬁrming their quality through welding tests. However, it should be noted that proper
welding materials must be selected for the welding to ensure the required performance of
the welded metal.
(2) High performance steels［ JISF, 2005 ］exhibit improved properties of strength, toughness, bending
formability, and corrosion resistance than conventional types of steel. The use of such highperformance steel materials is prescribed here.
1) Excellent toughness steels
Where cold bending work of structural members is carried out, the inside bending radiusof curves should be greater than 15 times the thickness because of the problem of loss of
toughness. However, where suﬃcient toughness can be secured by using excellent toughness
steels, bends with smaller inside bending radius are permitted. Speciﬁcally, bends with aninside bending radius of 5 or 7 times the thickness or greater are permitted if the result ofCharpy impact tests for absorbed energy, as speciﬁed in JIS Z2242, satisfy the values given
in Table C3.2.1 and the N content of the steel is ≤0.006%.
In general, steel toughness declines and the risk of brittle fracture tends to rise at lower
temperatures. These problems can also be improved by using excellent toughness steels.
Table C3.2.1 Allowable radius in cold bending work
Charpy absorbed energy

Inside bending radius in cold bending work

150J and over
200J and over

7t and over (t: thickness)
5t and over (t: thickness)

2) Lamellar tear resistant steels
Welded joints subjected to large tensile force in the thickness direction can fracture in
the thickness direction in a so-called lamellar tear. Where this is a concern, a lamellar tearresistant steel can be used along with improved welding methods. Lamellar tear resistantsteels with guaranteed z-tension test results and sulfur content are speciﬁed in JIS G3199.
(See Table C3.2.2)

49

Chapter 3 Materials

Table C3.2.2

Results of z-tension tests and sulfur content (JIS)Class

Average of 3 specimens

Value of each specimen

Sulfur content

Z15S
Z25S
Z35S

15% and over
25% and over
35% and over

10% and over
15% and over
25% and over0.010% and under
0.008% and under
0.006% and under

3) LP steel platesLongitudinally proﬁled (LP) steel plates are produced with variable thickness in thelongitudinal direction. LP steel plates have become available due to the development ofplate rolling technology. The application of LP steel plates to steel and composite structures
allows the weight of steel, and hence fabrication cost, to be reduced while eliminating ﬁller
plates in bolted joints and eliminating tapering work in welded joints.
4) Low preheating steels
With increasing the amount of alloying elements and with increasing steel thickness, theproblem of weld cracking tends to increase. In order to prevent weld cracking it is necessary
to preheat the steel. Low preheating steels whose PCM is lower than that of conventional
steel materials allow the preheating temperature to be reduced or allow reduction or elimination of preheating work.
5) Steels for large heat input welding
In general, as the amount of heat input by welding increases, the heat aﬀected zone tends
to become weaker. Where this causes a problem, special steels for large heat input welding
allow the required toughness to be secured. When using such steel materials, the welding
equipment, groove shapes, and welding conditions should be checked against the Design
Speciﬁcations for Highway Bridges 17.4.4［ Japan Road Association, 2002b ］.
6) Constant yield point steels
In general, as the thickness of steel increases, its yield point or strength tends to decrease.
Constant yield point steels provide the beneﬁt of reduced steel weight and reduction in design
complexity where the steel exceeds 40 mm in thickness.
7) Low yield strength steels
Low yield strength steels have excellent ductility and are used for seismic vibration control
devices in structures. These low yield steels absorb the seismic energy through plastic
deformation, thereby reducing the vibration of the structure.
8) Nickel added weathering steels
Nickel added weathering steels whose mechanical properties are in conformity with JIS
SMA and whose corrosion resistance is improved have come into use. These weathering
steels, which are Cr-free low alloy steels containing Ni, Cu, Mo, Ti, etc., are applicable overa larger range than conventional weathering steels (JIS G 3144).
9) Stainless steels
Stainless steels are used for harbor, oﬀshore, and river structures, etc. where regularcorrosion prevention is diﬃcult to implement. In addition to conventional stainless steel(SUS304), various new kinds of stainless steel with improved corrosion resistance and Nifree ferritic stainless steels have been developed. These stainless steels have been used forbridges as well as buildings in Europe and the USA. Considering the reduced maintenance,
improvement in LCC is expected for the adoption of the stainless steels because of excellent
corrosion resistance.
10) Bridge high-performance steels
Bridge high-performance steels (BHS) whose yield strength, tensile strength, toughness,
weldability, fabricability, and weather resistance are highly developed, have been proposed

50Standard Specifications for Steel and Composite Structures [Design]［ Miki et. al, 2003 ］, and some research relating to their application to actual structures

has been conducted. Utilization of the excellent performance of BHS is expected to reduce
bridge construction costs.

3.3 Concrete(1) The strength, ductility, and workability of concrete must be of speciﬁc quality suitable forconstruction.
(2) Ready-mixed concrete shall conform to JIS A 5308 in principle.

【 Commentary 】(1) This article derives from the materials provision (3.2.1) in the Design Speciﬁcations for Highway Bridges [JRA, 2002a]. Designers may also follow the Standard Speciﬁcation for Concrete
Structures [JSCE, 2002].
(2) This article is included since most construction in Japan is carried out with ready-mixed concrete. Even using ready-mixed concrete, though, the required properties cannot be obtained
unless construction work is carried out appropriately. Care is necessary during construction
since even material sourced from a plant certiﬁed by JIS may suﬀer from some problems. In
order to meet structure performance requirements, the use of high-performance concretes notconforming to JIS, such as high-strength, high-ﬂuidity, high-self-compactability, and low-heat ofhydration concretes, is increasing. The mix-proportion required to satisfy such speciﬁc performance requirements should be determined based on the provisions of the Standard Speciﬁcations
for Concrete Structures [JSCE, 2002].

3.4 Value of Material Properties for Design
3.4.1 General(1) The quality of steel or concrete is expressed not only in terms of tensile or compressive
strength but also through other material properties such as strength, deformation, heat,
durability, or water tightness according to design needs. Appropriate consideration must be
given to the inﬂuence of loading rate on strength and deformation properties.
(2) The characteristic value of material strength, fk , should be selected such that most test
values fall above it.
(3) Design material strength, fd , is given by the characteristic value of material strength, fk ,divided by the partial factor for the material, γm .
【 Commentary 】(1) The main materials used in steel and composite structures are steel and concrete. Many varietiesof steel and concrete are available, so it is necessary to select appropriate ones in considerationof how the structure will be used, environmental conditions, design working life, construction
conditions and so on.
Material properties are expressed not only in terms of tensile or compressive strength but also
through other values according to design needs. The various material properties can be classiﬁed
into mechanical, physical and chemical properties.
Strength properties can be expressed through measures of static strength, such as tensile

51

Chapter 3 Materials

strength, yield strength (yield point or proof stress), compressive strength and bond strength,
as well as fatigue strength, fracture toughness and so on. Deformation properties include timeindependent Young’s modulus and Poisson’s ratio, as well as time-dependent creep modulus
and shrinkage. In addition, there are the properties expressed through the relationship between
two mechanical factors, as in the case of a stress-strain curve. The physical properties include
heat properties, such as coeﬃcient of thermal expansion and speciﬁc heart, as well as density,
water-tightness and air-tightness. The quantitative treatment of density and heat properties isgeneralized. Acid erosion and resistance to sulfates are classiﬁed as chemical properties.
The values of material properties speciﬁed in this chapter can be used in the examinationof limit states under static or dynamic loading. However, values obtained through reliable experiments should be used in cases where strain rate has a signiﬁcant inﬂuence on strength ordeformation properties, e.g. when examining impact loading.
(2) The characteristic value of material strength fk is calculated from test results using Eq.(C3.4.1).
fk = fm − k σ = fm (1 − k δ)

(C3.4.1)

Where, fm : mean of test values, σ: standard deviation of test values, δ: coeﬃcient of variationof test values and k: coeﬃcient.
Coeﬃcient k is determined from the probability of obtaining a test value less than the characteristic value and the probability distribution of test values. The 5% fractile value is often
taken as the characteristic value. In this case, the value of coeﬃcient k is 1.64 if the normal
distribution is assumed for the test values. For ready-mixed concrete conforming to JIS A 5308,
the probability of obtaining concrete strength less than the nominal strength is approximately
4%, since it is speciﬁed that each test value must be more than or equal to 85% of the nominal
strength and the mean of three test values must exceed the nominal strength. Therefore, thecorresponding k value is 1.73.
When the lower limit of strength is guaranteed by a standard such as ISO or JIS, this value
can be taken as the characteristic value. An example of a guaranteed steel strength is given in
Table C3.3.1.
Table C3.3.1 Example of guaranteed steel strength(N/mm2 )Steel type
Yield point or
proof stress

SM400
SM400
SMA400
235
215

SM490

315
295

SM490YSM520
SMA490
355
335

SM570
SMA570Applicable plate thickness

450
430

Less than or equal to 40mm
More than 40mm

For load-carrying welded joints, the strength can be taken as the same as the base metal,
provided that appropriate welding materials are used and suﬃcient quality control is implemented
by a qualiﬁed welding engineer.

3.4.2 Structural steel(1) Strength
1) The characteristic values of tensile yield strength, fyk , and tensile strength, fuk , should
be determined based on values obtained through tensile tests.
2) The guaranteed value shall be taken as the characteristic value, fyk and fuk , for amaterial conforming to a standard such as ISO or JIS. In general, the nominal value ofcross sectional area shall be used for design calculations.
3) The characteristic value of compressive yield strength, fyk, shall be considered to be52Standard Specifications for Steel and Composite Structures [Design]equal to that of tensile yield strength, fyk .
4) In general, the characteristic value of shear yield strength shall be obtained using Equation (3.4.1).
fyk
fvyk = √3(3.4.1)(2) Fatigue strength The characteristic value of fatigue strength shall be determined based on
fatigue tests in which type of steel, shape, size, welding process, residual stress, fabrication
errors, the histogram of applied stress range, and environmental conditions are taken into
consideration.
(3) Stress-strain curve
1) An appropriate stress-strain curve should be determined according to the objective of
the examination.
2) In veriﬁcation for safety, the stress-strain curve shown in Figure 3.4.1 can be used.
σ
fyd

E/100

E

0

εyd

εud ε

Fig.3.4.1 Stress-strain curve of steel(4) Young’s modulus
1) In principle, Young’s modulus of the steel shall be determined through a tensile test
conforming to a standard such as JIS Z 2241.
2) Young’s modulus of steel can be generally taken as 205kN/mm2.
(5) Poisson’s ratio
Poisson’s ratio of steel can be generally taken as 0.3.
(6) Coeﬃcient of thermal expansion
The coeﬃcient of thermal expansion of steel can be generally taken as 1 × 10−5 /℃.

【 Commentary 】(1) In principle, the characteristic value of yield strength (yield point or proof stress) should bedetermined through tests. However, the guaranteed value is to be taken as the characteristic
value for a material conforming to a standard such as ISO or JIS, since strengths more than orequal to the guaranteed value have been obtained in previous tests.
According to JIS Z 2241 ”Method of tensile test for metallic materials”, the cross-sectional areaused to calculate strength should be the value measured before the test for structural steels and,in the case of concrete reinforcing steel, the nominal value. Although this does not necessarily
yield a conservative value of strength because of allowable error in the product size, the use of
the nominal cross-sectional area is permitted for design calculations since such over-estimationof strength does not have signiﬁcant inﬂuence on the performance veriﬁcation.
The behavior of steel in compression tests is fundamentally the same as that in tensile tests.
Consequently, yield points based on the true stress are the same in compression and tension. The
yield strength obtained by JIS Z 2241 is not based on the true stress, because the cross-sectional
area measured before the test is used in the stress calculation. However, the inﬂuence of thison the limit state examination is not signiﬁcant, so the compressive yield strength should beconsidered equal to the tensile yield strength.

53

Chapter 3 Materials

According to von Mises yield criterion, the characteristic value of shear yield strength can beobtained using Equation (3.4.1).
(2) Most fatigue problems occur at welded joints. The factors inﬂuencing the fatigue strength of awelded joint can be considered to be steel strength, joint type, welding process and condition,plate thickness, degree of misalignment (axial or angular), presence of weld defects, existenceof weld root, stress ratio (minimum stress/maximum stress) and residual stress due to welding.
The fatigue strength of a weld increases with increasing steel tensile strength. However, steel
strength barely inﬂuences the fatigue strength of welded joints. The degree of stress concentration is related to joint type, welding process and condition, plate thickness, fabrication errors(axial or angular misalignments), weld defects and existence of weld root. Therefore, in tests toevaluate fatigue strength, it is important to reproduce the conditions of stress concentration andstress ratio, including the eﬀect of residual stress, occurring in the actual structure as closely as
possible. In particular, attention should be paid to residual stress since it diﬀers between small
specimens and actual structures due to the diﬀerence in restraint level. In Fatigue Strength Recommendation for Steel Highway Bridges [JRA, 2002d], the fatigue strength (S-N curve) is given
for typical welded joints based on the results of an enormous number of past fatigue tests. Thisdata should in general be used for fatigue design. The design fatigue strength of reinforcing bars
should be determined according to Standard Speciﬁcations for Concrete Structures ”Structural
Performance Veriﬁcation” [JSCE, 2002].
(3) The stress-strain curve of steel can be generally expressed using a model that consists of anelastic region, a yield plateau and a strain hardening region, as shown in Fig.C3.4.1 [JSCE, 1996].
However, the actual shape of the curve varies with the type, chemical composition and production
method of the steel. The equations and parameters in them are modeling examples. There areother models such as the Ramberg-Osgood model, the Swift model, the Ludwik model and then-th power hardening rule. Consequently, a model suitable for the purpose of the examination
should be selected. Although a perfect elasto-plastic stress-strain relationship would be expected
to give the most conservative result, the bi-linear type stress-strain relationship with a strain
hardening slope of E/100 given here is speciﬁed for safety veriﬁcation since most of the steel used
for structures has a strain hardening region. The strain hardening slope of E/100 can be roughly
considered as a straight line connecting the yield point and the 5% strain point.

dσ−ξ ε ε − ε ε= E ⋅edε
σ 1E−ξ ε ε − ε ε={1 − e
}+ 1
σ
ξ E
E′ =

σ

(

/

y

st /

y )

st /

y )

st

st

(

/

y

y

E’
Est

σ

y

E

0

ε

y

ε

MaterialξE / Estεst / εy

SS400

0.06

40

10

SM490

0.06

30

7

SM570

0.02

100

3

st

ε

Fig.C3.4.1 Stress-strain curve of steel with yield plateau andstrain hardening region [JSCE, 1996](4) Values of the Young’s modulus of steel as speciﬁed in certain design codes are given in Table

54

Standard Specifications for Steel and Composite Structures [Design]C3.4.1. Four in six codes specify a value of 200kN/mm2 . However, it is prescribed here that theYoung’s modulus should be 205kN/mm2 , which is closest to the conventionally used value of 2.1
106kgf/cm2 in order to maintain consistency with the design code for buildings.
Table C3.4.1 Values of Young’s modulus in certain design codes (kN/mm2 )Speciﬁcationsfor Highway
Bridges

Design Standard for Steel
Structures

Eurocode 3

AASHTOLRFD[JRA, 2002a]

Standard
Speciﬁcations
for Concrete
Structures[JSCE, 2002][AIJ, 2005][CEN, 2003][AASHTO, 1998]

Canadian
Highway
Bridge Design
Code[CSA, 2000]

200

200

205

210

200

200

3.4.3 Concrete
The strength, stress-strain curve, Young’s modulus, Poisson’s ratio, and the other material
properties of the concrete shall be determined through tests.
【 Commentary 】

This article designates the principles for determining design values for the material properties ofconcrete. Generally, the values speciﬁed in Standard Speciﬁcations for Concrete Structures [JSCE,2002] should be used.

3.5 Partial Factors for Materials
The partial factors for materials shall be properly determined in consideration of adverse variations in strength from characteristic values, variations between properties in specimens and actual
structures, the inﬂuence of properties on limit states, changes in properties with time, and diﬀerences between real characteristic values and values assured by standards such as ISO and JIS.
【 Commentary 】

This provision speciﬁes the considerations to be taken in determining the partial factors for materials.
Concerning structural steel, the values of material partial factor γm as given in Standard Speciﬁcations for Concrete Structures [JSCE, 2002] and Eurocode 3 [CEN, 2003] are shown in Table C3.5.1.
In verifying ultimate limit states according to Eurocode 3, the values 1.0 and 1.25 are used for the
resistance of cross sections to excessive yielding, including local buckling, and for the resistance ofcross sections in tension to fracture, respectively. The value of the partial factor for the fatigue limit isspeciﬁed according to the consequences of failure and the assessment method (i.e. the damage tolerant
method or the safe-life method). Ultimate limit states, fatigue limit states and serviceability limit
states in Table C3.5.1 can be thought of as corresponding to veriﬁcations for safety, durability andserviceability, respectively, in these speciﬁcations.
The mean yield point of Japanese-manufactured structural steel conforming to JIS is approximately
1.2 times the guaranteed value [Nara et al., 2004]. Taking the 5
One study [JSCE, 1994] reported that the diﬀerence in mean and standard deviation between theupper and lower yield points is approximately 3.5%. There is also a report showing that tensile tests
according to JIS give a yield point approximately 10% higher than the static yield point [JSCE, 1994].

55

Chapter 3 Materials

Table C3.5.1 Examples of partial factors for steel γmLimit state

Ultimate limit
Fatigue limit
Serviceability limit

Standard Speciﬁcations
for Concrete Structures[JSCE, 2002]

Eurocode 3[CEN, 2003]

1.05
1.05
1.0

1.00∼1.25
1.00∼1.35
1.00

Furthermore, the fatigue strength speciﬁed for each joint type in Fatigue Design Recommendations for
Steel Highway Bridges [JRA, 2002d] corresponds to the lower bound of test results using a specimenof the required quality or 97.7% fractile value.
Accordingly, it can be concluded that, for structural steel conforming to a standard such as ISO or
JIS, the value of γm should be 1.0 in veriﬁcations of structural safety, serviceability and durability, as
long as the guaranteed yield point and fatigue strength speciﬁed in the Fatigue Design Recommendations are taken as the characteristic values of static strength and fatigue strength, respectively.
The allowable stress of JIS-SM570 in Speciﬁcations for Highway Bridges is determined so as tomaintain a safety factor of 1.7 against the yield point and 2.2 against tensile strength. Accordingly,
safety against tensile strength is 2.2/1.7=1.29 times higher than that against the yield point. Considering this, and referring to overseas design codes such as Eurocode, it is considered that the safety ofmembers against fracture can be veriﬁed using the characteristic value of guaranteed tensile strengthand a material partial factor of 1.25.
References in Chapter 3
Japan Road Association(1985) ：Construction Handbook of Steel Bridges, Maruzen.
Japan Society of Civil Engineers(1985) ：Application of Lamellar-Tearing resistant steel to civil structures,
Civil engineering.
Japan Society of Civil Engineers(1992) ：General principles for the limit state design of steel and concrete
structures, Journal of Structural Mechanics and Earthquake Engineering, No.450/I-20, pp.13-20.
Japan Society of Civil Engineers(1994) ：Ultimate Strength and Design of Steel Structures, steel structures
series 6 ．
T. Tominaga and H. Yasunami(1994) ：An experimental study on ductility of steel bridge piers with thickwalled cross section and small number of stiﬀeners, Journal of Structural Engineering, Vol.40A, pp.189200.
Japan Society of Civil Engineers(1996) ：Tentative seismic design recommendations for steel bridges and newtechnologies for seismic design.
American Association of State Highway and Transportation Oﬃcials (1998) : LRFD Bridge Design Speciﬁcations, SI Unit Second Edition.
ISO(1998) ：ISO2394 General principles on reliability for structures ．
Canadian Standards Association (2000) : Canadian Highway Bridge Design Code.
Sasaki, E.(2000) ：An examination on required fracture toughness of steels for bridges, Report of study on
application of high performance steel to bridges, JSSC, pp.58-67.
Japan Society of Civil Engineers and Japanese Society of Steel Construction(2000) ：Benchmark for seismic
analysis of steel structures and improvement of seismic design method.
Japan Society of Civil Engineers (2002) ：Standard Speciﬁcation for Concrete Structures, Structural Performance Veriﬁcation Volume.
Japan Road Association(2002a) ：Speciﬁcations for Highway Bridges and Commentary, I Common Speciﬁcations Volume.
Japan Road Association(2002b) ：Speciﬁcations for Highway Bridges and Commentary, II Steel Highway
Bridges.

56Standard Specifications for Steel and Composite Structures [Design]

Japan Road Association(2002c) ：Speciﬁcations for Highway Bridges and Commentary, V Earthquake-resistanceDesign Volume.
Japan Road Association(2002d) ：Fatigue Design Recommendations for Steel Highway Bridges.
CEN(2003) : Eurocode 3 Design of Steel Structures - Part 2: Steel Bridges -, prEN 1993-2 ．
Miki, C., Ichikawa, A., Kusunoki, T., and Kawabata, F.(2003) ：Proposal of new high performance steels forbridges (BHS500, BHS700), Journal of Structural Mechanics and Earthquake Engineering, No.738/I-64,
pp.1-10.
Japanese Society of Steel Construction(2004) ： International harmonization guideline of design standards forsteel structures, Steel bridges, JSS IV 06-2004.
Nara, T., Nakamura, S., Yasunami, H., Kawabata, F., and Shiwaku, T.(2004) ：A statistical survey on thickness and mechanical properties of structural steel plates for bridges, Journal of Structural Mechanics
and Earthquake Engineering, No.752/I-66, pp.299-310.
Japan Iron and Steel Federation(2005) ：High performance steels for bridge construction.
Architectural Institute of Japan (2005) : Design Standard for Steel Structures - Based on Allowable Stress
Concept -.

57

Chapter 4 Structural Analysis
4.1 General(1) The structural analysis carried out must be relevant to the veriﬁcation method used.
(2) It is important to note that structural analysis may not be always an appropriate means of
veriﬁcation.

【 Commentary 】(1) For the purpose of performance veriﬁcation, an index is speciﬁed for each performance requirement. Typical indexes are section force, displacement, and strain. Performance is then veriﬁed
by comparing the value of the index under the appropriate action with the limit value; the valueof the index under this action is treated as the demand, while the limit value is considered thecapacity of the structure. In general, structural analysis is the process of evaluating the behaviorof the structure under the design actions to obtain the value of the index. Linear structural
analysis is often suﬃcient to achieve this end. It is also possible to verify performance by evaluating the load-carrying capacity of the structure and comparing it with the design actions, butwhen this procedure is used, nonlinear structural analysis is required. The appropriate methodof analysis therefore depends on the type of performance veriﬁcation being carried out.
Structural analysis requires that the structure be modeled. In general, modeling is regarded
as a simpliﬁcation of reality that retains its important characteristics. In short, a model must beable to simulate reality up to the limit state. Models can be classiﬁed into three groups: action
models, structure models, and resistance models [ISO 1998]. A structure model is one in which
the value of the index is evaluated, while a resistance model is one by which the limit value interms of the index is evaluated. It must be noted, however, that the distinction between modeltypes is not always clear. A case in point, for example, is the instability of a structural system
as a whole where there is signiﬁcant interaction between action and structural behavior.
Most structural analysis is these days based on the ﬁnite element method. In the constructionof a ﬁnite element analysis (FEA) model, careful attention is also required with respect to thetypes of elements used, the number of elements, and the layout of elements. For structuralmembers that are much larger in one dimension than in the others, beam elements may be used;
where two of the dimensions are much larger than the other, plate/shell elements may be used.
Otherwise, solid elements may need to be employed. However, there are no clear-cut criteria
by which to judge which type of element should be used in modeling. A plate/shell element ismore generic than a beam element, which means that the assumptions employed in developing
such an element are less restrictive and it is likely to behave closer to reality. The same is true
with plate/shell elements and solid elements; the latter are more generic. However, the use of
more generic elements results in increasing data inputs and longer computation times. Still,advances in computer technology and FEA software in recent years have made it easier to use
generic elements. Against this background, the Fatigue Design Guidelines for Steel Bridges give
structural analysis factors for several types of structural analysis [JRA 2002].
Regardless of the type of element, it is essential to construct an appropriate ﬁnite element
mesh. Failure to do so would lead to unreliable results. Bearing this and other points in mind, it
is clear that ﬁnite element analysis can yield only approximate results and its accuracy can vary58

Standard Specifications for Steel and Composite Structures [Design]from analysis to analysis.
The appropriate analysis that this clause requires means choosing
an appropriate analysis method and constructing an appropriate analysis model. Some of thebasics involved in choosing an appropriate analysis method are explained below.
Linear Analysis
When the applied load is small, a structure’s deformation is generally small and linearly proportional to the magnitude of the load. Linear analysis, also often called small-displacement
analysis, is appropriate for this type of structural behavior. In the design of the civil infrastructure, this is usually the class of analysis used. Since the principle of superposition is valid in
linear analysis and thus the following equation holds true, results for various load combinations
and inﬂuence-line loads are very easily obtained:N
i=1

Fi = KN
αi U i(C4.1.1)i=1

ここに，
αi = load factor ，N ＝ the number of loads to be combined ，
F i =load vector to be combined ，K=stiﬀness matrix ，U i =displacement vector due to F i ．Since, in ﬁnite element analysis, thecomponents F i and U i are the load and the displacement at a node, are called the nodal load
vector and the nodal displacement vector, respectively.
Nonlinear Analysis
When strain and displacement become large, linear analysis tends to produce signiﬁcant errors
because their eﬀects are ignored. In such situations, the deformed conﬁguration of a structure isdistinctly diﬀerent from its original conﬁguration. Since a structure’s stiﬀness depends on its conﬁguration, the structural response changes as deformation progresses; this change in conﬁgurationmust be taken into consideration in analysis. The relationship between load and deformation
is nonlinear. The class of analysis required is called the geometrically nonlinear analysis or ﬁnite displacement analysis. It must be noted that large displacement does not necessarily mean
large strain. A ﬁshing rod can undergo large displacement without large strain, for example.
Therefore, geometrically nonlinear analysis can be grouped into two types: ﬁnite strain-ﬁnite
displacement analysis and small strain-ﬁnite displacement analysis.
As deformation increases, the material of the structure exhibits a nonlinear response. The
plastic deformation of steel is a typical example. This type of phenomenon also requires nonlinear
analysis; this is known as material nonlinear analysis.
Analysis that takes into account the eﬀects of both geometrical nonlinearity and material
nonlinearity is often required in the analysis of steel structures when ultimate strength is ofinterest.
The weighted residual method and the ﬁnite element method lead to the following generaldiscretized equilibrium equation:
F = K(U )(C4.1.2)

where ，F is the external force vector ，K is the internal force vector, and U is the displacement
vector. Usually proportional loading is applied so that Eq.(C4.1.2) can be rewritten as
αF 0 = K(U )(C4.1.3)

where ，F 0 is the base load vector and α is the load parameter.
Equilibrium Path
In some kinds of nonlinear analysis, only the displacement caused by a speciﬁc load is of

59

Chapter 4 Structural Analysis

interest. However, in many other cases, the load F versus displacement U relationship thatsatisﬁes Eq.(C4.1.2) is evaluated and the load F versus displacement U curve is plotted. This
curve is called the equilibrium path.
Today, most nonlinear structural analysis is conducted using the ﬁnite element method. Therefore, Eq.(C4.1.2) takes the form of a set of nonlinear equations to which exact solutions are rarely
available. Instead, solutions are obtained numerically. A popular method is the Newton-Raphson
technique in which the equation is linearized and solved repeatedly until convergence is reached,
When the equilibrium path is targeted, certain variables are picked out and given values. The
values of the remaining variables are then calculated. Depending on the variables chosen, threegroups of approaches are available: (1) load control; (2) displacement control; and (3) arc-length
control.
In a load-control approach, the value of α is given and, if the Newton-Raphson method isused, the following set of equations is to be solved repeatedly to obtain the solution:
αF 0 − K(U (m) ) = K T (U (m) )ΔU (m)(C4.1.4)

U (m+1) = U (m) + ΔU (m)(C4.1.5)

where,K T is the tangent stiﬀness matrix deﬁned by ∂K/∂U ．Eq.(C4.1.4) is the linearized equilibrium equation, a set of simultaneous linear equations. Solving this set, the displacement vector
is updated using Eq.(C4.1.5). This computation is continued until ΔU (m) becomes suﬃciently
small that convergence can be considered as achieved. In the above equations, superscript (m)indicates the number of repetitions of this computation. It is noted here that the constructionof the tangent stiﬀness matrix K T requires an incremental constitutive model (an incremental
stress-strain relationship). Besides, in addition to the update of the displacement vector, thestress states need to be updated.
There is a limit load that a structure can carry. To evaluate this limit, analysis must continue
beyond the limit, exploring the deterioration of the structure. It is diﬃcult to use load control
for this class of analysis. Instead, displacement control may be used since, in many cases, somedisplacement components continue to increase even during this stage of structural behavior. In
displacement control, one of the displacement components is prescribed and the load factor isthen unknown. Therefore, the load factor is one of the variables whose values are computedby the analysis. In using this displacement control approach, it is crucial to use a displacement component that continues to increase beyond the limit load. It should be noted also that
displacement control results in an asymmetric tangent stiﬀness matrix K T .
In some cases, all displacement components tend to increase. It is then diﬃcult to apply
displacement control. Arc length control can be used even in such cases. Arc length control isin fact the most versatile approach to tracing the equilibrium path.
There is no single method of arc length control; rather, there are several variations. In general,in addition to Eq.(C4.1.3), another equation is introduced to control the distance between two
points on the equilibrium path. An example of this type of equation is the following:
ΔS =

n


αi (Ui − Ūi )2 + b(α − ᾱ)2(C4.1.6)

i=1

where the quantity with the over-bar is the known value of a point on the equilibrium path, n is
the number of displacement components, and αi ，b are the coeﬃcients that adjust the values of thediﬀerent kinds of variable. The value that needs to be speciﬁed is ΔS, then all the displacement
components and the load factor are computed. Compared with the other two control approaches,
therefore, the number of unknown variables is one greater. Since ﬁnite element analysis involves

60Standard Specifications for Steel and Composite Structures [Design]

so many unknowns, this increase of one in the number of unknowns is not a problem at all. The
combination of Eqs.(C4.1.3) and (C4.1.6) inevitably leads to an asymmetric coeﬃcient matrix
for the linearized simultaneous equations of the Newton-Raphson method. One very powerfuland popular technique, the skyline method, circumvents the numerical problems associated withthis asymmetricity without much diﬃculty.
Buckling Analysis
Theoretically, buckling is a phenomenon at a point on the equilibrium path where multiple
branches of the equilibrium path are possible. The value of the buckling load and the associatedbuckling mode are usually obtained by so-called eigenvalue analysis. However, because of initial
imperfections in an actual structure, the problem is not necessarily one of branching. The loadcarrying capacity of the structure may be evaluated by tracing the equilibrium path even whenbuckling is the major phenomenon and controls the load-carrying capacity of the structure. Even
when analysis is carried out this way, however, eigenvalue analysis is usually conducted to obtainthe mode of the initial imperfection.
Ignoring the deformation before buckling and deriving the stiﬀness matrix including the eﬀect
of ﬁnite displacement, the following stiﬀness equation is obtained:
αF 0 = (K E + αK G (N 0 ))U(C4.1.7)

where K E is the stiﬀness matrix derived from small-displacement theory, K G is the geometricmatrix, N 0 is the internal force vector in the initial state due to base load vector F 0 , and α
is the load factor. Structural analysis may also be carried out using this stiﬀness equation, aprocess that is called linearized ﬁnite displacement analysis.
From Eq.(C4.1.7), the condition for the occurrence of buckling can be expressed as|(K E + αK G (N 0 ))| = 0(C4.1.8)

Solving Eq.(C4.1.8) is what is known as eigenvalue analysis. In equilibrium path tracing analysis,
eigenvalue analysis is sometimes also conducted, using the tangent stiﬀness matrix instead of thestiﬀness matrix associated with the initial state, so as to ﬁnd branching points and limit points.
Since such eigenvalue analysis includes the eﬀect of deformation, this is something of a nonlinear
approach to analysis. This class of analysis is therefore called nonlinear buckling analysis and isdistinguished from linear buckling analysis based on Eq.(C4.1.8).
By solving Eq.(C4.1.8), the load factor at the point of buckling is obtained and the bucklingload is evaluated as αcr F 0 . This is the load at which the branching of the equilibrium pathwould take place if it were to occur. Otherwise, it is the limit load. Eq.(C4.1.7) yields the
eigen vector U for eigenvalue αcr as well. The eigen vector is nothing but the buckling mode,
which is often treated as the geometrical initial imperfection (the initial displacement mode)
required in equilibrium path tracing analysis. The magnitude of the initial displacement isusually determined by giving it a maximum value equal to the tolerance speciﬁed in the designcodes.
For the sake of simplicity, the load-carrying capacity of a member is computed using theconcept of the eﬀective length. In short, the eﬀective length cr is evaluated by the following
equation:
π 2 EIcr =(C4.1.9)αcr N0where, N0 is the axial force induced in the initial state by base load vector F0 . Caution must be
used in this evaluation since the eﬀective length of a member with a small axial force would beChapter 4 Structural Analysis

61very large.
Constitutive Laws:
The equations governing structural behavior consist of three sets of equations: the equilibrium
equations, the strain-displacement relationships, and the stress-strain relationships. The stressstrain relationships are also called the constitutive laws or the constitutive model. Of these threeequation sets, the ﬁrst two can be deﬁned solely by rigorous mathematics. On the other hand,the stress-strain relationships depend on the actual materials. They need be constructed using
experimental data obtained for the material. Consequently, the stress-strain relationships areinevitably approximations, a fact that directly inﬂuences the accuracy of the analysis.
Steel exhibits a linear relationship between stress and strain up to a certain stress level (theyield stress) and this linear relationship holds good regardless of whether the stress increases ordecreases. Beyond the yield stress, the relationship becomes nonlinear and the material behavior
during stress relaxation may be completely diﬀerent from that during the increase in stress. This
class of material behavior is modeled by plasticity theory. Many plasticity models have been
proposed for various materials. Speciﬁcally, the model for steel has been constructed using thesecond invariant of the deviatoric stress, J2. This class of plasticity model for steel is therefore
often called the Mises (or von Mises) model or the J2 model.
In the analysis of ultimate strength, material behavior beyond the plateau and into the strainhardening region may need to be included. In such a case, a hardening model must be includedin the plasticity model. The isotropic hardening model, the kinematic hardening model, and the
combined hardening model (a combination of the two previous models) are the classic methods
and are well-known. Under monotonous loading conditions, there is little diﬀerence between these
hardening models and any of them can be used. Under cyclic loading, which is often considered inconjunction with seismic design, the kinematic hardening model is usually employed in practice.
It must be noted, however, that more sophisticated hardening models that can simulate actual
material behavior observed in experiments under cyclic loading have been developed since the
Hyogoken-Nanbu Earthquake.
The material behavior of concrete is completely diﬀerent in compression and tension. Concreteconsists of various small regions of diﬀerent materials, the sizes of which are not necessarily
insigniﬁcant, so it is not as homogeneous as steel. However, under compression, cracks occur ina rather distributed manner so its behavior under compression is generally modeled by assuming
the material is a continuum. Plasticity models have been proposed for concrete to describe its
mechanical behavior. Unlike steel, the material behavior of concrete is found to be dependent
on the hydraulic axis. Therefore, instead of the Mises model and the Tresca model, in which
the yield surfaces are parallel to the hydraulic axis in the principal stress space, the DruckerPrager model and the Mohr-Coulomb model are usually used, since their yield surfaces slopewith respect to the hydraulic axis.
In tension, explicit cracks (discontinuous surfaces) appear and deformation becomes localized.
In general, while the ﬁnite element method is good for the analysis of continua, its application to
problems that include discontinuities presents some diﬃculties. Basically, cracks are dealt withby one of two approaches: the discrete model, which simulates cracks by separating the nodes
along the crack, and the smeared model, in which cracks are simulated by changing the material
stiﬀness. Neither is much superior to the other; the discrete model tends to restrict crack growthaccording to the layout of the ﬁnite elements while the smeared model has diﬃculty in dealing
with stress changes due to the modiﬁcation of material constants. In the latter, the objectivityof the numerical results can take place unless the element size is taken into consideration whenmaterial constants are modiﬁed to simulate a crack.

62Standard Specifications for Steel and Composite Structures [Design]

Finite Element Mesh
When using the ﬁnite element method, the structure under consideration is divided into small
regions (elements) and the deformation of each element is expressed using rather simple functions.
The ﬁnite element method is nothing but an approximation technique based on discretization.
Consequently, it must be noted that the ﬁnite element method inevitably involves discretization
errors and that the element size must be suﬃciently small to obtain satisfactory results.
In linear structural analysis, it has been shown that errors in computing displacement areproportional to the square of the element size while errors in computing stress and strain areproportional to the element size. In parts of a structure where the stress gradient is large, suchas in the vicinity of stress concentrations, it is necessary to make the mesh ﬁner than in the otherareas. However, it is not easy to determine the appropriate mesh size and quantify the accuracyof the numerical results obtained.

4.2 Structural Analysis Factor(1) The value of the structural analysis factor, γa , shall be decided by taking account of various
uncertainties, such as those involved in the structural analysis method and the structuralmodel.
(2) In general, the structural analysis factor, γa , may be set to 1.0 in the case of linear analysis.
(3) In the case of nonlinear analysis, the relevance of the analysis method shall be veriﬁed ﬁrst
and then an appropriate value of structural analysis factor, γa , decided.
【 Commentary 】

The structural analysis factor is a partial factor that takes account of uncertainties in evaluating
structural performance under the design loads
Although nonlinear analysis may be most appropriate for computing the ultimate limit state, inpractice it cannot be used for all practical designs. Instead, linear analysis tends to be employed in
actual design. Since linear analysis has been used to design a great many structures over many years,
a structural analysis factor γa of 1.0 can be assumed for linear analysis.
In nonlinear analysis, the value of the structural analysis factor, γa , has to be set according to an
adequate examination of theoretical relevancy, the applicability of the numerical method used, andso on. A value of 1.0 may be acceptable when the relevancy and accuracy of the nonlinear analysis
method used are both found satisfactory.
Section 6.1 of Standard Speciﬁcations for Railway Structures (Steel-Concrete Composite Structures) [Railway Technical Research Institute, 2000] states that for the ordinary structures where linear
analysis gives satisfactory results, a structural analysis factor, γa , of 1.0 can be assumed except whenanalyzing the lifting of girder bridges, for which a value of 1.1 is required. It also states that linear
analysis is not suitable for long-span arch bridges and cable-stayed bridges. A linearized elastic ﬁnite
displacement that includes the eﬀect of geometrical nonlinearity is required. Since this analysis isreliable in accuracy, the structural analysis factor, γa , can be set equal to 1.0.
In the veriﬁcation of the fatigue limit state, if data for a similar structure elsewhere conﬁrms thatthe computed stress is smaller than the stress acting in the actual structure, the structural analysis
factor, γa , may be reduced by the ratio of the actual stress to the computed stress.
Section 6.1 of Standard Speciﬁcations for Railway Structures (Steel-Concrete Composite Structures)states that a structural analysis factor, γa , of 0.85 can be used for veriﬁcation of the fatigue limit state
if the inﬂuence of the number of load repetitions is taken into consideration. This is based on data forthe ratio of actual stress to computed stress, the maximum value of which is about 0.75. The value ofChapter 4 Structural Analysis

63

0.85 is considerably smaller, as the standard structural analysis factor, γa , for the ultimate limit state,
the service limit state and the fatigue limit state based on the fatigue limit is 1.0.
In Fatigue Design Guideline for Steel Structures [Japanese Society of Steel Construction, 1993],
Subsection 5.2.3 states that the value of the modiﬁcation factor α, which is equivalent to the structural
analysis factor used here, plays the role of adjusting the diﬀerence between computed stress and actual
stress. The appropriate value is to be determined from data such as measurements of similar structures
or from model experiments. The guideline provides an example of a veriﬁcation in which a value of0.85 is used following the Standard Speciﬁcations for Railway Structures (Steel-Concrete Composite
Structures) [Railway Technical Research Institute, 2000].
References in Chapter 4
Japanese Society of Steel Construction (1993) ：Fatigue Design Guideline for Steel Structures and Commentaries.
Railway Technical Research Institute (2000) ：Design Standards for Railway Structures and Commentary,
Steel and Composite Structures ．
Japan Road Association (2002) ：Fatigue Design Guideline for Steel Highway Bridges.
Japan Society of Civil Engineers (2005) ：Buckling Design Guidelines, Ver.2 [2005 Version].
ISO (1998) : ISO2394 International Standard, General Principles on Reliability for Structures ．

64Standard Specifications for Steel and Composite Structures [Design]

Chapter 5 Structural Member Resistance
5.1 General(1) The design resistance of structural members, as used in the veriﬁcations speciﬁed in Chapters
6∼10, shall be obtained by dividing the characteristic value of member resistance by thematerial partial factor.2(2) The characteristic values of member resistance shall be determined using the characteristic
values of material strength.

【 Commentary 】

Most existing design speciﬁcations recommend using the minimum yield strength of the steel material as the design material strength. The minimum yield strengths of steel materials are provided by
JIS based on tensile material tests on relatively small specimens under a limited range of strain rates.
The variance of yields strength within a rolled steel plate is not signiﬁcant, but it is not negligible insteel sections. Further, the yield strength depends on the test method such that the higher the strain
rate is, the higher the obtained yield strength. Yet the static yield strength should not be lower thanthe minimum yield strength. Taking into account all of these contributing factors, this design code
speciﬁes the resistance of members in terms of the design material strength, which is the characteristic
value of material strength as shown in section 3.4.2 divided by the partial factor of the material. Hereafter, as a general rule, the term ”resistance” is used for the stress resultant and ”strength” is used forthe stress. The dimensionless (normalized) resistance of members will generally be represented by theresistance corresponding to the characteristic value: the inﬂuence on resistance of changes in sectional
modulus will be taken into account in the member partial factor.

5.2 Partial Factor for Uncertainty in Resistance
The partial factor for uncertainty in resistance (structural member factor) shall be determinedin accordance with the formulas for calculating member resistance, while also taking into consideration uncertainty in the calculation method, the inﬂuence of member size variance, and theimportance of the member (the inﬂuence of a member reaching the limit state on the structure asa whole).
【 Commentary 】

Table C5.2.1 lists the standard partial factors for members. The factor depends on whether thecharacteristic value of resistance is set to the mean or the minimum. In general, its value is set as thecharacteristic value of resistance corresponding to the appropriate fractile value (for example 5%).
Table C5.2.1 Standard Partial Factor for Members
Partial factor for members, γb

Safety1.1∼1.3

Service
1.0

Durability
1.0∼1.1

In order to obtain a similar member resistance to that calculated using the resistance formulae in

65

Chapter 5 Structural Member ResistancePart A of the Design Code for Steel Structures [JSCE, 1997a], the value for safety in Table C5.2.2 canbe used as the partial factor for members in the various resistance formulae given in Section 5.3.
Table C5.2.2 Partial Factor for Members when Using Resistance Formulae in Section 5.3
Partial factor for members, γbTensile Resistance in Axial Direction
Eq.(5.3.1) or (5.3.2)
Compressive Resistance in Axial Direction
Eq.(C5.3.1)
Bending Resistance
Eq.(C5.3.2)
Shear Resistance of Webs
Eq.(C5.3.22), (C5.3.27)

Group 1 (Ref.Table C5.3.2)
Groups 2 and 3 (Ref.Table C5.3.2)
Rolled I or H sections, Box sections, π-shape sections
Fabricated I or H sections

Local Buckling Strength
Eq.(C5.3.35)∼(C5.3.59)

Eq.(C5.3.35)∼(C5.3.38),(C5.3.59))
Eq.(C5.3.43)
Eq.(C5.3.57)

1.00
1.04
1.08
1.04
1.08

1.00

Resistance of Steel Pipes
Eq.(C5.4.1)∼(C5.4.5)
Resistance of Cables
Eq.(5.5.1)

1.10
1.14
1.01

1.08
Table C5.2.3

Though these values are basically the inverse of the resistance factors given in Part A of the
Design Code for Steel Structures [JSCE, 1997a], the reduction in the region where the slenderness
ratio parameter is smaller than λ̄0 is not considered here for simpliﬁcation.
The partial factors for cable members are deﬁned by applying the multiplying factor for the ultimate
load in [JRA, 2002] to the design material strength derived from the 0.7% total elongation resistance.
For reference, [HSBA, 1980] employs a member partial factor of 1.0 because the tensile strengthcharacteristics of cables have low variance, and so are highly reliable.
Table C5.2.3 Partial Factor for Cable Members
Types of Structural Cable Material
IWSC Type
Structural Strand Rope (St.R)
CFRC Type
Structural Spiral Rope (Sp.R))
Structural Locked Coil Rope (L.C.R)
Parallel Strand Wire Cable (P.W.S)
Parallel Wire Cable (P.W.C)
Pseudo Parallel Wire Cable (S.P.W.C)

Partial factor for members, γb
1.18
1.18
1.11
1.11
1.05
1.05
1.05

5.3 Steel Member Resistance
5.3.1 Tensile resistance
The tensile resistance of structural members shall be taken as the smaller of the values calculated
by Equations (5.3.1) and (5.3.2).
Nrd

=

Nrd

=

Ag fydγb
An fudγb(5.3.1)(5.3.2)

66

Standard Specifications for Steel and Composite Structures [Design]where,

Nrd
Ag
An
fyd
fud
γb

：design tensile resistance of the member：gross area of the cross section to be veriﬁed：net area of the cross section to be veriﬁed：design yield strength：design tensile strength：structural member factor【 Commentary 】

The inﬂuence of variations in sectional modulus, such as in cross-sectional area and plate thickness,
which aﬀect the axial resistance of tension members, is considered in the safety factor (member partial
factor), thus it is not included in the characteristic value of member resistance. For example, whensteel plates are speciﬁed and supplied with a strict plate thickness tolerance, a responsible engineer
can reduce the safety factor and include the inﬂuence in the response value described in Chapter 6.

5.3.2 Compressive resistanceThe compressive resistance of steel structural members in the axial direction shall be taken as
the smaller of the resistance value for the strong axis and the weak axis calculated on the basis of
the buckling curve in consideration of factors such as structural member imperfections, eccentricloading, residual stress, and variance in the yield strength in the cross section as well as the local
buckling strength of plate elements constituting the member.
【 Commentary 】

The design compressive resistance in the axial direction can be calculated in consideration of local
buckling of structural members using, for example, Eq.(C5.3.1). Three types of buckling curves aredeﬁned for diﬀerent groups of cross sections and manufacturing processes by using the ECCS curves
as the buckling curves of columns based on Ref.[SGST, 1980]. The compressive resistance of members
based on these curves includes the inﬂuence of variance in sectional modulus according to Ref.[JSCE,1994]. The deﬁnitions given in Chapter 11 can be utilized for the eﬀective buckling length of frame
members.
⎧
Ag Qc fyd⎪⎪(λ̄ ≤ λ¯0 )
⎪
⎨
γb

Nrd =
(C5.3.1)⎪
Ag Qc fyd (β − β 2 − 4λ̄2 )⎪⎪¯⎩(λ̄ > λ0 )γb2λ̄2
β = 1 + α(λ̄ − λ̄0 ) + λ̄2where ，

Nrd
Ag
fyd
λ̄



r
E

：Design compressive resistance in axial direction of member：Gross area of cross section to be veriﬁed：Design yield strength：Slenderness ratio ，
1 Qc fyk 
λ̄ =
π
E r
：Eﬀective buckling length of member; standard eﬀective lengths are given in Table
C5.3.1 for boundary conditions at each end of a member based on member length
L and with pin connections at each end. When restriction is not suﬃcient, theeﬀective buckling length can be raised to a reasonable value.
：Radius of gyration of total cross section to be veriﬁed：Young’s modulus of steel

67

Chapter 5 Structural Member Resistance

Table C5.3.1 Eﬀective Buckling Length of Members 

1

2

3

4

5

6

If the buckled waveform is shaped like thedotted line

Theoretical value of effective buckling

s
n
o
i
t
i
d
n
o
c
t
r
o
p
p
u
S

0.5

0.7

L

L

2

L

2

Fixed

Free

Fixed

Free

Free

Fixed

Fixed

Fixed

Free

Fixed

Free

Free

Fixed

Fixed

Fixed

Free

Fixed

Free

Fixed

Fixed

Fixed

Fixed

Fixed

Fixed

L

lengthUpper

Condition for rotation

end

Condition for horizontal
displacement

Lower

Condition for rotation

end

Condition for horizontal
displacement

L

L

Table C5.3.2 Categorization of Cross Section of Steel Columns
Section Type
Rolled box sections

Welded box sections

Coordinate axes

Group

α

λ0

1

0.089

0.2

1

0.089

0.2

1

0.089

0.2

2

0.224

0.2

3

0.432

0.2

2

0.224

0.2

3

0.432

0.2

Both axes included

Both axes included

Rolled I-sections

t

≤ 40

Both axes included

Welded I-sections

t

≤ 40

Both axes includedt > 40Both axes included
Both axes included

OthersBoth axes included

λ̄0：Limit slenderness ratio given in Table C5.3.2 according to the sectional shapeα
Qc：Initial imperfection coeﬃcient given in Table C5.3.2

and manufacturing process：Non-dimensional strength of short column that suﬀers local buckling

68Standard Specifications for Steel and Composite Structures [Design](σrd Af c )Ag fyd：Local buckling strength of plate supported on both edges, plate supported on
one edge, stiﬀened plate or steel pipe obtained from Eqs.(C5.3.35), (C5.3.38),(C5.3.43), (C5.4.2), respectively：Cross-sectional area of plate element or steel pipe whose σrd has been calculated：Summation of plate elements that constitute the cross-sectional area
Qc =

σrd

Af c


5.3.3 Bending resistance
5.3.3.1 Classification of cross section
Structural members are classiﬁed as follows according to the maximum width-thickness ratioof the sectional element subject to bending or combined compression and bending (that is, themember’s resistance to local buckling):(1) Compact section: sections that may develop a plastic moment resistance(2) Non-compact section: sections in which the stress in the extreme compression ﬁber of thesteel, assuming an elastic distribution of stresses, may reach the yield strength, but local
buckling is likely to prevent development of a plastic moment resistance(3) Slender section: sections in which local buckling will occur before the yield stress is reachedin one or more parts of the cross section.
【 Commentary 】

Eurocode 3 [CEN, 2003] categorizes cross sections into the following four classes.
Class 1：cross-sections are those which can form a plastic hinge with the rotation capacity

Class 2：cross-sections are those which can develop their plastic moment resistance, but haveClass 3：cross-sections are those in which the stress in the extreme compression ﬁbre of therequired from plastic analysis without reduction of the resistance.
limited rotation capacity because of local buckling.
steel member assuming an elastic distribution of stresses can reach the yield strength,
but local buckling is liable to prevent development of the plastic moment resistance.
：cross-sections are those in which local buckling will occur before the attainment ofyield stress in one or more parts of the cross-section.

Class 4In this code, there is in general no redistribution of moments because response values are basicallycomputed by elastic analysis. Thus, sections categorized as Class 1 and Class 2 according to Eurocode
3 are deﬁned as compact sections that fully develop a plastic moment. This cross-section categorizationis also used in [AASHTO (1998)].
Each design code has diﬀerent conditions for the categorization of member cross sections. For
example, the formulae deﬁning the conditions for compact sections consisting of steel I-beam ﬂanges
and webs in compression under bending are compared in Table C5.3.3. On the whole, the ISO (1997)
Table C5.3.3 Conditions of Compact Sections for Steel I-Beam(a) Compression flangebE≤p(where, b：width of outstandingtfypart of flange, fy ：Characteristic value of yield stress.
AASHTOEurocode
ISO
Part APart B
p
0.382
0.343
0.37
0.310
0.309



(b) WebE
αb≤p(where, α：Ratio of compressiontfypart in web, b：web depth ，t：web thickness.)
AASHTOEurocode
ISO
Part APart B
1.88
1.42
1.9
1.28
1.13

69

Chapter 5 Structural Member Resistanceand AASHTO codes are similar and have easier conditions, while JSCE Part A and B [JSCE, 1997a,b] provide for considerably strict conditions. In general, the cross section categorization given by the
ISO code is to be used, as shown in Table C5.3.4.
Table C5.3.4 Maximum Width-Thickness Ratio of Cross-Sectional Element under Compression
and/or Bending.［ ISO ，1997 ］

Cross section element

Stress distribution in the element

Webs of I-sections,Webs or flanges of weldedbox sections

Moment:Maximum b/t Ratio
Compact
Non-compact

3 .8

E
fy

4 .2

E
fy

Compact Non-compact
Compression and moment
K1

E
fy

0.37

E
fy

3.8

Compact
Flanges of I-sections,Free flanges of welded box
sections

Non-compact

Compression orstrong axis moment
Compression and moment

0.37

α α

0.37

Compact

Non-compact

α α

4.2

K2

0.45

E
fy

0.69

E
fy

0.69

E
fy

E
fy

K3

E
fy

K4

E
fy

K 1 = 1 − 0.63N / N p , K 2 = 1 − 0.67 N / N p , K 3 = 0.425 − 9.1(ψ + 1) + 10.4(ψ + 1) 2 ,K 4 = 0.57 + 0.2ψ + 0.07ψ 2
N/Np refers to the fully cross section for doubly symmetric sections and ψ is positive as indicated above.

5.3.3.2 Bending resistanceThe bending resistance of steel structural members shall be determined based on the nominal
bending resistance corresponding to the classiﬁcation of cross section, taking into account theinﬂuence of initial deﬂection and residual stress as well as elastic lateral-torsional buckling.

【 Commentary 】

The bending strength of steel structural members excluding steel pipes should be determined using
Eq.(C5.3.2). However, if the compressive ﬂange is directly secured to a concrete slab or similar, λ̄b

70Standard Specifications for Steel and Composite Structures [Design]

must always be taken as less than λ̄b0 .
⎧
Mn
⎪
⎪
⎪
⎪
⎨ γb
Mrd =
⎪
⎪
⎪ Mn (βb −
⎪
⎩
2λ̄2b

(λ̄b ≤ λ̄b0 )βb2 − 4λ̄2b )γb(C5.3.2)(λ̄b > λ̄b0 )βb = 1 + αb (λ̄b − λ̄b0 ) + λ̄2bWhere ，

Mrd
Mn

：Bending strength of beam members with respect to the strong axis
：Standard bending strength of beam sectioni) Compact Section

Mn = fyd Z(C5.3.3)ii) Non-Compact Section

Mn = fyd W(C5.3.4)iii) Slender Section

Mn = fyd Wef f(C5.3.5)

Fig.C5.3.1 Eﬀective Sections of Beams

fyd
Z
W
Wef f

： Design strength of material：Plastic section modulus：Elastic sectional modulus of compression ﬂange：Eﬀective sectional modulus of compression ﬂange computed considering the ef-

fective width due to local buckling. The eﬀective width should be taken as shownin Fig.C5.3.1 ．
Eﬀective width of compression ﬂange:
Plate supported at all edges:

be
=
b

0.7
Rf

Plate supported at one edge:

be
=
b

0.7
Rf

0.80

(C5.3.6)
0.64(C5.3.7)

Eﬀective width of web
he
=
hc

1.0
Rw

0.80

λ̄b0
αb

：Limit slenderness ratio of beam (Table C5.3.5)

λ̄b：Slenderness ratio of beam


λ̄b =

(C5.3.8)：Initial imperfection coeﬃcient (Table C5.3.5)

Mn̄
ME(Mn̄ is given by Eq.(C5.3.10) ，ME is given by Eq.(C5.3.12).)(C5.3.9)

71

Chapter 5 Structural Member Resistance

Table C5.3.5 Parameters in Bending Resistance Formula for Beams
Rolled I or H sections
box sections, π-shape sections
Fabricated I or H sections

Mn̄

αb

λ̄b0

0.15

0.40

0.25

0.40

：Characteristic value of standard bending resistance of beam section given by

Eq.(C5.3.10), (standard value)Mn̄ = Mn

Rf , Rw

fyk
fyd(C5.3.10)

fyk ：Characteristic value of material strength (standard value)：Width-thickness ratio of ﬂange and web, respectively
1
R=
π
k



12(1 − ν 2 )
k



1.05
fyk b
= √
E t
k

ME

fyk b
E t

(C5.3.11)：Buckling coeﬃcient
Flanges supported at all edges
Flanges supported at one edge
Webs

b
t
Z
E
ν



k = 4.0
k = 0.425
k = 23.9：Total width of plate (Refer to Fig.C5.3.1. For webs, replace with h)：Plate thickness：Plastic sectional modulus：Young’s modulus of steel：Poisson’s ratio：Elastic transverse torsional buckling moment of simply supported beam. When theloading condition is diﬀerent from this, eigenvalue analysis for elastic buckling may
be used to obtain the transverse torsional buckling moment.
Cb1 π 2 EIy
ME =Cb2 ht + Cb3 βz +2

(Cb2 ht + Cb3 βz )2 +

1 Iw
γ Iy

2 GJ
1+ 2
π EIw


(C5.3.12)

γ = 1 − Iy /Ix
Where,

Iy , IzJ
Iw：Length of simply supported beam for out-of plane deformation (cm). Gener-

Cb1

ally, this length may be taken as the distance between the ﬁxed points of thecompression ﬂange. However, if the constraints at both ends are consideredadequate, then this value may be reduced to a rational value ．
：Equivalent moment factor (Refer to Table C5.3.6 for intermediate loading)：Moment of inertia with respect to the weak and strong axes, respectively：St. Venant’s torsion constant：Warping torsion constant

Cb1 =

1.0
≤ 2.5
0.6 + 0.4β

β=

M2
M1

(C5.3.13)

72Standard Specifications for Steel and Composite Structures [Design]

Table C5.3.6 Various Parameters of Beams Subject to Intermediate Loading

Mmax

Loading condition

Pl
4

Pl
3

Pl
4

ql

Cb 3

1.365

0.553

0.406

1.096

0.500

0.480

1.040

0.422

0.570

1.132

0.459

0.525

1.286

1.563

0.782

1.736

1.406

2.767

2

24

Pl
8

M1 , M2

Cb 2

2

8

ql

Cb 1

： Bending moments at each end of member, where M1 ≥ M2 . The sign of thebending moment is to be taken as positive when compressive stress occurs in theﬂange.
ht：Distance between the position at which load acts (height) and the shear center.

Cb2(The sign shall be taken as positive when the position at which the load acts is
closer to the tension side in bending than the shear center)：Coeﬃcient for correcting the eﬀect of the position at which the load acts according
to the loading condition (Refer to Table C5.3.6)：Coeﬃcient expressing the asymmetry of the cross section

βz


βz =

Y (Z 2 + Y 2 )dA − Yz
2Iz
A(C5.3.14)

Yz ：Distance from the center of gravity to the shear center
Cb3：Coeﬃcient for correcting the eﬀect of the asymmetric cross section according to

the loading condition (Refer to Table C5.3.6)
The above descriptions are for the characteristic values of bending resistance of members with box
or H sections. The bending resistance of H sections about weak axis is out of scope because structuralmembers are designed as they are subjected to bending only about strong axis in real structures. In
addition, beams for which the inﬂuence of shear force on web capacity must be considered are also out
of scope although the shear force as well as bending moment applies to general beams.
The reduction of bending resistance of beams due to lateral-torsional buckling is given by PerryRobertson type strength curve to keep consistent with columns. The curves for rolled and welded
H sections are diﬀerent. In general, lateral-torsional buckling is diﬃcult to occur for box and π

73

Chapter 5 Structural Member Resistancesection beams. However, it can occur for considerably deep beams with these sections. The same
lateral-torsional buckling strength curve as the rolled H sections is tentatively used here for box andsection beams. As the reference for readers, the slenderness ratioof box sections taking the yield moment as the standard bending
resistance is shown below.
th2ttf = p t, Iz =(3pb + h), Iy = (3hb2 + b3 ),6
6
2b2 h2 p th
tb2 h2 (ph − b)2 (h + pb)
,J =
, q=
Iw =
24(ph + b)
ph + bb
The lateral-torsional buckling moment of a simply supported
beam in uniform bending moment is given by Eq.(C5.3.15).
ME =

π


π 2 EIw
1
EIy GJ 1 + 2γ
 GJ(C5.3.15)

Fig.C5.3.2 Dimension of boxsection

Where,
γ =1−

Iy
Iz

(C5.3.16)

The torsion constant ratio κ2 is ，
κ2 =

π2 E
π 2 EIw
=
2 GJ
48 G

b


2

(pq − 1)2 (p + q)p(pq + 1)(C5.3.17)

where,
2b(pq − 1)=ph − b2(C5.3.18)

When the member length  is more than 2∼3 times of (ph − b), it can be thought that k 2 << 1.
Therefore, ME is expressed as follows.
ME =

π


EIy GJγ(C5.3.19)

Taking the yield moment as the standard bending resistance of the section,
Mn = fyd W =2fyd Izh(C5.3.20)

Thus, the slenderness ratio can be obtained by
λ̄2 =

Mn
2fyd Iz 
=
ME
h π



γ
EIy GJ(C5.3.21)

and
λ̄2

E b
= 0.2963fyd (pq + 1)(3p + q)2(p + 3q)1−

3q + pq 2 (3p + q)

(C5.3.22)

Fig.C5.3.3 is the graph of Eq.(C5.3.22).
Assuming a box section beam with p = 1.0, /b = 10 and F = 235N/mm2 (JIS-SS400 steel), λbecomes more than 1.11. So, the reduction of bending resistance due to lateral-torsional buckling
occurs when q = h/b > 3.2, otherwise it does not have to be considered.
Short beams suﬃciently supported in lateral direction can reach bending resistances of the section(Mp or My ), whereas the bending resistance of long beams is determined by elastic lateral-torsional

74Standard Specifications for Steel and Composite Structures [Design]

Fig.C5.3.3 Relationship between aspect ratio and slenderness ratio for box sections

buckling moment. Consequently, Mn /ME is used as slenderness ratio to lateral-torsional bucklingcorresponding to the bending resistance of the section Mn . Inﬂuence of loading conditions and boundary conditions is taken into account in the calculation of elastic lateral-torsional buckling moment ME .
Eq.(C5.3.12) is obtained from theoretical solution of elastic buckling by approximating the inﬂuenceof loading conditions. When the loading condition is diﬀerent from this or suﬃcient restriction it applied to both ends, eigenvalue analysis for elastic buckling may be used to obtain the lateral-torsional
buckling moment.
A coupled buckling (lateral-torsional buckling and local buckling) strength evaluation method using
the eﬀective width is adopted in this speciﬁcation. There are some cases where Q-factor can beconveniently used when ﬂanges and webs are composed of stiﬀened plates. For such cases, the eﬀective
width should be obtained by evaluating the resistance of the plate element as single plate, and thenthe bending resistance of the section should be calculated with the consideration of the shift of neutral
axis (Eﬀective Section Method).
Speciﬁcations for Highway Bridges [JRA, 2002] have the provisions based on the yield moment
My for the welded beams with sections having relatively large width-thickness ratio. However, rolled
beams with small slenderness ratio can be expected to reach fully plastic moment. Thus, the bending
resistance of Mp is speciﬁed for the sections composed of plates whose slenderness ratios are smaller
than the plastic limit (The ﬁrst hinge method).

5.3.4 Shear resistance of web
The shear resistance of the webs shall be determined properly in consideration of factors suchas the constraining eﬀect of ﬂange and stiﬀeners, initial deformation, and residual stress due towelding.
【 Commentary 】

The design shear resistance of a web can be generally determined based on shear buckling strengthof a single panel under pure shear loading or based on diagonal tension ﬁeld theory as described below.
(1) Based on shear buckling strength [Bleich, 1952]
Vrd = Vcr =τcr thγb(C5.3.23)

75

Chapter 5 Structural Member Resistance

where ，⎧⎪
⎨ 1.0
τcr /fvyd =1 − 0.614(λs − 0.6)⎪
⎩ 1/λ2s12(1 − ν 2 )
kτ

h
λs =
t


4.00 + 5.34/α2
5.34 + 4.00/α2kτ =where ，



fvyd
α
ν
E
h
t

(λs ≤ 0.6)√
(0.6 < λs ≤ 2)√
( 2 < λs )(C5.3.24)

fvyd
E(C5.3.25)(α ≤ 1)(α > 1)(C5.3.26)：Design shear strength：Aspect ratio of web panel (= a/h))：Poisson’s ratio of steel：Young’s modulus of steel：Web height：Plate thickness(2) Based on diagonal tension ﬁeld theory [JSCE, 2005]
Vrd
Vt

Vcr + Vt + Vf
γb= σt ht(sin θ cos θ − αc sin2 θ)=(C5.3.27)(C5.3.28)

where ，
σt /fydw
fydw
fvydw

= 1 − (τcr /fvydw )0.6

(C5.3.29)：Design material strength of web：Design material shear strength of web

θ

=

2
tan−1
3

1
α

(C5.3.30)

α：Aspect ratio of web panel (= a/h)αc=

α{1 − (Cc − Ct )/a}(C5.3.31)

a：Distance between vertical stiﬀeners
2
Cc =
sin θ
2
Ct =
sin θ




Mpf c
σt t
Mpf t
σt t

⎫
a ⎪
⎪
(0 ≤ Cc ≤ ) ⎪
2 ⎬
a ⎪
⎪
⎭
(0 ≤ Ct ≤ ) ⎪2(C5.3.32)

Mpf c , Mpf t：Fully plastic moment of compression ﬂange and tension ﬂange, respectively, given by the following Eq.(C5.3.33):⎫
1
fyf c bf c t2f c ⎪⎬4⎪
1
Mpf t = fyf t bf t t2f t ⎭4

Mpf c =

(C5.3.33)

76

Standard Specifications for Steel and Composite Structures [Design]

fydf c , fydf t
bf c , bf t
t f c , tf t：Design material strength of compression ﬂange and tension ﬂange, respectively：Width of compression ﬂange and tension ﬂange, respectively：Plate thickness of compression ﬂange and tension ﬂange, respectively

Vf = min

4Mpf c 4Mpf t,
Cc
Ct(C5.3.34)

However, plate girders carry shear and bending loads. Vf is generally not counted due to bending
stress on the ﬂanges.

5.3.5 Local buckling resistance(1) The local buckling resistance of plates supported at both ends or at one edge and of stiﬀened plates subject to compression shall be determined in consideration of factors such as
boundary conditions and initial imperfections due to welding, including initial deformation
and residual stress.
(2) Plates supported at both ends or at one edge and stiﬀened plates in locations with particularductility requirements shall be of dimensions that guarantee the required ductility.

【 Commentary 】(1) The local buckling strength of a plate supported at both ends and subject to uniform compression
should be computed using Eq.(C5.3.35). However, this does not apply to the web plate of plate
girders.
⎧f⎪⎪ yd(R ≤ 0.70)
⎪
⎨ γb
σrd =
(C5.3.35)
0.86
⎪
0.7
fyd
⎪
⎪
(0.70 < R)⎩Rγbwhere ，σrdfyd
R：Design local buckling strength：Design material strength：Width-thickness ratio ，
1 12(1 − ν 2 ) fyk b
R=
π
k
E t
ν ：Poisson’s ratio
k ：Buckling coeﬃcient, k = 4.0
E ：Young’s modulus of steel
fyk ：Characteristic value of material strength (standard value)b ：Distance between ﬁxed edges of plate (refer to Fig.C5.3.4)
t ：Plate thickness(2) The local buckling strength of a plate supported at both ends and subject to in-plane bending
should be computed using Eq.(C5.3.36). However, this does not apply to the web plate of plate
girders.
⎧fyd⎪⎪(R ≤ 1.00)
⎪
⎨ γb
σrd =
(C5.3.36)
0.72
⎪
fyd
⎪
⎪ 1
(1.00 < R)⎩R
γb

Chapter 5 Structural Member Resistance

Fig.C5.3.4 Distance between the ﬁxed edges of

Fig.C5.3.5 Stress level at edge ofplate supported at both ends

plate supported at both ends

where ，σrdfyd
R：Design local buckling strength (refer to Fig.C5.3.5)

σrd
fyd
R

：Design local buckling strength

77：Design material strength：Width-thickness ratio ，
1 12(1 − ν 2 ) fyk b
R=
π
k
E t
ν ：Poisson’s ratio
k ：Buckling coeﬃcient, k = 23.9
E ：Young’s modulus of steel
fyk ：Characteristic value of material strength (standard value)b ：Distance between ﬁxed edges of plate (refer to Fig.C5.3.4)
t ：Plate thickness(3) The local buckling strength of a plate supported at both ends and subject to a combination of
in-plane bending and uniform compression should be computed using Eq.(C5.3.37). However,this does not apply to the web plate of plate girders.
⎧
fyd
⎪
⎪
(R ≤ 0.70)⎪⎨ γb(C5.3.37)
σrd =
0.86
⎪
fyd
⎪
⎪ 0.7
(0.70 < R)⎩Rγbwhere ，

：Design material strength：Width-thickness ratio ，
1 12(1 − ν 2 ) fyk b
R=
π
k
E tf
ν ：Poisson’s ratio
k ：Buckling coeﬃcient ，k = 4.0
E ：Young’s modulus of steel
fyk ：Characteristic value of material strength (standard value)b ：Distance between ﬁxed edges of plate (refer to Fig.C5.3.4)
t ：Plate thickness
f ：Stress gradient coeﬃcient ，f = 0.32φ2 + 0.08φ + 1.00
φ ：Stress gradient ，
σ1 − σ2φ=(0 ≤ φ ≤ 2)σ1
σ1 , σ2 ：Stress at each edge of plate.
The sign of compressive stress is to be taken as positive. σ2 ≤ σ1 (refer to
Fig.C5.3.5) ．
(4) The local buckling strength of a plate supported at one edge and subject to in-plane compression

78Standard Specifications for Steel and Composite Structures [Design]

should be computed using the following Eq.(C5.3.38):
⎧
fyd
⎪
⎪
(R ≤ 0.70)
⎪
⎨ γb
σrd =
0.64
⎪
0.7
fyd
⎪
⎪
(0.70 < R)⎩Rγbwhere ，

ν
k
E
fyk
b
t

σrd
fyd
R

(C5.3.38)：Design local buckling strength：Design material strength：Width-thickness ratio ，
1 12(1 − ν 2 ) fyk b
R=
π
k
E t
：Poisson’s ratio：Buckling coeﬃcient ，k = 0.425：Young’s modulus of steel：Characteristic value of material strength (standard value)：Distance from support point to free edge (refer to Fig.C5.3.6)：Plate thickness

Fig.C5.3.6 Width of cantilever part of plate

Fig.C5.3.7 Rectangular plate

supported at one edge

subject to uniform compressive
stressThe local buckling strength of a plate subject to compressive stress can be computed basedon the elastic buckling stress of a rectangular plate of constant thickness subject to a uniform
compressive stress, as shown in Fig.C5.3.7:
σE = kπ2 E12(1 − ν 2 )tb2With the base width-thickness ratio parameter:



b
fyk
12(1 − ν 2 ) fyk
=
R=
σE
πt
k
E

(C5.3.39)(解 5.3.40)

Local buckling strength is determined by evaluating the margin in resistance after elastic bucklingof a plate with a large width-thickness ratio, taking into account also the reduction in local
buckling strength due to residual stress and initial deﬂection. Here, the minimum bucklingcoeﬃcient k is assumed to be b = ∞: Under uniform compression, a plate supported at bothedges takes k = 4.0 and a plate supported at one edge takes k = 0.425.
In Eq.(C5.3.37), the stress gradient parameter f in the width-thickness ratio parameter R is
multiplied by the stress gradient φ = 0 buckling coeﬃcientf when there is a stress gradient.
f=k(φ = φ)k(φ = 0)(C5.3.41)

79

Chapter 5 Structural Member ResistanceStress gradient parameter f is given for φ = 0, 1, 2 in Table C5.3.7. The deﬁnition of f is
obtained, for the other φ, by interpolating on a quadratic parabola as follows: ，
f = 0.32φ2 + 0.08φ + 1.00

(C5.3.42)

Table C5.3.7 Relationship between buckling coeﬃcient k,
stress gradient parameter f and stress gradient2
Stress gradient φ = σ1σ−σ
1

φ=0

φ=1

φ=2

4.0
1.0

7.81
1.40

23.9
2.44

Buckling coeﬃcient k
Stress gradient parameter f(5) The local buckling strength of a stiﬀened plate subject to unidirectional compression should, inprinciple, be computed using Eq.(C5.3.43). The stiﬀness and arrangement of stiﬀeners should
be satisﬁed 7.3.1. Speciﬁcally, the stiﬀness should be larger than the required value in theSpeciﬁcations for Highway Bridges [JRA, 2002], and the arrangement should be uniform interval.
σrd = Nusp

where ，

σrd
fyd
Nusp

fyd
γb

(C5.3.43)：Design local buckling strength：Design material strength： Standard compressive resistance of stiﬀened plate elements obtained from

Eq.(C5.3.44)

Nusp =

where ，

σculp

bt
1
+ hr tr + btσculpnnbt + (n − 1)hr tr(n − 1)σr(C5.3.44)：Non-dimensional standard compressive strength of plate supported at bothedges obtained from Eq.(C5.3.45)
σr ：Non-dimensional standard compressive strength of T-section of one longitudinal stiﬀener and plate panel between longitudinally stiﬀened members
obtained from Eq.(C5.3.46)
n ：Number of panels divided by stiﬀeners in the longitudinal direction (n ≥ 2)
b ：Total width of stiﬀened platet ：Thickness of plate panel
Values of σculp and σr can be obtained using the following equations:
σculp =

⎧
⎪
⎨ 1.0

0.7
Rcp

0.86


σr =
s2 − 4λ̄∗2
s
−
⎪
⎩
2λ̄∗2

(< 1)

(C5.3.45)(λ̄∗ ≤ 0.2)(λ̄∗ > 0.2)

(C5.3.46)

80

Standard Specifications for Steel and Composite Structures [Design]in which the following notation is used:

β=

s

=

λ̄∗

=

η

=

r

=

⎧
⎨
⎩

1 + 0.339(λ̄∗ − 0.2) + λ̄∗2

0.2
fyr
fyk ηβa
fyk
E πr
1
√
σculp

IT
AT

1
1.164C 0.251(0 < C ≤ 0.54)

1.0(0.54 < C)

h2r tr − bt2 /n2AT a 3 It
C=bITh 3 ttIt = t3
1
bt3
IT =h3r tr −3nbt+ h r trAT =ne=where ，

a
hr
tr
ht
tt
Rcp

(C5.3.47)(C5.3.48)(C5.3.49)(C5.3.50)(C5.3.51)(C5.3.52)(C5.3.53)(C5.3.54)− e2 AT(C5.3.55)(C5.3.56)：Span of stiﬀeners in the transverse direction：Height of stiﬀener in the longitudinal direction：Thickness of stiﬀener in the longitudinal direction：Height of stiﬀener in the transverse direction：Thickness of stiﬀener in the transverse direction：Width-thickness ratio of compression plate enclosed by transverse and longi-

tudinal stiﬀeners
E：Young’s modulus of steel

fyk
fyr

：Characteristic value of material strength (standard value))：Standard value of material strength (235 N/mm2 )(6) The local buckling strength of a plate supported on all edges and subject to shear stress should
be computed by:
⎧
fvyd
⎪
⎪
(Rr ≤ 0.60)
⎪
⎨ γb
τrd =
(C5.3.57)
0.32
⎪
0.6
f
⎪
vyd
⎪
(0.60 < Rr )⎩Rrγbwhere ，

τrd

：Design shear strength

fvyd
Rr

：Design material shear strength：Width-thickness ratio ，

1
Rr =
π

12(1 − ν 2 )kr

fvyk bE t

Chapter 5 Structural Member Resistance

fvyk
ν
E
kr

81

：Characteristic value of material shear strength：Poisson’s ratio：Young’s modulus of steel：Buckling coeﬃcient

kr =

⎧
⎪
⎪
⎨ 5.34 + 4.0⎪⎪⎩ 4.0 + 5.34



a
b

a
1≥
b

2

b
a
b
a

2

1<

(C5.3.58)

a：Distance between ﬁxed edges of plate (in the longitudinal
direction) (refer to Fig.C5.3.8)
b ：Distance between ﬁxed edges of plate (in the transverse
direction) (refer to Fig.C5.3.8)
t ：Plate thickness

Fig.C5.3.8 Distance between ﬁxed edges of plate(7) The local buckling strength of a plate support at both edges and subject to local loading should,
in principle, be computed using Eq.(C5.3.59).

σrd =

⎧
f
⎪
⎪ yd
⎪
⎨ γb
⎪
⎪
⎪
⎩

0.7
R

(R ≤ 0.70)
0.80(C5.3.59)

fyd
γb(0.70 < R)

Where, σrd is the design local buckling strength, which must correspond to stress level σp1 at a
position on the upper edge of the panel in question. As shown in Fig.C5.3.9, when the distancesfrom the edge of the panel in question to the upper and lower boundaries of the loading are taken
as d1 and d2 , respectively, the relationship between σp1 and the stress level σp0 at the loading or
local load P shall be obtained using the following equation:
σp1 = σp0 1 −where ，

fyd
R

d1
d

=

P
ct

1−

d1
d

：Design material strength：Width-thickness ratio ，R = 1.05

fyk b
kp E tkp ：Local buckling coeﬃcient given by Eq.(5.3.61)(C5.3.60)

82Standard Specifications for Steel and Composite Structures [Design]

kp = 0.8 + 2.4

b
a

2



⎫
⎪
a
⎪
+
ηp ⎪
⎪
⎬
a
c

c

⎪
⎪
⎪
⎪
⎭

ψp2 + 3ψp + 1
ηp =(1 + ψp )3E：Young’s modulus of steel

fykb：Characteristic value of material strength (standard value)(C5.3.61)：Distance between ﬁxed edges of plate (in the longitudinal direction) given in

Fig.C5.3.9tca：Plate thickness： Width of local loading on the upper edge of the panel shown in Fig.C5.3.9：Distance between ﬁxed edges of plate (in the transverse direction) shown in

Fig.C5.3.9.
When a exceeds acr calculated using Eq.(C5.3.62), acr should be used instead of
a.
⎧ 2
⎨ b
+b+c
(b ≤ c)acr =(C5.3.62)
10c⎩ 1.5b + 0.6c(c < b)Fig.C5.3.9 Dimensions and stress levels of panel subject to local loadingψp: Ratio of σp2 to σp1 computed by Eq.(C5.3.63)
ψp =

σp2
d − d2=σp1
d − d1(C5.3.63)

The elastic buckling stress of a constant thickness rectangular plate subject to local loading(width c) on its upper edge and simply supported on all edges is given by Eq.(C5.3.64).
σpcr = kp

π2 E12(1 − ν 2 )tb2(解 5.3.64)

Based on this stress, the slenderness ratio is deﬁned as follows.

fyk
12(1 − ν 2 ) fyk
b
R=
=
σpcr
πt
kp
E
The local buckling strength of a plate subject to local loading is determined by considering the
reduction of the local buckling resistance due to residual stress and initial deformation with thebuckling coeﬃcient calculated by Eq.(C5.3.65). The resistance larger than elastic buckling stress83

Chapter 5 Structural Member Resistanceis adopted for relatively large R-value region since the post-buckling resistance can be expected. ．
Design method of a plate subject to local loading against buckling can be found in some foreign
design codes such as BS5400 [1982] and DASt.Ri012 [1978]. The calculation method of bucklingcoeﬃcient is given in each code. In this speciﬁcation, Eq.(C5.3.65), which is the approximationof the coeﬃcient given by Moriwaki et al. [1983], is adopted as the formula to obtain bucklingcoeﬃcient kp .
kp = 0.8 + 2.4
Where, a = acr for a > acr , and
⎧ 2
⎨ b
+b+c
acr =
10c
⎩ 1.5b + 0.6c

b
a

2



c
a

+

a
c

(解 5.3.65)(b ≤ c)(c < b)In Eq.(C5.3.61), a correction factor ηp ψp based on the reference [Takimoto, 1989] is introduced
to take the inﬂuence of ψp .
It should be noted that the meaning of buckling coeﬃcient for a plate subject to local loading
may be diﬀerent even if the same symbol (k) is used. The same type deﬁnition of the bucklingcoeﬃcient as a plate in compression is adopted in this speciﬁcation as shown in Eq.(C5.3.64).
Careful attention should be paid to the treatment of σp when the equation in this speciﬁcation
is applied. In-plane stress induced by local loading is complicated. Methods for strict treatmentof this can be found in some references [Ito, 1984; JSCE, 1988; DASt.Ri012, 1978]. Since σp1 andσp2 are shown here as the expedient values to verify buckling resistance, it is not appropriate touse them for other resistance evaluation like fatigue.

5.4 Resistance of Steel Pipes(1) The tensile resistance and compressive resistance of steel pipes shall be determined according
to the provisions in 5.3.1 and 5.3.2.
(2) The bending resistance of steel pipes shall be determined on the basis of local buckling
resistance against compressive stress in the axial direction, bending stress, or a combinationof the two stresses.
(3) The shear resistance of steel pipes shall be determined in consideration of factors such as
boundary conditions, initial imperfections due to welding, including initial deformation andresidual stress, and whether the pipe is stiﬀened with rings or diaphragms.

【 Commentary 】(1) The design bending resistance of a steel pipe is generally computed using Eq.(C5.4.1).
Mbu = Mn
where ，
W
fyd
σrd

σrd
fyd

(C5.4.1)

Mn = fyd × W：Sectional modulus of the outer edge of the steel pipe
：Design material strength：Design compressive strength corresponding to local buckling of the steel pipe,

obtained from Eq.(C5.4.4)(2) The design local buckling strength of a steel pipe under compression stress is generally computed

84Standard Specifications for Steel and Composite Structures [Design]using Eq.(C5.4.2).
⎧ f
yd
⎪
⎪
⎨ γb
σrd =
⎪
0.0330⎪⎩ 0.723 +Rt
where ，

σrd
fyd
Rt

(Rt ≤ 0.119)(C5.4.2)fyd
γb(0.119 < Rt ≤ 0.355)：Design compressive strength corresponding to local buckling of the steel pipe
：Design material strength：Radius-thickness ratio ，

fyk r
E t
：Characteristic value of material strength (standard value)：Young’s modulus of steel：Wall thickness of steel pipe
：Radius of steel pipe (distance from center to outer edge)

Rt = 1.65
fyk
E
t
r

(3) The design local buckling strength of a steel pipe under bending stress is generally computed
using Eq.(C5.4.3).
⎧
fyd
⎪
⎪
⎨ 1.20 γb
σrd =⎪0.0330⎪⎩ 0.867 +Rt(Rt ≤ 0.099)(C5.4.3)fyd
γb(0.099 < Rt ≤ 0.279)

Where ，σrd : Design bending strength in compression of the steel pipe
fyd , fyk , Rt , t, r : as deﬁned in (Eq.(C5.4.2)) ．
(4) The design local buckling strength of a steel pipe under both bending and compressive stresses
is generally computed using Eq.(C5.4.4).
⎧ f
yd
⎪
⎪
⎨ f γbσrd =⎪0.0330⎪⎩ 0.723f +Rt
where ，

σrd(Rt ≤ 0.119)
fyd
γb

0.119
0.355
< Rt ≤
f
f(C5.4.4)：Design compressive strength corresponding to local buckling of steel pipef：Coeﬃcient depending on stress gradient f = 1 +φ：Stress gradientφ10

σ1 − σ2(0 < φ < 2)
σ1
：Total stress level on the side of the steel pipe where compression occurs. The
sign shall be taken as positive for compressive stress.
：Total stress level on the side of the steel pipe where tension occurs. The sign
shall be taken as positive for compressive stress.
φ=

σ1
σ2

fyd , fyk , Rt , t, r is deﬁned in (Eq.(C5.4.2))(5) The design shear strength of a steel pipe is generally computed using Eq.(C5.4.5) when it isstrengthened with rings or diaphragms.
⎧
fvyd
⎪
⎪
⎨
γb
τrd =
⎪
0.57fvyd 1⎪⎩
Rr1.25 γb(Rr ≤ 0.638)(C5.4.5)(0.638 < Rr ≤ 1.50)

85

Chapter 5 Structural Member Resistance

where ，

τrd
Rr

：Design shear strength of steel pipe
：Radius-thickness ratio parameter,

Rr = 2.63
E
t
r
fvyk

fvyk
E

0.8

r
t

：Young’s modulus of steel：Wall thickness of steel pipe
：Radius of steel pipe (distance from center to outer edge)：Characteristic value of material shear strength

5.5 Resistance of Cables
The design resistance of cables shall be taken as the value calculated by equation (5.5.1).
Nrd =where,

Nrd
fd
An
γb

An fd
γb

(5.5.1)：design resistance of cables：design strength of the material：nominal cross sectional area of the cable：structural member factor【 Commentary 】

As a general rule, the wires in parallel wire strands must not have joints except when using the AS
construction method.
In computing the strength of wire joints in the AS construction method, the partial factor of
members at the joints can be made smaller value than that for the non-jointed portions according
to a responsible engineering judgment based on a consideration of the eﬃciency of ﬁeld joints. It
must be veriﬁed through tests at the plant that the strength of joints exceeds that of non-jointed
portions. As an example, in [HSBA, 1980], the allowable stress of wires making up a cable is reduced. 610N/mm2 ) from the standard value of 6400kgf/cm2(=. 630N/mm2 ) at joints. The
to 6200kgf/cm 2(=.
.
characteristic value of material strength for cable wires can be deﬁned either as the ultimate strengthof the wire or as 0.7% or 0.8% of total elongation strength. The latter is generally used.
For further reference, the results of investigations by the Honshu-Shikoku Bridge Authority [HSBA,
2003] are presented here as a recent example. The investigation concluded that 0.8% of the actual
measured value of total elongation resistance can be used as the standard wire strength for design
when wires with the same speciﬁcation and manufactured by the same method as those used for Akashi
Kaikyo Bridge are employed in future projects. These suspension bridge cables were manufactured
using very special techniques and the standard of quality control was particularly high. The total. 1760N/mm2 )elongation for deﬁning resistance was revised from 0.7% to 0.8% when the 180kgf/mm2(=.
. 1570N/mm2 ) wire used forwire developed for the Akashi Kaikyo Bridge replaced the 160kgf/mm2(=.
the Seto-Ohashi and other bridges constructed earlier by the HSBA (corresponding to the design code
mentioned above, [HSBA, 1980]). The resistance of the wires for the Akashi Kaikyo Bridge is deﬁned as. 1370N/mm2) in the speciﬁcation, but actually measured values for 3,016
a minimum of 140kgf/mm2 (=.
. 1495N/mm2 ) and a standard
specimens were very stable, with an average value of 152.5kgf/mm2(=
.
.
.
2
2
2
16.3N/mm
).
A
value
of
150kgf/mm(=
1470N/mm) was adopted as thedeviation of 1.66kgf/mm2(=.
.
standard value for design by rounding down this average value.

86Standard Specifications for Steel and Composite Structures [Design]

References in Chapter 5
Bleich, F.(1952) ：Buckling Strength of Metal Structure, McGRAW-HILL.
DASt-Richtlinie 012(1978) ：Deutscher Ausschuss fur Stahlbau ．
Study Group of Structures in Tokai(1980) ： Evaluation of Strength of Steel Structural Members and Its Application to a Reliability Design, Bridge and Foundation Engineering, Vol.14, No.11.
Honshu-Shikoku Bridge Authority(1980) ：Design Speciﬁcations for Superstructure.
BS5400(1982) ：British Standards Institution; Part 3 ．
Moriwaki, R., Takimoto, T. and Mimura, Y.(1983) ： Ultimate Strength of Girders under Patch Loading, Proceedings of JSCE, No.339.
Ito, K.(1984) ：An Example of Stability Veriﬁcation of Plate Girder Web under Vertical Patch Loading according to ．
Japan Society of Civil Engineers(1988) ：Collaborate Research Report on Strength and Design of Thin-walled
Structures, Kansai Branch.
Takimoto, T.(1989) ： Buckling Strength of Girder Webs under Patch Loading, R&D Kobe Steel Engineering
Reports, Vol.39.
Japan Society of Civil Engineers (1994) ：Ultimate Strength and Design of Steel Structure, Steel Structure
Series 6 ．
Japan Society of Civil Engineers (1997a) ：Design Code for Steel Structures, PART A; Structures in General.
Japan Society of Civil Engineers (1997b) ：Design Code for Steel Structures, PART B; Composite Structures.
ISO(1997) ：ISO10721 Steel Structures, Part 1：Material and Design ．
AASHTO(1998) ：LRFD Bridge Design Speciﬁcations, SI Unit Second Edition ．
Japan Road Association (2002) ：Speciﬁcations for Highway Bridges and Commentary ．
Honshu-Shikoku Bridge Authority(2003) ：Committee Repot on Safety Factor of Cables for Strait Crossing
Road.
Japan Society of Civil Engineers(2005) ：Buckling Design Guidelines, Ver.2 [2005 Version].
CEN(2003) ：Eurocode 3 Design of Steel Structures, Part 2: Steel Bridges -, prEN 1993-2 ．

87

Chapter 6 Demand for Safety and Verification
6.1 General(1) Safety shall be veriﬁed in consideration of all actions that might arise during the erection
period and the design working life.
(2) Structural safety and public safety shall be the performance items veriﬁed to meet the safety
requirement.
(3) An appropriate limit state shall be established for each performance item and safety shallbe veriﬁed against the limit states of all performance items.

【 Commentary 】

In the speciﬁcations, two performance requirements are prescribed for safety: structural safety andpublic safety. The former deals with the safety of the structure itself as judged, for example, by its loadcarrying capacity, while the latter relates to ensuring the safety of any members of the public present
in the neighborhood of the structure. Depending on the circumstances of the structure’s location,
public safety may not be a factor. In this chapter, therefore, the speciﬁc veriﬁcation procedures only
for structural safety are provided. It should also be noted that the safety of structural members
and structural elements is dealt in this chapter, while the safety of connections is left for Chapter
11 ”Joints.” The performance requirements given in this chapter are the basic ones for composite
structures and their veriﬁcation, but the computation of load-carrying capacities in some situations
are diﬀerent in the case of composite structures and they have some unique structural components,
such as shear connectors. Their safety is therefore discussed separately in Chapter 15 ”Design ofComposite Girders” for the beneﬁt of readers.
Structural safety is usually veriﬁed by ensuring that the loading capacity of the structure exceeds
demand. As actions such as loads increase, deformation and induced stress increase and the structure
may change state from elastic behavior to elasto-plastic behavior, and/or from stable behavior to
unstable behavior. This will eventually lead to structural failure. To be speciﬁc, in the course of thisfailure process, structural performance needs to be veriﬁed from various viewpoints associated withelastic response, plastic response, buckling, stability as a rigid-body, stability of the whole structure,displacement/deformation, and so forth.

6.2 Performance Requirement for Safety
6.2.1 Structural Safety
Steel and composite structures shall satisfy the requirements for load-carrying and displacement/deformation capacity and also shall be stable under the actions given in Chapter 2.
【 Commentary 】

Structural safety concerns two aspects of structural performance: load-carrying capacity and stability. The phenomena associated with load-carrying capacity include member fracture, local bucklingof a plate, buckling of a member, and buckling of the whole structure. The load-carrying capacity ofthe structure is inﬂuenced by material strength (tensile strength, compressive strength, shear strength,

88Standard Specifications for Steel and Composite Structures [Design]etc.), buckling strength, deformation capacity, fabrication and erection imperfections, and so on. The
major causes of loss of stability are sudden loss of stiﬀness due to buckling and the collapse, sliding,or uplift of the whole structure and/or part of the structure.
As actions such as loads increase, deformation and induced stress increase. As a result, a structurethat is in an elastic state may become elasto-plastic, and/or a stable structure may become unstable.
Eventually, failure will take place. Even if part of a structure reaches a state of failure, the failure of
the whole structure has to be prevented under the actions speciﬁed in Chapter 2. To that end, it isdesirable to verify this performance requirement by direct simulation. However, at the current stage ofdevelopment, such a simulation is not practical for day-to-day design. Therefore, the basic approach inthis code is to verify that members and connections possess suﬃcient load-carrying capacity. It should
be noted that design for seismic loads of level 2 is exceptional; the capacity of the whole structure is tobe veriﬁed even in the current design practice. This class of design is dealt with in the Seismic Volumeof the standards speciﬁcations.
The limit states that control structural performance with respect to load-carrying capacity, displacement/deformation, and stability can be set at various points during the course of progressive
failure for a member or for the whole structure, depending on the objective, the importance, therestorability requirements of the structure, and so on. The importance of the structure is determinedfrom its expected working life, the function of its members, and the eﬀect that collapse would have.
The load-carrying capacity, displacement/deformation capacity, and stability need to be determinedby considering these aspects appropriately.
In practice, the actions to which a structure is subjected, the method of structural analysis, thepartial factors, and so on can vary depending how the strength limit states are set. In past design codesfor steel and composites structures, the elastic limit was assumed to be the load-carrying capacity thatcan generally be relied on for structural safety, regardless as to whether the code is based on allowablestress design or limit state design. However, if the cross section of a member is compact, the state where
the whole cross section becomes plastic may be taken as the load-carrying capacity of the member.

6.2.2 Public Safety
The public shall be protected from any possible hazard that a steel or composite structure mightpose throughout its service life.
【 Commentary 】

If a structure sheds cover concrete or high-tensile bolts (due to delayed failure), injury may occur
to the public and damage any property below. Public safety is the performance that is required toprevent such incidents.
No speciﬁc veriﬁcation methods are given here, but depending on the surroundings of the structure,design engineers are required to institute performance requirements and to carefully select materials
and the implementation of preventive measures.

6.3 Verification of Structural Safety
6.3.1 Verification of load-carrying capacity
The veriﬁcation of load-carrying capacity shall entail ensuring that the design action eﬀect issmaller than the design member capacity.
【 Commentary 】

89

Chapter 6 Demand for Safety and Verification

Although performance-based design does not impose any restrictions on the choice of approach tothe veriﬁcation of structural safety, the reliability-based design method is becoming the global standard.
Nevertheless, suﬃcient probabilistic data are not always available, so quite often the probability of
failure cannot be evaluated directly. Therefore, this code employs the partial-factor method as thebasic veriﬁcation approach. Details of the partial-factor method are given in Chapter 1 ”General” of
the General Provisions Volume.
6.3.1.1 Verification of load-carrying capacity of members in framed structure
The load-carrying capacity of a structural member in a framed structure shall be veriﬁed for all
applicable cases among the following:(1) axial force(2) bending moment(3) combined axial force and bending moment(4) shear force or a combination of shear force and torsional moment(5) combined axial force, bending moment, and shear force(6) biaxial stress in the above ﬁve cases when signiﬁcant【 Commentary 】

For each veriﬁcation item of structural safety, the veriﬁcation equations in the Design Code for
Steel Structures [JSCE, 1997] are presented here as an example of a possible veriﬁcation approach in
the form of the partial factor method.
(1) Veriﬁcation of axial force capacity
The safety performance of a member subjected to axial force can be veriﬁed using the following
equation:
γiwhere ，

γi
Nsd
Nrd

Nsd
≤ 1.0
Nrd

(C6.3.1)：structure factor：design axial force：design axial force resistance

Using this veriﬁcation equation, the demand, the resistance (limit value), and the partial factor inthis code are explained.
The structure under loading by the product of the characteristic design load and the load factor isanalyzed by the relevant method. The axial force thus obtained is then multiplied by the structural
analysis factor. This ﬁnal axial force result is the demand, Nsd , in Eq.(C6.3.1). The design axial force
resistance, Nrd , is the lower bound of the capacity evaluated by considering the scatter in material
properties, size, and shape as well as the eﬀects of the fabrication process and possible local bucklingby way of partial factors. More details of this process are available in Chapter 5. Performance isveriﬁed if the resistance (limit value) is found to be greater than the demand; here the structure factor
that represents the importance of the structure needs to be taken into account.
(2) Veriﬁcation of bending moment capacity
The safety performance of a member subjected to bending moment can be veriﬁed using the following equation:
γi

Msd
≤ 1.0
Mrd

(C6.3.2)

90Standard Specifications for Steel and Composite Structures [Design]where ，

γi
Msd
Mrd

：structure factor：design bending moment：design bending moment capacity based on the classiﬁcation of cross sectionsin 5.3.3.1 (Table C5.3.3.)
In the allowable stress design method widely-used at present, the bending moment capacity of amember is given by one of the following limit states being reached: yielding at the edge of a crosssection, global lateral-torsional buckling, or local buckling. However, in view of performance-based
design, it would be more desirable if the bending moment capacity beyond the local buckling of a thinwalled member or up to the plastic moment of a thick-walled member could be taken into account indesign. To that end, the interaction of plastic deformation, local buckling, and global lateral-torsional
buckling needs be evaluated properly and the classiﬁcation of the cross sections based on the plastic
limit width-thickness ratio and the elastic limit width-thickness ratio would then be required. For theveriﬁcation of a composite girder, it is necessary to evaluate the design bending-moment eﬀect and thedesign bending moment capacity by taking the composite action into consideration, the details of which
are given in Chapter 15. It should be noted that the veriﬁcation equation is commonly expressed in
the following form, in which the components in two directions (y-direction, z-direction) are summed:

a
b

Msdy
Msdz
+ d γi≤ 1.0(C6.3.3)
c γi
Mrdy
Mrdz
where ，a, b, c, d：the constants, the values of which depend on the classiﬁcation of the crosssection, the shape of the cross section, and so on.

＜ Example of Verification of Capacity under Bending Moment (Design Code for Steel

Structures Part A (JSCE 1997)) ＞
Slender Section, Non-compact Section, Compact Sectiona) Veriﬁcation of cross-section capacity


Msdy
Msdz
γi
+
≤ 1.0
Mrdy
Mrdz
b) Veriﬁcation of member capacity


γi

Msdy
Msdz
+
Mrdy
Mbrdz

(C6.3.4)

≤ 1.0

Compact section
Box-, I-, and H-shaped cross sections:a) Veriﬁcation of cross-section capacity
Box-shaped, π-applied and circular cross sections:
2

Msdy
Msdz
3
Msdy
Msdz
+ γi
≤ 1.0 for
≤
γi
4
Mrdy
Mrdz
Mrdy
Mrdz
2

Msdy
Msdz
3
Msdy
Msdz
γi
+
≤ 1.0 for
>
γi
Mrdy
4
Mrdz
Mrdy
Mrdz

(C6.3.5)(C6.3.6)(C6.3.7)

I- and H-shaped cross sections:γib) Veriﬁcation of member capacity
γiα


2
Msdy
Msdz
+ γi
≤ 1.0
Mrdy
Mrdz



Msdy
Mrdy



α
+

Msdz
Mbrdz

(C6.3.8)

α 
≤ 1.0

(C6.3.9)

Chapter 6 Demand for Safety and Verification

where ，

Msdy , Msdz

Meqy , Meqz

Mrdy , Mrdz

Mbrdz

91

α = 1.4 for box-shaped cross sections
α = 1.0 for I- and H-shaped cross sections with B/D < 0.3
α = 0.4 + B/D ≥ 1.0 with B/D
B ：ﬂange width
D：height of the cross section：design bending moments about the weak and strong axes acting in the crosssection to be veriﬁed, respectively. When the bending moments vary linearly
along the member, Msdy , Msdz in Eq.(C6.3.7) may be replaced by the equivalent bending moments Meqy , Meqz , respectively.
: equivalent bending moments about the weak and strong axes, respectively,
given by the following formula:
Meq = 0.6M1 + 0.4M2 ≥ 0.4M1
where ，M1 , M2 are the bending moments at the ends of the member, and M1 >M2 where the bending moment is positive when stress in the ﬂange underconsideration is compressive.
: design bending-moment capacities about the weak and strong axes, respectively, of the cross section to be veriﬁed, which are evaluated by referring to
the classiﬁcation of cross sections in section 5.3.3.1. Using the base bendingmoment capacities Mny , Mnz given in section 5.3.3.2, they can be expressed asfollows:
Mrdy = Mny /γb , Mrdz = Mnz /γb
For a cross section that cannot attain the plastic moment Mp , the veriﬁcationmust be ensured for both tension and compression sides with Mtrdy , Mcrdy andMtrdz , Mcrdz：design bending moment of the member for the veriﬁcation, which includes
the inﬂuence of lateral-torsional buckling about the weak axis. The capacity isgiven by Eq.(C5.3.2) in section 5.3.3.2, for example.

Explanation of the veriﬁcation example
In principle, Eqs.(C6.3.4) and (C6.3.5) are used in this veriﬁcation example. Eq.(C6.3.4) is theveriﬁcation equation for the ultimate bending moment of each cross section in which local bucklingeﬀect is taken into account, and Eq.(C6.3.5) is the veriﬁcation equation for lateral-torsional buckling
capacity, which includes the eﬀect of interaction with local buckling. In a beam with a compact section(that is, with a width-thickness ratio of the constituent plates so small that the plastic moment canbe reached under bi-axial moments), a capacity greater than that evaluated by the simple additionof Eqs.(C6.3.4) and (C6.3.5) can be expected. Therefore, for rational design, the application of thenonlinear interaction strength Eqs.(C6.3.6) to (C6.3.9) is approved in this code.
(3) Veriﬁcation of capacity under combined axial force and bending moment
The safety performance of a member subjected to both axial force and bending moment can be
veriﬁed using the following equation:


Nsd
Msdy
Msdz
+
+
≤ 1.0
(C6.3.10)
γi
Nrd
Mrdy
Mrdz
where ，

Nsd , Msdy , Msdz
Nrd , Mrdy , Mrdz

：design axial force and design bending moments：design axial force capacity and design bending-moment capacities

referring to the classiﬁcation of cross sections (Table C5.3.3) in section
5.3.3.1

92Standard Specifications for Steel and Composite Structures [Design]＜ Example of Verification of Capacity under Combined Axial Force and Bending Moment(Design Code for Steel Structures Part A (JSCE 1997)) ＞
Slender Section, Non-compact Section, Compact Section
1) Tensile axial force
The safety performance of a member subjected to both tensile axial force and bending moment canbe veriﬁed using the following equation:


Nsd
Msdy
Msdz
+
+
γi
≤ 1.0
(C6.3.11)
Ntrd Mtrdy
Mtrdz


Msdy
Msdz
Nsd
γi −
+
+
≤ 1.0
(C6.3.12)
Ntrd
Mcrdy
Mcrdz


Msdy
Msdz
Nsd
+
+
≤ 1.0
(C6.3.13)
γi −
Ntrd
Mcrdy
Mbrdz
2) Compressive axial force
The safety performance of a member subjected to both compressive axial force and bending moment
can be veriﬁed using the following equation:


Nsd
Msdy
Msdz
+
+
γi
≤ 1.0
(C6.3.14)
Ncrdl
Mcrdy
Mcrdz


Msdy
Msdz
Nsd
γi −
+
+
≤ 1.0
(C6.3.15)
Ntrd
Mtrdy
Mtrdz


Nsd
Msdz
Msdy
+
γi
+
≤ 1.0 (C6.3.16)
Ncrd
Mcrdy (1 − Nsd /Ncry ) Mbrdz (1 − Nsd /Ncrz )Compact section
1) Tensile axial force
The capacity of a compact section subjected to both tensile axial force and bending moment canbe veriﬁed using the following equation:


Nsd
Msdy
Msdz
γi −
≤ 1.0
(C6.3.17)
+
+
Ntrd
Mcrdy
Mbrdz
Further veriﬁcation is required using the following veriﬁcation equations for the respective crosssection types:a) Cross-sectional capacity of box-shaped cross section or circular hollow cross section
2

Msdy
Msdz
Msdy
Msdz
3
+ γi
≤ 1.0 for≤(C6.3.18)
γi
4
Mnpy
Mnpz
Mnpy
Mnpz
2

Msdy
Msdz
3
Msdy
Msdz
γi
+
≤ 1.0 for>(C6.3.19)
γi
Mnpy
4
Mnpz
Mnpy
Mnpz

where ，



Nsd Mpy
Mpy
Mnpy = C 1 −≤Ntrd γbγb
C = 1.18 for a box-shaped cross section ，C = 1.25
Nsd Mpz
Mpz
Mnpz = C 1 −≤Ntrd γbγbfor a circular hollow cross sectionb) Cross-sectional capacity of I- or H-shaped cross sections

2
Msdy
Msdz
+ γi
≤ 1.0
γi
Mnpy
Mnpz

(C6.3.20)

93

Chapter 6 Demand for Safety and Verification
where ，



Mnpy = 1.19 1 −

Nsd
Ntrd

2 

Mpy
Mpy
≤
γb
γb



Nsd Mpz
Mpz
Mnpz = 1.18 1 −≤Ntrd γbγb2) Compressive axial force
The capacity of a compact section subjected to both compressive axial force and bending moment
can be veriﬁed using the following equations.
a) Box-shaped and circular hollow cross sections
The capacity of a cross section can be veriﬁed using the following equations:
2

Msdy
Msdz
+ γi
γi
Mnpy
Mnpz
2

3
Msdy
Msdz
γi
+
γi
Mnpy
4
Mnpz
3
4

with ，≤

1.0 for

Msdy
Msdz
≤
Mnpy
Mnpz

(C6.3.21)≤

1.0 for

Msdy
Msdz
>
Mnpy
Mnpz

(C6.3.22)


Nsd Mpy
Mpy
Mnpy = C 1 −
≤
N
γ
γb
trd
b


C = 1.18 for a box-shaped cross section and C = 1.25
Nsd Mpz
Mpz
Mnpz = C 1 −≤Ntrd γbγbfor a circular hollow cross section.

The capacity of a member can be veriﬁed using the following equation:

α 
β
Msdy
Msdz
γi
+ γi
≤ 1.0
Mnuy
Mnuz

where ，

(C6.3.23)




Nsd
Nsd Mpy
Mnuy = 1 −
1−
Ncrd
Ncry
γb



Nsd
Nsd Mbuz
Mnuz = 1 −
1−
Ncrd
Ncrz
γb
α = 1.3 +Nsd 1000≥ 1.4
Ncrdl (/ry )2

β = 1.3 +Nsd 1000≥ 1.4
Ncrdl (/rz )2b) I- and H-shaped cross sections
The capacity of a cross section can be veriﬁed using the following equation:
γi


2
Msdy
Msdz
+ γi
≤ 1.0
Mnpy
Mnpz


(C6.3.24)

2 
Nsd
Mpy
Mpy
≤
where ， Mnpy = 1.19 1 −
Ncrdl
γb
γb


Nsd Mpz
Mpz
Mnpz = 1.18 1 −≤Ncrdl γbγbThe capacity of a member can be veriﬁed using the following equation:

α 
α 
Msdz
Msdy
α
+
≤ 1.0
γi
Mnrdy
Mnrdz

(C6.3.25)

94Standard Specifications for Steel and Composite Structures [Design]

α = 1.0(B/D < 0.3)

B
Nsd
≥ 1.0
(B/D ≥ 0.3)+
α = 0.4 +ND crdl
Nsd
Nsd Mpy
Mnrdy = 1 −
1−
Ncrd
Ncry
γb



Nsd
Nsd Mbrdz
Mnrdz = 1 −
1−
Ncrd
Ncrz
γb
where ，

BD

：ﬂange widthfyd：design material strengthAgry , rz
Zy , Zz
Nsd
Msdy , Msdz

Meqy , Meqz

Mbrdz

Mcrdy , Mcrdz

Mtrdy , Mtrdz

Mpy , Mpz

：height of the cross section：eﬀective buckling length of a member. The standard values are given in Table

C5.3.1, but they have to be adjusted when the constraints are insuﬃcient.
：gross area of the cross section to be veriﬁed：radii-of-gyration of the gross area about the weak and strong axes, respectively：plastic section modulus of the gross area about the weak and strong axes,
respectively：absolute value of design axial force (N ) ．
：design bending moments about the weak and strong axes acting in the crosssection to be veriﬁed, respectively. However, when the moments vary linearly,
Mdy , Mdz may be replaced by the equivalent bending moments, Meqy , Meqz ,respectively.
：equivalent bending moments about the weak and strong axes, respectively,
given by the following formula:
Meq = 0.6M1 + 0.4M2 ≥ 0.4M1
where ，M1 , M2 are the bending moments at the ends of the member, and
M1 > M2 where the bending moment is positive when stress in the ﬂange
under consideration is compressive.
：design bending moment capacity of a beam member to be veriﬁed, which takes
into account the lateral-torsional buckling about the weak axis. For example,
it can be evaluated using Eq.(C5.3.2) in section 5.3.3.2.
：design bending-moment capacities about the weak and strong axes, respectively, of the cross section to be veriﬁed with the focus on the compressive
side. These capacities are evaluated by referring to the classiﬁcation of crosssections in section 5.3.3.1. Using the base bending-moment capacities of thecross section of a beam shown in section 5.3.3.2, Mny , Mnz , those capacities
can be expressed by the following equations:Mcrdy = Mny /γb ,Mcrdz = Mnz /γb： design bending-moment capacities about the weak and strong axes, respectively, of the cross section to be veriﬁed with the focus on the tensile side.
These capacities are evaluated by referring to the classiﬁcation of cross sections in section 5.3.3.1. Using the base bending-moment capacities of the crosssection of a beam shown in section 5.3.3.2, Mny , Mnz , those capacities can be
expressed by the following equations:Mtrdy = Mny /γb ,Mtrdz = Mnz /γb： plastic moments about the weak and strong axes of the cross section to be
veriﬁed, respectively, given by the following equations:
Mpy = fyd Z,
Mpz = fyd Zz

95

Chapter 6 Demand for Safety and Verification

Ncry , Ncrz

Ncrdl

Ncrd
Ntrd
Qc

：Euler buckling loads about the weak and strong axes, respectively, given by

the following equations with slenderness ratios λ̄ in Eq.(C5.3.1):
Ag fydAg fydNcry =,
Ncrz =
2λ̄y
λ̄2z：axial compressive resistance of the cross section that takes local buckling into
account, which is given by the following equation:
Qc fyd Ag
Ncul =
γb：axial compressive force capacity of the member that takes local buckling into
account, as given by Eq.(C5.3.1)： axial tensile force capacity of the cross section given by the smaller of thevalues given by Eqs.(C5.3.1) and (C5.3.2)：eﬀective section modulus to include local-buckling eﬀect, which is ”the dimensionless strength of a short column undergoing local buckling” given by
Eq.(C5.3.1)

Explanation of veriﬁcation example
In Design Speciﬁcations for Highway Bridges, which is based on allowable stress design, the limit
states due to yielding, the overall buckling of a member, and the local buckling of a cross section
are assumed to be independent of each other even when the member is subjected to both axial force
and bending moment. Veriﬁcation equations that require only linear structural analysis have been
constructed for each of those limit states, respectively. On the other hand, even for a member subjected
to bending moment, the inﬂuence of local buckling is included by reducing the eﬀective cross-sectional
area in the above equations, while capacity can be expected to be greater than the initial yield point
for a member with a compact section.
The above approach recognizes two cases of axial tension and axial compression, with veriﬁcation
equations established separately for the limit states associated with the two cases. For rational design,
the nonlinear veriﬁcation Eqs.(C6.3.18) to (C6.3.25) can be used for the veriﬁcation of a member witha compact section.
(4) Veriﬁcation of capacity under shear force or under combined shear force and torsional moment
1) The eﬀective area of the cross section of a member subjected to shear force is the gross area of
the web and is computed using the following equation:
γiwhere ，

Vsd
Vrd

Vsd
≤ 1.0
Vrd

(C6.3.26)：design shear force：design shear resistance2) The safety of a member subjected to combined shear force and torsional moment is veriﬁed using
the following equation:


Vsd
Tsd
+
γi
≤ 1.0
(C6.3.27)
Vrd
Trd
where ，

Vsd
Vrd
Tsd
Trd

：design shear force：design shear resistance：design torsional moment about the shear center：design torsional moment resistance about the shear center

The safety of a member such as a web against shear force in a plate girder or similar structure canbe veriﬁed using approach 1) above based on the assumption that shear stress is constant over the96Standard Specifications for Steel and Composite Structures [Design]

web. However, the safety veriﬁcation of a ﬂange requires the computation of shear stress by the shear
ﬂow theory, because shear stress varies along the center line of the plate.
Approach 2) above, which takes into account torsional moment as well as shear force, is used forcases such as curved members the where torsional eﬀect cannot be ignored if loading is applied in the
direction of the strong axis. In general, a box girder is designed with high torsional resistance when asigniﬁcant torsional moment is expected.
＜ Example of Verification of Capacity under Combined Shear Force and Torsional Moment (Design Code for Steel Structures Part A (JSCE 1997)) ＞
Slender Section, Non-compact Section, Compact Section

1) By assuming that the gross area of the web is the eﬀective area of the cross section when amember is subjected to shear force, the safety of the member against the shear force is veriﬁed using
the following equation:
γi

Vsd
≤ 1.0
Vrd

(C6.3.28)

2) The safety of a member (box girder) against shear force and torsional moment is veriﬁed using
the following equations:



Tsds
Tsdω
Vsd
+
+
≤ 1.0
Vrd
Tsrd Tωrd


Msdz
Msdω
γi
+
≤ 1.0
Mtrdz
Mωrd


Msdz
Msdω
≤ 1.0
+
γi
Mcrdz
Mωrd

γi

(C6.3.29)(C6.3.30)(C6.3.31)

Note that the St. Venant torsion, Tsds , and warping torsion, Tsdω , are negligible forκ¡0.4 and κ ＞
10, respectively, where torsional constant ratio κ is given by the following equation:κ=where ，

Vsd
Vrd
Tsds
Tsdω
Msdz
Msdω
Tsrd

：design shear force：design shear force resistance：St. Venant torsion in the cross section：warping torsion in the cross section：bending moment in the cross section： bi-moment in the cross section：design St. Venant torsion resistance of a cross section,

τrd Kh：torsional constant of a cross section：converted edge-distance for St. Venant torsion⎧⎨ t (open cross-section)
2Ac
τrd =
(closed cross-section)⎩
t 1/tds：plate thickness：area enclosed by the centerline of plate thickness：coordinate along the centerline of plate thickness：design warping torsion resistance of a cross section
Tsrd =

K
h

t
Ac
s
Tωrd

GK
EIωω

(C6.3.32)

97

Chapter 6 Demand for Safety and Verification

Mtrdz

Mcrdz

Izz
Zt , Zc
Mωrd：design bending moment resistance to verify the capacity on the tension sideof the cross section given by
Izz fydMtrdz =
Zt γb：design bending moment resistance to verify the capacity on the compression
side of the cross section given by
Izz fydMcrdz =
Zc γb：moment of inertia about the strong axis of the cross section：distances from the origin of z-axis (neutral axis) to the edges on the compression and tension sides, respectively (mm)：design bi-moment resistance of the cross section given byIωω fydωmax γb：moment of inertia about the warping：warping function：torsional constant ratio：span with respect to torsion：shear modulus：Young’s modulus
Mωrd =

Iωω
ωmax
κ

G
E

Eq.(C6.3.28) is an approximate equation for verifying
the safety of a member such as a plate girder or similar
structural member subjected to shear force. By assumingAfthe distribution of shear stress is constant over the web,as shown in Fig.C6.3.1, the eﬀective area Ae of the crossw
Aw
section becomes equal to the area of the web. However, thiskind of approximation cannot be made for a ﬂange. Shear
ﬂow theory, in which shear stress varies along the centerlineof plate thickness, must be employed and the shear stress
Fig.C6.3.1 Shear stress in web
thus computed needs be used to verify the safety of theﬂange.
Veriﬁcation of structural safety against combined torsional moment and shear force needs to be
carried out when the eﬀect of torsion in a curved member becomes signiﬁcant due to loading applied in
the direction of the strong axis. In a plate girder or similar thin-walled member, the torsional moment
is the sum of St. Venant torsion and warping torsion. The St. Venant torsion causes only shear stressin the cross section while the warping torsion induces normal stress due to warping as well as shear
stress in equilibrium with that normal stress. In Eq.(C6.3.29), Tsds is the St. Venant torsion and Tsdωis the warping torsion associated with warping. In Eqs.(C6.3.30) and (C6.3.31), Msdz is the bending
moment about the strong axis and Msdω is the bi-moment. In a thin-walled member subjected totorsional moment, both St. Venant torsion and warping torsion act. However, in general St. Venanttorsion is dominant in a closed cross section such as a box girder, while warping torsion is greater inan open cross section such as an I-, π-, or U-shaped section. Since the contributions of the St. Venanttorsion and the warping torsion can be estimated from the torsional constant ratio κ computed by
Eq.(C6.3.32), it is stated that in Eq.(C6.3.29) only the warping torsion Tsdω needs to be consideredin the case of κ < 0.4 and that only the St. Venant torsion Tsds is important in the case of κ > 10.
For 0.4 < κ < 10, bending-torsional theory in which the eﬀects of both the St. Venant torsion Tsds
and the warping torsion Tsdω are taken into account must be employed to verify safety. In general,a member under signiﬁcant torsion is designed to have a box section which possesses large torsional

τ=S/A

98

Standard Specifications for Steel and Composite Structures [Design]

moment resistance.
(5) Veriﬁcation of capacity under combined axial force, bending moment and shear force
The safety performance of a member subjected to combined axial force, bending moment, and shear
force should be veriﬁed using the following equation:
γi2where ，

Nsd , Msd , Vsd
Nrd , Mrd , Vrd



Nsd
Msd
+
Nrd
Mrd1



2
+

Vsd
Vrd

2 
/1.21 ≤ 1.0(C6.3.33)：axial force, design bending moment, and design shear force：design axial force resistance, design bending moment resistance,and design shear force resistanceThis veriﬁcation equation deals with the situation where both normal and shear stresses act by utilizing the shear energy hypothesis. This hypothesis is good only for the elastic state, so no classiﬁcationof cross sections is needed. For the veriﬁcation of capacity against such a resultant, experience showsthat the resistance in terms of stress can be increased by 10% in general, leading to the appearance of
the ﬁgure 1.21 (the square of 1.1) in the denominator on the left hand side.
Note that when torsional moment is considered in addition to bending moment and shear force,the eﬀect of the torsional moment has to be included in all terms associated with the bending moment
and the shear force.
＜ Example of Verification of Capacity under Resultant Stress (Design Code for Steel
Structures Part A (JSCE 1997)) ＞

In a situation where both axial and shear stresses are signiﬁcant, the resultant stress should beveriﬁed. Two such cases are illustrated here.
1) The safety performance of a member against combined axial force, bending moment, and shear
force should be veriﬁed using the following equations
γi2



Nsd
Msdy
Msdz
+
+
Nrd
Mrdy
Mrdz



2
+

Vsdy
Vsdz
+
Vrdy
Vrdz

2 
/1.21 ≤ 1.0(C6.3.34)

2) When the eﬀect of torsional moment needs to be considered additionally, the following equationmust be used:

2 
2 
Vsdy
Nsd
Msdy
Msdz
Msdω
Vsdz
Tsds
Tsdω
2
γi
+
+
+
+
+
+
+
/1.21 ≤ 1.0 (C6.3.35)
Nrd
Mrdy
Mrdz
Mωrd
Vrdy
Vrdz
Tsrd
Tωrd
where ，

Nsd
Msdy , Msdz

：absolute value of design axial force：design bending moments about the weak and strong axes in the cross section,

respectively
Vsdy , Vsdz
Tsds
Tsdω
Msdω
Nrd

：design shear forces in the y- and z-axes in the cross section, respectively：St. Venant torsion in the cross section：warping torsion in the cross section：bi-moment in the cross section：axial force resistance of the cross section given by

An fydγb：design material strength：net area of the cross section to be veriﬁed
Nrd =

fyd
An

Chapter 6 Demand for Safety and Verification

Mrdy , Mrdzy, z
Iyy , Izz
Vrdy , Vrdz

τrd
Aey , Aez
Tsrd
K
h

t
Ac
s
Tωrd
Mωrd
ω
Q
Iωω

99

：design bending moment resistances about the weak and strong axes of thecross section to be veriﬁed, respectively
Iyy
Izz
fyd , Mrdz =fyd
Mrdy =
yz：distances from the neutral axes of y- and z-axes to the respective edges of
the cross section：moments of inertias about the weak and strong axes of the cross section to
be veriﬁed, respectively：design shear force resistances in the direction of the weak and strong axes of
the cross section to be veriﬁed, respectively
Aey τrdAez τrdVrdy =, Vrdz =γbγb：shear strength given byfydτrd = √
3：eﬀective areas associated with the shear forces in the y- and z-axes, respectively：design St. Venant torsion resistance,
τrd K
Tsrd =
h：design torsional constant of the cross section：equivalent edge-distance for St. Venant torsion⎧⎨ t (open cross section)
2Ac=(closed cross section)⎩
t 1/tds：plate thickness：area enclosed by the centerline of plate thickness：coordinate along the centerline of plate thickness：design warping torsion resistance of the cross sectionIωωτrdTωrd =(Q/t)max：design bi-moment resistance of the cross sectionIωω fydMωrd =
ωmax γb：warping function：torsional function：warping constant(6) Veriﬁcation of capacity when a state of signiﬁcant biaxial stress is induced in the previous ﬁve cases(1)∼(5)
A state of signiﬁcant biaxial stress can develop in the members of a moment frame, for example,
when a continuous stringer and a cross girder share a ﬂange. The capacity under such a biaxial stressstate needs be veriﬁed according to section 6.3.1.2 in addition to the veriﬁcation given in (1) to (5) in
section 6.3.1.1.

6.3.1.2

Verification of load-carrying capacity of plate(1) The load-carrying capacity of a plate shall, in principle, be veriﬁed for normal stress andshear stress using the following equations. These stress components shall be obtained fromforces and/or moments acting in the cross section.

100Standard Specifications for Steel and Composite Structures [Design]where ，

γi

σ
≤ 1.0
σrd

(6.3.1)

γi

τ
≤ 1.0
τrd

(6.3.2)γi
σ：structural factor

σrd
τ
τrd

：design strength：maximum normal stress in the cross section：maximum shear stress in the cross section：design shear strength(2) The load-carrying capacity of a plate shall be veriﬁed for all applicable cases among thefollowing:1) in-plane forces
2) out-of-plane forces
3) combined in-plane and out-of-plane forces
4) stiﬀened plate subjected to in-plane forces
5) a steel pipe subjected to a combination of forces in the transverse section【 Commentary 】

For each veriﬁcation item of plate load-carrying capacity, a veriﬁcation equation using the partialfactor method is presented here based on the Design Code for Steel Structures Part A [Japan Societyof Civil Engineers, 1998] and Ultimate Strength and Design of Steel Structures [Japan Society of Civil
Engineers, 1994].
1) Veriﬁcation of plates subject to in-plane forces
The veriﬁcation of plates subject to in-plane forces is performed by calculating the normal stressand shear stress from the applied cross-sectional force using Eqs.(6.3.1) and (6.3.2). Furthermore,because these veriﬁcation equations apply to the maximum normal stress and maximum shear stressin the cross-sectional plane of the plate, they are applicable to generic plates without variations inshape or thickness.
Veriﬁcation of the biaxial stress state is performed using the eﬀective stress σef f given by
Eq.(C6.3.36) and using Eq.(C6.3.37) derived from shear strain energy theory.
σef f =

σx2 − σx σy + σy2 + 3τ 2

2
σef
1
f
γi2
≤ 1.0
2
(σrd ) (1.1)2(C6.3.36)(C6.3.37)√
The following equation, obtained by letting τrd = σrd / 3, can also be used in Eqs.(C6.3.36) and(C6.3.37).

2 

 
2 
2 
σx
τ
σx
σy
σy
2
−
+
/1.21 ≤ 1.0(C6.3.38)
+
γi
σrd
σrd
σrd
σrd
τrd
where ，

σx , σyσrdττrd：normal stress：design strength obtained from Eq.(C5.3.35) or Eq.(C5.3.38)：shear stress：design shear strength obtain from Eq.(C5.3.57)

Where the values 1.12 and 1.21 represent an adjustment factor relating to the accuracy of the equations;these values were set because research results relating to ultimate strength in the biaxial stress state

101

Chapter 6 Demand for Safety and Verification

were smaller than research results relating to the ultimate strength in the uniaxial stress state. However,this value could also be set to 1.0 if the design engineer judges that suﬃcient accuracy is guaranteed.
Veriﬁcation of buckling is performed using the following equation with the stress component calculated from the cross-sectional force.

 
2 
 
2 
2 
σx
σy
τ
σx
σy
2
γi
≤ 1.0
(C6.3.39)
+
+
+
+
σcrdx
σbrdx
σcrdy
σcrdy
τrd
σx , σy：normal stresses acting in mutually perpendicular directions.

σcrdx , σcrdy
σbrdx , σbrdy
ττrdThese stresses should be taken as zero in the case of uniform
tensile stress.
：design strength obtained using Eq.(C5.3.35) and Eq.(C5.3.38)：design strength obtained using Eq.(C5.3.36)：shear stress：design shear strength obtained using Eq.(C5.3.37)

where ，

This buckling veriﬁcation applies only to ﬂat rectangular plate elements of uniform thickness thatare simply supported at the perimeter. If the plate element cannot be treated as ﬂat and rectangular,
or if the boundary conditions are diﬀerent or the plate thickness is not uniform throughout the ﬂatelement, a veriﬁcation of the limit state needs to be performed using an appropriate structural analysis
method.
2) Veriﬁcation of plates subject to out-of-plane forces
The veriﬁcation of plates subject to out-of-plane forces consists of veriﬁcation of stress and veriﬁcation of the biaxial stress state. As a general rule, the maximum value in the cross-sectional plane isused for each stress component. In other words, veriﬁcation of stress means veriﬁcation at the outeredge of the plate and this can be performed by using the edge stress from the cross-sectional force andthe maximum shear stress as calculated using Mohr’s circle.. Even in the biaxial stress state, veriﬁcation can be performed using Eq.(C6.3.37) by using the maximum value of each stress component in
the same way.
Although veriﬁcation of the shear stress distribution in the plate thickness direction is not required
here because it applies to thin plates, the distribution of shear stress over the plate thickness isadditionally required if the plate is treated as a thick plate. Veriﬁcation of the biaxial stress state is
performed using the eﬀective stress. In plates that are subject to out-of-plane forces, because membraneeﬀects can be anticipated in addition to plate characteristics as the out-of-plane deformation increases,
strength may be higher in consideration of this point. However, this kind of strength increment is notconsidered because its applicability has not been appropriately identiﬁed in this code.
3) Veriﬁcation of plates subject to in-plane and out-of-plane forces
For plates subject to in-plane and out-of-plane forces, it is assumed that veriﬁcation of the combined
stress and veriﬁcation of the biaxial stress state are performed for the worst-case loading conditions
with reference to items 1) and 2) in section 6.3.1.2 and, if necessary, buckling of the plate should beveriﬁed. Each stress is taken as a combined stress resulting from the stress due to in-plane forces andthe stress due to out-of-plane forces as shown below.

where ，

σrd = σrd,ip + σrd,op(C6.3.40)

σxrd = σxrd,ip + σxrd,op(C6.3.41)

σyrd = σyrd,ip + σyrd,op(C6.3.42)

τrd = τrd,ip + τrd,op(C6.3.43)

σrd,ip , σxrd,ip , σyrd,ip , τrd,ip
σrd,ip , σxrd,op , σyrd,op , τrd,op：stress due to in-plane forces：stress due to out-of-plane forces102Standard Specifications for Steel and Composite Structures [Design]

In the veriﬁcation of buckling, it is necessary to fully investigate what eﬀect the out-of-plane forces
have on plate buckling. Furthermore, depending on the boundary conditions, increased strength may
be predicted due to membrane stress. For this reason, a great deal of care is required depending on
the perimeter support conditions.
4) Veriﬁcation of stiﬀened plates subject to in-plane forces
The veriﬁcation of stiﬀened plates subject to in-plane forces must conform to each requirement for
the veriﬁcation of plates. The term stiﬀened plate here refers to a ﬂat plate on which stiﬀeners of
suﬃcient stiﬀness are arranged with equal spacing. In cases where the stiﬀeners lack suﬃcient stiﬀness
or are not arranged with equal spacing, veriﬁcation of the limit state must be performed using anappropriate structural analysis method.
In the Buckling Design Guidelines [Japan Society of Civil Engineers, 2005], the following method
is introduced for veriﬁcation of the buckling strength of stiﬀened plates.
The veriﬁcation equation for a case where the plate is subject to axial forces in two directions is asfollows.

2 
2 
σxu
σyu
+ γi
= 1.0
(C6.3.44)
γi
σxul
σyul
where ，

σxu
σxul
σyu
σyul

：compressive strength of the stiﬀened plate：indicates the reference compressive strength of stiﬀened plateelements, such as from Eq.(C5.3.35)：bending strength of the stiﬀened plate：indicates the reference bending strength of stiﬀened plates, suchas from Eq.(C5.3.36)

Therefore, the veriﬁcation for a case where the plate is subject simultaneously to axial force andbending moment is given by the following equations.
γi (Nu∗p + Mu∗q ) ≤ 1.0(N/Ny )Nu∗ =(Nu /Ny )(M/My )Mu∗ =(Mu /My )where ，

Nu∗ , Mu∗
Nu , M u
Ny , M yp, q(C6.3.45)(C6.3.46)(C6.3.47)：strength parameters of axial forces and bending moment：load-carrying capacity for the case where only axial force or

bending moment is applied：yield axial force and yield bending moment：coeﬃcients

5) Veriﬁcation of steel pipe subject to a combination of forces in the cross-sectional plane
The local buckling strength of a steel pipe subject to a combination of axial force, bending moment,
torsional moment, and shear force in the cross-sectional plane conforms to the veriﬁcation equation
given as Eq.(C6.3.48) when Eqs.(C5.4.2), (C5.4.3), and (C5.4.5) are used as the strength equations.


2 
σcd
σbd
τd
γi
+ γi
+ γi
≤ 1.0
(C6.3.48)
σcul
σbul
τul
If Eqs.(C5.4.4) and (C5.4.5) are used, the veriﬁcation equation shown as Eq.(C6.3.49) is the standard.
2 
σcd + σbd
τd
γi
+ γi
≤ 1.0
(C6.3.49)
σcbul
τul

Chapter 6 Demand for Safety and Verification

where ，

γi
σcd
σbd
τd
σcul
σbul
σcbul
τul

103

：structure factor：compressive stress：bending compressive stress：shear stress：represents compressive strength, from Eq.(C5.4.2)：represents compressive strength, from Eq.(C5.4.3)：represents compressive strength, from Eq.(C5.4.4)：represents shear strength, from Eq.(C5.4.5)

The bending compressive stress σbd in Eqs.(C6.3.48) and (C6.3.49) is calculated from σbd = Mbd /W
using the bending moment acting on the steel pipe cross-section, Mbd , and the section modulus, W .
This veriﬁcation equation for a pipe subject to combination loads of this type was obtained from thecorrelation equation of buckling strength by Schilling.

6.3.2 Verification of Displacement/Deformation Capacity
A member required to have a particular displacement/deformation capacity shall be veriﬁed toensure that the displacement/deformation due to actions will not exceed the limit state.
【 Commentary 】

In statically indeterminate structures, there may be cases where the safety of the overall structure
is assured even if the load-carrying capacity of some of the members that make up the structureis exceeded. However, in such cases where the collapse of some members is tolerated as long as
overall safety is assured, veriﬁcation requires consideration of the nonlinear properties of the members.
Further, a great deal of care is required with regard to the precision, range of applicability, etc. of theveriﬁcation method. In cases of this type, it is necessary to conﬁrm that the deformation capacities ofmembers where plastic deformation is tolerated exceed the deformation capacities anticipated in thedesign. For example, even when calculating the load-carrying capacity in systems with a mechanismthat assumes the occurrence of plastic hinges, veriﬁcation of plastic rotational capacity is required toensure that the actual structural members will exhibit suﬃcient plastic hinge functionality.
Furthermore, there are also cases where the load-carrying capacity of a member is veriﬁed based on
curvature, limit strain, or other measures of deformation instead of cross-sectional force. In these cases,
it is necessary to use appropriate veriﬁcation indices by taking into account the target ultimate state
and the properties of the member. In designs where plastic deformation is tolerated, it is necessary
to investigate whether structural stability is lost when the displacement or deformation of a member
becomes large.

6.3.3 Verification of Stability(1) The stability of a structure with regard to rigid-body motion shall be veriﬁed for all possible
transitional directions and rotations.
(2) The stability of a structure shall be veriﬁed by ensuring that the strongest action acting on
the whole structure or part of the structure will not exceed its capacity.

【 Commentary 】(1) Stability here refers to the rigid body stability of all or part of the structure under load. Although
the veriﬁcation of the stability of all or part of the structure is closely related to earthquake resistance, the rigid body stability under normally acting loads, such as support forces in the verticaldirection and overturning forces on beams, must be investigated separately from earthquake

104Standard Specifications for Steel and Composite Structures [Design]

resistance.
(2) It is suﬃcient to verify stability by using the partial-factor method in the same way as in section
6.3.1, ”Veriﬁcation of load-carrying capacity”. In selecting the partial factors used in the partialfactor method, it is preferable to carry out the investigation based on failure probabilities. If
it is possible to conﬁrm that the failure probabilities are less than the target values, then it
is suﬃcient to use methods that directly evaluate failure probabilities, methods that use the βreliability index, allowable stress design methods, etc.
The following is an example of a veriﬁcation method based on the partial-factor method[Railway Technical Research Institute, 2000].
1) Veriﬁcation of overturning of bridge beams
In cases where bridge beams are subjected to forces resulting from centrifugal loads, windloads, etc., the veriﬁcation shown below is carried out and the structure must be safe against
overturning in all situations.
γiwhere ，

Msd
Mrd

Msd
≤ 1.0
Mrd

(C6.3.50)：design overturning moment of the base end of the bridge beam：design resistance to overturning of the base end of the bridge beam

Although the horizontal forces acting on a bridge beam include vehicle lateral loads andlateral pressure from vehicle wheels in addition to centrifugal loads, wind loads, and forces
due to the eﬀects of earthquake, these eﬀects are not expected to be imposed simultaneously
by all vehicles on the bridge beam and also opposite forces can be expected to cancel eachother out. Consequently, as long as veriﬁcation is performed for the eﬀects of wind loads
and earthquakes, as a general rule it acceptable to not perform veriﬁcation of overturning
due to vehicle lateral loads and lateral pressure loads from vehicle wheels.
2) Veriﬁcation of uplifting of bridge beams
For continuous beams, cantilevered beams, etc., veriﬁcation of uplift is performed using thefollowing equation; either an anchor device or a heavy load is added to counteract this force.
γiwhere ，

Rsd
Rrd(−Rsd )
≤ 1.0
Rrd

(C6.3.51)：design reaction force occurring at the support point： design load-carrying capacity of the anchor device or weight of the counter-weightIn cases where the spacing between supports in a continuous beam is small and the dead load issmall, or where the center span is signiﬁcantly longer than the end spans, or where a cantilever
beam has a long cantilever arm or a long suspended span, an uplifting force may act on theend support points due to the live load and also sometimes due to the dead load. If this kindof uplifting force is not suﬃciently suppressed by ﬁtting an anchor device or adding a heavy
weight, there is a risk of instability arising and the bridge collapsing, particularly in the caseof cantilever beams. Even for continuous beams, if the support point lifts up then it becomessubject to impact loading and excessive stresses even if the bridge does not collapse, and this is
not desirable. Although it is intrinsically undesirable to have span ratios that lead to this kindof uplifting force, there are cases where the positions of support points cannot be adjusted forreasons such as the surrounding environment. To verify cases where an uplifting force may act
on the support points in this way, care is required because it is not thought to be suﬃciently safe
to simply consider the normal live load in the worst position in terms of member stress.

105

Chapter 6 Demand for Safety and Verification

6.4 Verification of Structural Safety by Nonlinear Structural Analysis
Structural safety may be veriﬁed by evaluating the ultimate load-carrying capacity of the whole
structure by nonlinear structural analysis.
【 Commentary 】

In the veriﬁcation of structural safety described in section 6.3, structural analysis is primarily used
for the purpose of calculating response values within the elastic range, while load-carrying capacities
are set based on load-carrying capacity curves at the member level based on previous experimental
results, etc. This means that safety is assured by taking account of the eﬀects on load-carrying
capacity of imperfection, nonlinearity, and so on. At present, fundamental theories of structural
analysis develop and the more widespread availability of computers able to numerically handle thecalculations, relatively rational design methods that oﬀer the designer ﬂexible nonlinear structural
analysis even from the point of view of performance design are expected to be introduced aggressively.
In veriﬁcation based on nonlinear structural analysis, the use of artiﬁcial concepts such as eﬀective
buckling length and the evaluation of boundary conditions between members become unnecessary.
Furthermore, the methods of nonlinear structural analysis can be applied to designing redundancy
in the overall structure, opening up the possibility of creating new structural modes. However, it is
1 consider the analytical model conﬁguration, such as how to set initial imperfections
necessary to: and residual stress, and the element types and partitioning; 
2 conform to the initial soundness as
3 specify the limit state; and 
4 specify appropriate partial factors.
regulated by construction codes; Furthermore, it is necessary to diﬀerentiate between two safety limit states when specifying the limit
state. The ﬁrst of these limit states means that the design does not tolerate additional deformation
after buckling; this is veriﬁed by taking the initial buckling (buckling of the overall structure, bucklingof constituent components, or local buckling of fragments) as the safety limit. The second limit state is
veriﬁed by taking the load-carrying capacity or the deformation capacity of the overall structure as thesafety limit. This design method provides assurance of overall load-carrying capacity or deformation
properties in cases where the structure is statically indeterminate and some strength after initialbuckling can be anticipated, as well as in cases where stiﬀness is expected to change and the forces are
expected to be redistributed due to yielding without buckling occurring.
The following is an example of veriﬁcation by elasto-plastic ﬁnite displacement analysis based on
Ultimate Strength and Design of Steel Structures [Japan Society of Civil Engineers, 1994].
＜ Veriﬁcation method with load-carrying capacity or deformation performance of the overall struc-ture as the safety limit ＞
For veriﬁcation taking the load-carrying capacity or deformation performance of the overall structure as the safety limit, veriﬁcation can be performed by a method that uses load parameters, given
as Eq.(C6.4.1) that represents overall behavior, or by deﬂection given as Eq.(C6.4.2).
γi γa γbγi γawhere ，

γi
γa
γb

1
≤ 1.0
αu

δu
≤ 1.0
δrd

(C6.4.1)(C6.4.2)：structure factor：structure analysis factor：member factor (however, here it is the safety factor in consideration of theuncertainty of the load-carrying capacity of the overall structure)

106Standard Specifications for Steel and Composite Structures [Design]

αu

γf i
Li
δu
δrd

：load parameter in the safety limit state. This refers to the load parameter

when the structure reaches the safety limit state during elasto-plastic ﬁnitedisplacement analysis and incrementing the load vector α γf i Li (α : load
parameter).
：load factor：design load vector：maximum deﬂection in safety limit state found by elasto-plastic ﬁnite displacement analysis：critical value of deﬂection in the safety limit state (γb is included in this)

6.5 Verification of Structural Safety through Experiment
Structural safety may be veriﬁed by evaluating the eﬀect of actions such as cross-sectional forces,
stress and displacement, or load-carrying capacity experimentally.
【 Commentary 】

Although veriﬁcation of structural safety through experiment is a method that was originally used
implicitly in design standards, in this code it is explicitly designated as a veriﬁcation method. Experiments for the veriﬁcation of structural safety are of two types depending on the goal: those that
determine the resistance value and those that determine the response value. The former experiments
are used as a means to specify the load-carrying capacity of structural members or the overall structure. This method is mainly used in situations where there the performance record, in the form of theload-carrying capacity curve for a new structural form, is insuﬃcient and in cases where a relatively
rational design is desired. Furthermore, the resistance value also includes the limit wind speed atwhich aerodynamically unstable vibrations arise . On the other hand, an example of the latter is thesetting of the wind load and the loading eﬀects for a structure that has a complex shape unsuitable
for specifying in terms of a wind force coeﬃcient.
References in Chapter 6
Japan Society of Civil Engineers (1994) ：Ultimate Strength and Design of Steel Structures, Steel Structure
Series 6 ．
Japan Society of Civil Engineers (1997) ：Design Code for Steel Structures, PART A; Structures in General.
Railway Technical Research Institute(2000) ：Design Standards for Railway Structures and Commentary, Steeland Composite Structures ．
Honshu-Shikoku Bridge Expressway Company Limited(2001) ：Lecture for Wind-resistance Design Code.
Japan Road Association (2002) ：Specifications for Highway Bridges and Commentary, I Common Specifications Volume, II Steel Highway Bridges Volume.
Japanese Society of Steel Construction(2004) ：International Harmonization Guideline of Design Standards for
Steel Structures(Steel Bridges), JSS IV 06-2004.
Japan Society of Civil Engineers (2005) ：Buckling Design Guidelines, Ver.2 [2005 Version].
Japan Road Association(2005) ：Wind-resistant Design Manual for Highway Bridges.
ISO(1998) ：ISO2394 International Standard, General Principles on Reliability for Structures”.

107

Chapter 7 Required Serviceability
Performance and Verification
7.1 General(1) Steel and composite structures must remain serviceable under the actions speciﬁed in Chapter 2 throughout their in-service period.
(2) Performance items related to serviceability include vehicle operating performance, train operating performance, and pedestrian comfort according to how the structure is utilized.
(3) Serviceability shall be veriﬁed for the limit state established for each performance item bysetting proper veriﬁcation indices representative of the performance item, except in cases
where use of the structure is restricted or where the structure is rendered unusable due tometeorological conditions or earthquakes.

【 Commentary 】

Steel and composite structures must remain serviceable under the actions speciﬁed in Chapter 2
throughout their in-service period except in cases where use of the structure is restricted or where thestructure is rendered unusable due to meteorological conditions or earthquakes.
Performance items related to serviceability include vehicle operating performance, train operating
performance, and pedestrian comfort according to how the structure is utilized.
Fatigue resistance, corrosion resistance, resistance against material deterioration, and maintainability should be considered as Durability in Chapter 8.

7.2 Required Performance for Serviceability
7.2.1 Vehicle operating performance
Steel and composite structures shall be designed to provide safe passage of vehicles and to avoid
undesirable psychological reactions among passengers in vehicles under the expected actions andmeteorological conditions.
【 Commentary 】

This section establishes the required performance with respect to vehicle operation for road bridges
so as to ensure that vehicles can use the structure safely and to avoid undesirable psychological reactions
among passengers under expected actions (permanent actions such as the dead load as well as variableactions such as the live load and wind) and expected meteorological conditions.
The vehicle operating performance requirements are shown in Table C7.2.1. Vehicle operating
performance is speciﬁed for ordinary conditions, rain, strong winds, and winter conditions.
Under ordinary conditions, undesirable psychological reactions among passengers in vehicles are to
be avoided. Items to be veriﬁed are the soundness of the road, the stiﬀness of the road, and operating
visibility.
Vehicle operating performance in rain, strong winds, and under winter conditions is related tosafety performance. The performance requirements to be veriﬁed in these cases take into consideration
roadway drainage, the incidence of strong winds, measures taken to mitigate the eﬀects of strong
winds, and road surface freezing. Vehicle operating performance also includes design to maintain the

108Standard Specifications for Steel and Composite Structures [Design]

Table C7.2.1 Performance requirements for vehicle operation
Performance requirements
Vehicle operating performance
under ordinary conditions
Vehicle operating
performance

Vehicle operating performance
under rain conditions
Vehicle operating performance
under strong winds conditions
Vehicle operating performance
under winter conditions

Veriﬁcation indexes
Soundness of the roadStiﬀness of the road
Operating visibility
Taking into consideration roadway
drainage
Taking into consideration the incidenceof strong winds, measures taken to mitigate the eﬀects of strong winds
Taking into consideration road surface
freezing

functionality, such as by securing the expansion gap and girder gap, in Level 1 earthquakes.V
The need to consider vehicle operating performance in dense fog, snow, and drifting snow is minimal
at the design phase, so it is not considered here. However, after considering the climate characteristicsof the region and details of the structure, performance requirements should be established if necessary.
Then it is necessary to consider the action, meteorological conditions, and degree of importance ofthe structure, establishing the serviceability performance level appropriately. Performance levels areshown in Table C7.2.2.
Table C7.2.2 Example of performance requirements for vehicle operation
Level

Level 1

Loading conditions andweather conditions

Performance requirement

Details

・Live load during design

Vehicle operating performance under ordinary
conditions

Providing smooth passage of vehicle, Ensuring the comfortableof passengers.

Vehicle operating performance under extreme
conditions

Providing safety passage of vehicle.

service life
・Weather condition 1

Level 2(low wind velocity andlight rainfall)・ Weather condition 2(high wind velocity andrainfall exceeding a certain level)

Since vehicle operating performance is inﬂuenced by meteorological conditions including wind andrain, it is appropriate to establish performance levels according to meteorological conditions. Weather
Condition 1 in Table C7.2.2 represents meteorological conditions such as wind velocity, rainfall, or roadsurface freezing that have no inﬂuence on vehicle operation; the expected performance must be satisﬁedin this case. Weather Condition 2 represents conditions that inﬂuence vehicle operating performanceand it is reasonable to allow some drop in expected vehicle operating performance; for example, a
speed restriction may be imposed on a toll road.
It may be appropriate to satisfy Condition 1 performance even with Weather Condition 2 according
to the purpose of the structure and its degree of importance.

7.2.2 Train operating performance
Steel and composite structures carrying railway tracks shall be designed to provide smoothpassage of trains and to avoid undesirable psychological reactions among train passengers under

109

Chapter 7 Required Serviceability Performance and Verification

the expected actions and meteorological conditions.

【 Commentary 】

Steel and composite structures that carry trains should be veriﬁed for the operating performanceof trains under normal running conditions as well as for the passenger ride comfort, as provided for by[Railway Technical Research Institute, 2000] and [Railway Technical Research Institute, 2006]. Thisveriﬁcation of train operating performance aims to ensure that the railway vehicles run smoothly under
the usual actions (that is, the permanent actions of the dead load, etc. and the variable actions of train
loading and impact loading, etc.). The veriﬁcation of ride comfort aims to secure passenger comfort
with respect to vehicle vibrations induced by trains operating on the structure.
The performance requirements for train operating performance are given in Table C7.2.3. In thisspeciﬁcation, there are two performance requirements each for train running performance under ordinary conditions and ride comfort.
Table C7.2.3 Performance requirements for train operation
Performance requirement
Train operating
performance

Veriﬁcation indexes

Train running performance
under ordinary conditions
Ride comfort

Structure vibrations
Displacement/deformation of structure
Structure vibrations
Displacement/deformation of structure

In [Railway Technical Research Institute, 2006], train running performance under ordinary conditions is one of the performance requirements for safety while ride comfort is one of the performancerequirements for serviceability. In this speciﬁcation, because safety relates to structural safety andpublic safety, train running performance under ordinary conditions is included as one of the serviceability performance requirements and is considered one of the performance requirements that ensuresrailway passenger comfort. For train running performance under seismic loading, refer to [Railway
Technical Research Institute, 2006].
The example of required performance levels for train operation is shown in Table C7.2.4. No
performance requirements for train operating performance are provided for extreme weather conditions
such as heavy rain and strong winds. The reason for this is that countermeasures to restrict service,
such as by stopping train operation, limiting speed, etc, are required under extreme weather conditions,so there is no need to consider extreme weather when designing railway structures. For this reason,
only one level of requirements for train operating performance is provided.
Table C7.2.4 Example of performance requirements for train operation
Level

Loading conditions
weather conditions

andPerformance items

Contents

vice life

Train running performance
under ordinary conditions.

・Weather Condition 1 (lowRide comfort

Providing smooth passageof railway vehicles over the
structure
Ensuring the comfort of passengers with respect to railway vehicle vibrations while
passing over the structure.

・Live load during design ser-

Level 1wind velocity and light rainfall)110Standard Specifications for Steel and Composite Structures [Design]

7.2.3 Pedestrian comfort
Structures shall be designed to avoid undesirable psychological reactions among pedestrians
under the expected actions and meteorological conditions.
It is recommended that structures be designed to provide safety and accessibility for all users,
including the elderly and handicapped.
【 Commentary 】

This speciﬁcation provides, as a walking comfort performance requirement for structures designed
for use by pedestrians, that pedestrian unease and annoyance should be maintained to a certain level.
At the same time, the idea of the universal design should be incorporated as far as possible so as toachieve structures that are easily accessible structures for all, including the elderly and handicapped.
The check items for walking comfort performance are given in Table C7.2.5.
Table C7.2.5 Check items for walking comfort performance
Performance requirement
Walking comfort

Walking comfort
under normal conditions

Check item
Condition of pavement
Vibration during walking
Visibility during walking

A walking comfort performance level can also be speciﬁed according to the weather conditions.
Table C7.2.6 Example of performance requirement for walking comfort
Level

Level 1

Level 2

Loading
condition
weather conditions

and・Live load during the de-sign service life
・Weather condition 1 (lowwind velocity and light rainfall)・Weather condition 2 (highwind velocity and rainfall
exceeding a certain level)

Performance requirement

Details

Walking comfort under ordinary conditions

No unease or annoyance felt
by pedestrians.

Walking comfort under extreme conditions

Pedestrian safety is assumed
and there is a tolerable levelof vibration, unease and annoyance.

Under weather condition 1, as shown in Table C7.2.6, walking comfort must not be inﬂuenced byweather conditions, such as wind velocity, rainfall and pavement surface freezing. Ordinary walking
comfort should be secured under these conditions. For weather condition 2, walking comfort is inﬂuenced by the weather. It is reasonable to accept certain impairment of ordinary walking comfort.
Walking comfort under extreme conditions such as storms, strong winds or in winter can also be
considered.
Depending on the purpose and importance of the structure, weather level 1 conditions can besatisﬁed even under weather condition 2 by special arrangement. For example, walking comfort during
severe storms that would normally make it impossible to walk can be assured by the introductionof wind breaks. Similarly, snow shelters or snow melting equipment may be introduced to maintainwalking comfort.

Chapter 7 Required Serviceability Performance and Verification

111

7.2.4 Other Considerations for Users
Non-structural aspects of structures, including aesthetics and water-tightness, shall also be
designed to avoid undesirable psychological reactions among users under the expected actions andmeteorological conditions.
【 Commentary 】

Other considerations should be paid to users so as to avoid harmful or uncomfortable eﬀects on
the direct users of a structure in addition to verifying vehicle operating performance, train running
performance, and pedestrian comfort. Excessive deformation of a structure or deterioration of its
appearance should not be allowed to make users feel uneasy or uncomfortable. Generally, users will
have undesirable psychological reactions to structures if the cracking or discoloration of the surface ofa structure is greater than a certain limit. Therefore, measures to prevent a deteriorated appearance
should be provided in advance by examining the possible inﬂuence on users.
Rainwater inﬁltration through unacceptably large cracks or between joints in steel components may
cause water leakage. Generally the inﬂuence of cracks on the concrete surface, joints in steel plates,and boundaries between concrete and steel must be examined for water-tightness.

7.3 Verification of Serviceability
7.3.1 Verification of vehicle operating performance
Vehicle operating performance under ordinary, wet, windy, and winter conditions shall be veriﬁed
in principle as speciﬁed below.
(1) Veriﬁcation of vehicle operating performance under ordinary conditions
Performance requirements for vehicle operating performance under ordinary conditions
shall be road surface soundness, stiﬀness, and operating visibility. Assessments shall be as
follows.
Road surface soundness: Road surface ﬂatness and friction coeﬃcient shall meet a speciﬁed
criterion for each item.
Stiﬀness: Deformation due to live load shall not be greater than a speciﬁed criterion.
Operating visibility: Visibility shall be the minimum required for the design velocity.
(2) Veriﬁcation of vehicle operating performance under wet conditions
Vehicle operating performance under wet conditions shall be veriﬁed by conﬁrming thatthe surface drainage system has a capacity be greater than a predetermined level of rainfall.
(3) Veriﬁcation of vehicle operating performance under windy conditions
Vehicle operating performance under windy conditions shall be veriﬁed by conﬁrming thatthe wind velocity over the structure is less than the speciﬁed criterion or that a speed limit
dependent on wind velocity is imposed.
(4) Veriﬁcation of vehicle operating performance under winter conditions
Vehicle operating
performance under winter conditions shall be veriﬁed by conﬁrming that the ﬂoor slab selected is less prone to icing or that anti-freezing measures are adopted.
【 Commentary 】

Vehicle operating performance under ordinary expected conditions, in wet conditions, in windy
conditions, and in winter conditions is veriﬁed for each suitable veriﬁcation index. Examples of veriﬁcation items and veriﬁcation indices for required vehicle operating performance are shown in Table
C7.3.1.

112

Standard Specifications for Steel and Composite Structures [Design]

Table C 7.3.1 Check items and examples of check indicesfor vehicle operating performance requirements
Performance requirement

Check item

vehicle operation underordinary conditions

Vehicleoperation

Example of index

Soundness of the roadvehicle operation underrain conditions
vehicle operation understrong winds conditions

Stiﬀness of the road
Operating visibility
taking into consideration
roadway drainage,
taking into considerationof strong winds

vehicle operation under
winter conditions

taking into consideration
road surface freezing

Road unevenness, Friction coeﬃcient
Deﬂection
Forward visibility
Roadway drainage performance
Incidence of strong winds, measures taken to mitigate the eﬀects
of strong winds,（ Speed restriction、
shielding etc ）Structure of uneasily freezing, Measures of surface freezing(1) Vehicle operating performance under ordinary conditions is veriﬁed in terms of the soundness of
the road, the stiﬀness of the road, and visibility for vehicle operation using suitable veriﬁcation
indices.
1) Road surface soundness
Road surface soundness is represented by road unevenness, pavement cracking, diﬀerential
expansion, and the friction coeﬃcient between tire and road. Poor road surface soundness may
result in vibration or other vehicle noise, loss of safety, and poor passenger comfort. If theveriﬁcation indices satisfy the speciﬁed criteria, vehicle operating performance in terms of safety
and passenger comfort is secured. Ideally, the criteria should be set based on test runs, etc.
The friction coeﬃcient between the tire and road surface inﬂuences on vehicle operating performance. There are two coeﬃcients related to friction; one is the longitudinal skid resistancecoeﬃcient and the other is the lateral force coeﬃcient. According to the latest speciﬁcations for
stopping distance under braking by the [Japan Road Association (1983)], the longitudinal skid
resistance coeﬃcient must be from 0.29 to 0.44 assuming moist conditions. On the other hand,
the line of curved sections of road is prescribed according to the design speed in consideration ofa lateral force coeﬃcient from 0.1 to 0.15.
2) Stiﬀness
If secondary stress leads to damage that has not been anticipated and a safety performance
problem arises because of excessive deﬂection or vibration, the required performance of the bridge
as given by the [Japan Road Association (2002)] might not be met.
Table C7.3.2

Design limit value of girder deflection (m)Type of girder

Simple girderand continuous girder

Cantilever ofGerber girder

L ≤ 10

L/2000L
20000/L
L/500
L/500

L/1200L
12000/L
L/300
L/300

type of bridge
Steel girder
Steel girderof slab10 < L ≤ 40

40 < L
Steel girder of other type slab
Suspension bridge
Cable stayed bridge
Other type bridge

L/350
L/400
L/600

L/400

Chapter 7 Required Serviceability Performance and Verification

113

By limiting the deﬂection allowed under a live load with no impact, the necessary stiﬀness canbe secured for the structure. It is necessary to establish a proper criterion for live-load deﬂection
to be used in verifying ordinary vehicle operating performance. The deﬂection criterion is established according to the type and scale of the targeted structure and using the design conditions.
Use the design criteria of a similar structure, if not refer to examinations. For example, thedeﬂection criterion shown in Table C7.3.2 is prescribed by the [Japan Road Association (2002)].
3) Operating visibility
It is necessary to be aware of an obstacle (or oncoming vehicle) ahead of the vehicle and braketo a stop so as to avoid a collision (i.e. within the vehicle stopping distance) or avoid the obstaclewith adequate forward visibility. If forward visibility provided by the [Japan Road Association,
2004] is satisﬁed, the safety of vehicle operation may be secured.
(2) To secure vehicle operating performance in wet conditions, it is necessary to install drains suchthat rain water does not collect on the road. If standing water does accumulate on the road,then vehicle operating safety performance cannot be secured and vehicle hydroplaning can easily
occur. Veriﬁcation of vehicle operating performance in wet conditions means calculating therate of assumed rainfall for the region (rainfall intensity). Further, it is necessary to verify thedrainage capacity of the drain design, the drainpipe diameter, and the drain inclination, etc.
Drain performance might deteriorate with sediment buildup, so it is necessary to verify drain
performance on the assumption that sediment is managed to a certain level.
(3) Vehicle operating performance can be reduced under windy conditions, making slower driving
necessary. Windy conditions under which driving are permitted may be deﬁned, for example, as
the range of wind velocities from 10m/s to 25m/s. Then a storm warning may be given for windvelocities of 25m/s or more and driving is then restricted［ Tajima,1994 ］.
Phenomena that can inﬂuence vehicle operating performance under windy conditions include
the following:a. Wind-induced girder vibration ，b. Wind-induced structural member vibration ，c. Sudden change in velocity of wind impinging the structure.
Wind-induced girder vibration can inﬂuence vehicle operating performance directly, so it isnecessary to control it below a certain limit. It should be veriﬁed that acceleration, based onvibration amplitude in wind tunnel tests [Japan Road Association 1991, Honshu-Shikoku Bridge
2001], does not exceed criteria established from vehicle operating performance or unpleasantness
induced in users.
Wind-induced vibration of structural members also inﬂuences the safety and fatigue resistanceof the members, while the anxiety it may cause users cannot be disregarded. For this reason, it isnecessary to limit the amplitude within a cert over. It is necessary to ensure that wind velocity
ﬂuctuations remain within the range where driving safety can be secured. Veriﬁcation means
conﬁrming that ﬂuctuations from a certain range of mean wind velocities are below the criterion
for safe vehicle operation as set by analysis or by driving simulation. Quantitative evaluation ofwind velocity ﬂuctuations may be based on wind tunnel tests or numerical ﬂuid analysis combinedwith measurements from a similar case. If this veriﬁcation shows that safety performance is notachieved, an eﬀective countermeasure to obstruct the wind and ease velocity ﬂuctuations is toinstall windshields or similar. However, such shielding may increase the wind loading and cause
deterioration in wind performance, so it is necessary to carry out an appropriate examination.
(4) A frozen road surface in winter can reduce the resistance to sliding between tire and road surface,
thereby aﬀecting vehicle operating performance.
In comparison with a concrete slab deck, a steel plate deck is prone to condensation freezing
and snow compaction, so careful consideration of the type of slab is necessary in regions where

114Standard Specifications for Steel and Composite Structures [Design]road surface freezing occurs.
Depending on the intended purpose and degree of importance of the structure, required performance may be maintained by preventing road surface freezing and snow accumulation. Possible
measures to achieve this are the spreading of anti-freeze materials, road heating, and pipe meltingof snow. However, if anti-freeze materials are used, the danger of promoting rust and having
a detrimental inﬂuence on the surrounding environment must be considered. In the future, alternative measures deriving from research into controlling road freezing [Shigenobu Miyamoto,1998] by building-in thermal storage materials, etc. are expected.

7.3.2 Verification of train operating performance
The train operating performance and ride comfort of steel and composite structures that carryrailway tracks shall, in principle, be veriﬁed under normal conditions as speciﬁed below.
(1) Veriﬁcation of train operating performance under normal conditions
Train operating performance in ordinary conditions shall generally be veriﬁed by conﬁrmingthat structure displacement as determined through static analysis is less than a criterion
determined from the viewpoint of an operating safety limit.
(2) Veriﬁcation of riding comfort
Riding comfort in ordinary conditions shall generally be veriﬁed by conﬁrming that structure
displacement as determined through static analysis is less than a criterion determined fromthe viewpoint of a riding comfort limit.
【 Commentary 】(1) Though there are various deﬁnitions relating to train running performance, this speciﬁcation
states that train running performance under ordinary conditions should be veriﬁed by conﬁrmingthat the train wheels pass smoothly and safely over the rails.
It is necessary to conﬁrm that the response of all vehicle wheels satisﬁes the requirements
for derailment quotient, wheel load reduction ratio, and lateral pressure. The desired method ofcarrying out this veriﬁcation is to use dynamic interaction analysis in which both railway vehicles
and the structure are modeled.
However, such dynamic interaction analysis is complex in terms of structural design. A convenient alternative has been to carry out the veriﬁcation using values of structural displacementand deformation obtained from static analysis. When using this method, it should be checkedthat deﬂection of the girder caused by train loading (at assumed maximum loading) and the impact load is below the limit value of deﬂection determined by train running performance underordinary conditions. The limit value of girder deﬂection as provided for by [Railway TechnicalResearch Institute, 2006] is shown in Table C7.3.3 as the condition that the wheel load reduction
ratio is 0.37 or less.
(2) Various deﬁnitions concerning ride comfort have been proposed. In general, ride comfort isclassiﬁed as overall ride comfort during some time period (ride comfort over a section) andmomentary ride comfort at an individual point (point ride comfort). The latter, point ride
comfort, is generally used to evaluate ride comfort on railway bridges. The veriﬁcation index
used should be the acceleration response of the train vehicle body. That is, it is necessary to
conﬁrm that the maximum acceleration among all vehicles making up a train satisﬁes the ride
comfort limit value provided in [Railway Technical Research Institute, 2006]. The method ofcarrying out this veriﬁcation of ride comfort should ideally be a dynamic interaction analysis
that models both the railway vehicles and the structure.
However, such dynamic interaction analysis is complex in terms of structural design. A con-

115

Chapter 7 Required Serviceability Performance and Verification

Table C7.3.3 Design limit value of girder deflection determinedby train running performance under ordinary conditions
Numberof spans

Train types

SingleShinkansen
Multiple

Electric cars/diesel cars

SingleMultiple

Locomotive

SingleMultipleMax. speed(km/h)
260
300
360
260
300
360
130
160
130
160
130
130

〜40

Span Lb (m)
40〜60
70〜

Lb /700
Lb /900
Lb /1100
Lb /1200
Lb /1400
Lb /1500
Lb /1700
Lb /1900
Lb /2000
Lb /500
Lb /500
Lb /500
Lb /600
Lb /400
Lb /600
Lb /700

venient alternative has been to carry out the veriﬁcation using values of structural displacement
obtained from static analysis. When using this method, it should be checked that deﬂectionof the girder caused by train loading (under normal service conditions) and the impact load is
below the limit value of deﬂection determined by the limit state of ride comfort. The limit valueof girder deﬂection, on condition that the ride comfort coeﬃcient as provided in [ride comfort
speciﬁcation in previous Japan national railway (JNR)] is 1.5Hz or over and the maximum acceleration of each vehicle body is 2.0m/sec2 or less, is prescribed as shown in Table C7.3.4 according
to [Railway Technical Research Institute, 2006].
Where frequent occurrence of high winds is expected, such as in the case of sea and rivercrossings, measures to mitigate the wind such as the installation of windbreak fencing should
be considered even though train operating performance is provided only for Level 1 weather
conditions.
Table C7.3.4 Design limit value of girder deflection determined by ride comfort
Train types

Numberof spans
SingleShinkansen
Multiple

Electric cars/diesel cars

SingleMultiple

Locomotive

SingleMultipleMax. speed(km/h)
260
300
360
260
300
360
130
160
130
160
130
130

〜20

〜30

Lb /2200
Lb /2800
Lb /3500
Lb /2200
Lb /2800
Lb /3500

Lb /1700
Lb /2000
Lb /3000

Span Lb (m)〜40〜50
Lb /1200
Lb /1700
Lb /2200〜60

70〜

Lb /1000
Lb /1300
Lb /1100
Lb /1800
Lb /1500
Lb /1700
Lb /2000
Lb /2800
Lb /2200
Lb /500
Lb /500
Lb /700
Lb /900
Lb /1100
Lb /800
Lb /500
Lb /900
Lb /700116

Standard Specifications for Steel and Composite Structures [Design]

7.3.3 Verification of pedestrian comfort
Pedestrian comfort under ordinary conditions shall, in principle, be veriﬁed in terms of pavementsoundness, walking-induced vibration, and visibility as speciﬁed below.
(1) Veriﬁcation of pavement soundness
Pavement soundness shall be veriﬁed by conﬁrming that ﬂatness is assured, slip resistancecoeﬃcient is within a range of an assessment index, and gradient is not greater than aspeciﬁed criterion.
(2) Veriﬁcation of walking-induced vibration
Walking-induced vibration shall be veriﬁed by conﬁrming that vibration velocity and acceleration, which may aﬀect walking comfort, are not greater than criteria speciﬁed for thenatural frequencies of the structure or that the natural frequencies are outside the range ofresonance.
(3) Veriﬁcation of visibility
Pedestrian visibility shall be veriﬁed by conﬁrming that visibility is not less than a speciﬁed
criterion and that there is a large variation in brightness to allow discrimination of guidance
block edges and stairway steps.
【 Commentary 】

Pavement surface soundness, walking-induced vibration and visibility should be checked against
the appropriate indices. In Table C7.3.5, check items and examples of indices for walking comfort
performance requirements are shown.
Table C7.3.5 Check items and example of check indicesfor walking comfort performance requirements
Performance requirement

Walking
comfortWalking comfort
undernormalconditions

Check item

Example of index

Soundness of pavement
surfaceWalking-induced vibration

Flatness of surface, slip resistance coefﬁcient, gradient of surface
Velocity, acceleration, natural frequencies

Visibility while walking

Forward visibility, brightness of pavement surface, brightness diﬀerential ofsteps, guide blocks and environs.

(1) The soundness of the pavement surface can be expressed in terms of ﬂatness, slip resistancecoeﬃcient, and gradient. Flatness can be represented by the surface smoothness, cracks in the
pavement, and the ﬂatness of expansion joints. The ﬂatness of structure surfaces must be securedso that walking comfort is assured and pedestrians do not suﬀer any unease.
It should be checked that the slip resistance coeﬃcient of the pavement is within the rangeof assessment indices that assure serviceability. This coeﬃcient is especially important because
it inﬂuences not only walking serviceability but also safety. The slip resistance coeﬃcient of thepavement surface should be experimentally determined using the CSR index as measured using
an O-Y・PSM (O-Y・Pull Slip Meter) or using the BPN index as measured by a BPST (British
Portable Skid Resistance Tester).
The road surface gradient should be checked for compliance with limit values for longitudinal
gradient and superelevation. For stairway, ramp, or gradient with steps, the limit value of
longitudinal gradient should be determined in consideration of users and its serviceability forthem: pedestrians, bicycles, baby carriages, wheelchairs, etc. In [Japan Road Association, 1979],

Chapter 7 Required Serviceability Performance and Verification

117

it is speciﬁed that the standard value for a stairway gradient is 50%, while the gradient of a ramp
or a gradient with steps should not exceed 12% and 25%, respectively. It is desirable to reduce
the gradient of ramps by introducing the idea of universal design and taking into consideration
the elderly and handicapped. For example, in [Japan Road Association, 1979], it is shown thatthe maximum gradient that a wheelchair user can climb unaided is 8% while bicycles can easily
climb a slope of up to 5%. It is also speciﬁed that the introduction of elevators or escalators
should be considered when necessary.
(2) Pedestrians may feel uncomfortable if vibrations are induced by walking, so it must be checkedthat the vibration responses of a structure, i.e. the response velocity or acceleration, are within
limit values and that the natural frequencies are not within the resonance range.
Structure vibrations may be induced by vehicles, pedestrians, or the wind. The limit values
for these vibrations should be values determined through experiments that focus on the humanperception of vibrations. Vibration velocity or acceleration due to walking should be evaluatedbased on a dynamic analysis of the structure using a moving vehicle model in the case of roadbridges and with a moving pedestrian model for pedestrian bridges, because vibration is aﬀectedby structural type, loading conditions, and their interactions. For wind-induced vibration, results
obtained in wind tunnel tests can be utilized to evaluate walking comfort.
However, this type of dynamic analysis or wind tunnel testing might be too time-consuming forconventional design work. If simpliﬁed veriﬁcation based on experiments or analysis is proposed,
a simpliﬁed method may be adopted.
1) Running-induced vertical vibrations For limit values and an evaluation index, refer to [Japan
Road Association, 1979; BSI, 1978].
In [Japan Road Association, 1979], it is speciﬁed that main girder vibrations caused by the live
load shall not cause unease among pedestrians. It also illustrates that, to avoid resonance withwalking pedestrians at a frequency of around 2 Hz, the ﬁrst natural frequency of the structure
should fall outside the range 1.5 to 2.3 Hz. Furthermore, to avoid feelings of unease among
pedestrians due to bending vibration even when this resonance range has been avoided, it isexplained that it is desirable to reduce the maximum acceleration to below 100 gal for thevibration caused by the 2 Hz periodical excitation under normal live loading of one person per
square meter.
According to a research conducted by [Obata, et al., 1996], pedestrians can also feel uneasy
at 4 Hz, which corresponds to the half resonance condition with 2 Hz excitation. This is also
true for a natural frequency of around 3 Hz in the case of pedestrian bridges over which joggers
often pass. It is desirable to decide on suitable check indices considering local conditions and the
expected users.
In [BSI, 1978], acceleration is calculated by a method proposed by Blanchard, et al. in 1977 and
it is speciﬁed that this acceleration must not exceed the limit value. In Blanchard’s calculation,
the excitation force per pedestrian leg can be represented by a sinusoidal curve expressed as
F = 180 sin(2πf t)(N) moves at a speed of V = 0.9f (m/s). The maximum acceleration can thenbe obtained as shown in Eq.(C7.3.1).
Maximum acceleration
Where ，

f1
f
w
K
ψ

a = (2πf1 )2 wKψ

(m/s2 )

(C7.3.1)：First natural frequency of the bridge (Hz): Walking frequency, same as natural frequency of bridge (Hz)：Maximum static deﬂection of superstructure when loaded with one pedestrian(700N) (m)：Shape factor corresponds to structural type
：Dynamic response coeﬃcient with damping factor h as parameter118Standard Specifications for Steel and Composite Structures [Design]

It is proposed that the maximum acceleration obtained by the above equation should not exceed√
the acceleration limit value 0.5 f1 (m/s2 ), which is expressed as a function of the natural
frequency of the superstructure.
2) Running-induced horizontal vibration
There are no particular speciﬁcations in [Japan Road Association, 1979] and [Japan Construction Engineers’ Association, 1984] for the horizontal vibrations of pedestrian bridges. So far, no
special consideration has been given to horizontal vibration in design. However, the inﬂuenceof horizontal vibrations under the inﬂuence of a moving crowd of people cannot be ignored forbridge types such as cable-stayed bridges and suspended deck bridges. In checking horizontal
vibrations, the study [Yoneda, 2003] is a good reference.
(3) Pedestrian visibility is considered one of the required performance factors for comfortable usage ofa structure. It may be reasonable to specify the performance requirement for pedestrian visibility
according to the purpose, location, and importance of the structure. In verifying pedestrianvisibility, the foreground visibility and road surface brightness should satisfy the limit value
speciﬁed for the structure. Refer to [Japan Road Association, 1979] or [Japan Road Association,
1981] for the checking of road surface brightness.

7.3.4 Verification for Other Considerations
Other considerations for users shall be veriﬁed in principle using appropriate indices and related
criteria.
【 Commentary 】

The appearance of a concrete-covered structure should not suﬀer deterioration by surface cracking.
The limit value of crack width with respect to appearance depends on the type of structure and thesurrounding environment. In [Railway Technical Research Institute, 2002], a general limit value ofaround 0.3 mm is proposed based on historical performance and experience. Further, appropriate
measures must be provided for in the case of visually signiﬁcant structures in accordance withthe surface texture of the steel and concrete. It is important to pay attention to steel coatings andconcrete surface ﬁnish as well as preventing discoloration and the accumulation of dust on the surfaceof members.
The water-tightness of a structure should not be compromised by cracks on the concrete surface.
Waterprooﬁng work must be considered when good water-tightness is required of a structure. The
limit value of crack width for water-tightness depends on the required level of water-tightness and thetype of cross-sectional forces that dominate. As an example, [Japan Society of Civil Engineers, 2002]
proposes a general limit value of less than 0.1∼0.2mm.
References in Chapter 7
Japan Road Association(1979) ：Technical Standards for Pedestrian Overpass.
Japan Road Association(1981) ：Technical Standards for Structure of Roadway Lighting.
Japan Construction Engineers’ Association, 1984 ：Guidebook for Pedestrian Bridge.
Japan Road Association(1991) ：Wind-resistant Design Manual for Highway Bridges.
Tajima,T.(1994) ：Inﬂuence of Lateral Wind on Driving on Oﬀshore Bridge, Honshu-Shikoku Bridge Expressway Company Technical Report,Vol.18, No.71, pp.9-18.
Obata, T., Hayashikawa, T. and Satoh, K.(1996) ：Study on Vibration Serviceability Limit State of Pedestrain
Brides based on Human Vibration Sensibility, Jouranal of Structural Engineering/Eaarthquake Engineering, No.537/I-35, pp.217-231.
Japan Society of Civil Engineers (1997) ：Design Code for Steel Structures, PART A; Structures in General.
Miyamoto S., Murota M.(1998) ：oad Icing on Steel Deck Bridges and its Control by Phase Change Material,

Chapter 7 Required Serviceability Performance and Verification

119

Bridge and Foundation Engineering, No.6, pp.25-31.
Railway Technical Research Institute(2000) ：Design Standard for Railway Structures and Commentary, Steeland Composite Structures ．
Japanese Society of Steel Construction(2001) ：Guidelines for Performance-Based Design of Civil Engineering
Steel Structures.
Honshu-Shikoku Bridge Expressway Company Limited(2001) ：Lecture for Wind-Resistance Design Code.
Railway Technical Research Institute(2002) ：Design Standards for Rrailway Structures and Commentary,
Steel and Composite Structures ．
Japan Society of Civil Engineers (2002b) ：Guidelines for Performance Veriﬁcation of Hybrid Structures (tentative) ．
Japan Road Association (2002) ：Speciﬁcations for Highway Bridges and Commentary, II Steel Highway Bridges
Volume ．
Yoneda, M.(2003) ：A Simpliﬁed Method to Evaluate Maximum Lateral Response of Pedestrian Bridges due
to Synchronized Walking by Pedestrians, Journal of structural engineering, Vol.49A, pp.263-272.
Japan Road Association (2004) ：Practical Guide and Implementation of Road Construction Ordinance ．
Railway Technical Research Institute(2006) ：Design Standard for Railway Structures and Commentary, Displacement Limits ．
Blanchard, J.B.I.Davis and J. Ｗ.Smith(1977) ：Design criteria and analysis for dynamic loading of foot-bridges,
UK. TRRL Report SR.275 ．
BSI(1978) ：Steel, Concrete and Composite Bridges, Part2. Speciﬁcation for Loads, 7.1.5 Vibration Serviceability, BS 5400 ．

120Standard Specifications for Steel and Composite Structures [Design]

Chapter 8 Required Durability Performanceand Verification
8.1 General(1) Steel and composite structures must continuously maintain the required level of performance
under the expected actions throughout the design working life.
(2) Performance veriﬁcation items related to the durability of steel and composite structures include fatigue resistance, corrosion resistance, resistance to material deterioration, and maintainability.
(3) Veriﬁcation of fatigue resistance, corrosion resistance, resistance to material deterioration,and maintainability must involve the setting of adequate indices representing performance
item and veriﬁcation of the limit state established for each item.
【 Commentary 】

There is a time-dependent deterioration of the performance of steel and composite structures dueto the actions to which they are exposed. The durability of a structure is deﬁned as its or its members’ability to resist this performance deterioration. In other words, ensuring that performance is maintained at the required level (in terms of safety, serviceability, etc.) throughout the design working life
under the assumed actions should ensure that the durability performance is satisﬁed.
Of the factors that lead to performance deterioration over the design working life of a structure,
one is the damage caused by mechanical deterioration (fatigue) and another is the damage caused byelectro-chemical deterioration (corrosion) or chemical deterioration (carbonation, salt attack, alkaliaggregate reaction, etc.). Examples of this seen to date in steel and composite structures that have
suﬀered damage or been repaired include fatigue of steel members or ﬂoor slabs (related to fatigue
resistance), deterioration of steel (related to corrosion resistance) and deterioration of concrete-basedmaterials. In order to ensure that the durability performance of steel and composite structures ismaintained throughout their design working life, controlling these types of damage is important.
Additionally, to ensure that the durability of structures is maintained, it is important to carry out
suitable maintenance in which design and construction are considered. Concretely, it is important todraw up a maintenance plan during the design phase and to carry out maintenance based on this plan
once the structure enters service. But it is also important to improve the maintenance methods usedwhile taking into consideration the state of the structure at each maintenance step.
A conceptual schema showing a structure’s durability performance and maintenance is shown in
Fig.C8.1.1. This ﬁgure shows that after entering service, the performance of a structure deteriorates
with time. It also shows that meeting the performance requirements of a structure throughout its
design working life means carrying out repairs if, during the maintenance phase, the performancerequirements are not satisﬁed. In this manner, this standard shows that the durability performancerequirements of a structure can be maintained by considering how maintenance, which is most likely
dealt with separately from design, is carried out from the design phase until renewal of the structure.
Consequently, an important aspect of maintaining durability performance is to make maintenanceeasier by putting in place in advance equipment necessary for maintenance, such as inspection scaﬀolds
or metal hanger ﬁttings for painting.
If any performance requirement of a structure is found to be not satisﬁed at any time, reinforcement
and/or repair is carried out according to the maintenance plan. Sometimes, certain parts of structuralmembers may be replaced because their functionality deteriorates. However, in the conventional designChapter 8 Required Durability Performance and Verification

121

process, reinforcement and repair have not been considered during the initial design phase. As aresult, not only is the workability of repair and reinforcement operations poor, but also the cost andtime required are more than necessary. For this reason, this chapter prescribes the new requirementthat maintainability must be considered when designing a structure. Moreover, the Maintenance andManagement volume should be consulted for all aspects of this work after the structure enters service.
In some cases, (JSSC, 2001) durability is basically considered a veriﬁcation of safety and is includedin the safety requirements. In such cases, veriﬁcation entails predicting the degree of damage andthe associated change in strength with time after the structure enters service. As noted above, by
dealing with performance requirements against durability, using such measures as fatigue resistance,
corrosion resistance, resistance against material deterioration and maintainability, durability should bemaintained. To make this very clear, and given that performance requirements other than safety mustalso be satisﬁed at all times after a structure enters service, durability is considered a performance
item in this standard.

Performance
Prediction of
performance
deterioratio

Required performancein maintenanceRequired performance level

Performance
Evaluation

Evaluation

Inspection

Inspection

Start

Plan ofmaintenanceRe-evaluation

Evaluation of
performance

Evaluation of
performance
Performance >Required
performance

Performance >Required
performance
Repair

Fig.C8.1.1 Conceptual scheme of durability and maintenance of steel and composite structures

8.2 Required Durability Performance
8.2.1 Fatigue resistanceSteel and composite structures must never suﬀer fatigue failure due to repeated loading during
the design working life. Namely, the design must take into account fatigue resistance such that nosteel member cracks or fails even if a crack is initiated and then propagates.

122Standard Specifications for Steel and Composite Structures [Design]【 Commentary 】

Any action such as wind load or traﬃc load acting repeatedly on steel and composite structures
can cause fatigue crack initiation and propagation leading to fatal damage. For this reason, at thedesign stage it must be ensured that fatigue damage does not occur. To maintain steel and composite
structures in healthy condition it is necessary to take appropriate measures against fatigue. The usual
methods of preventing fatigue-cracking are to increase the thickness of members, therefore enhancing
their stiﬀness, or to decrease stress. Another possibility is to improve structural details or welded
joints so as to reduce local stress concentrations. For instance, smoothing the proﬁle of a weld toe toreduce stress concentration is one method that has been used.
The fatigue resistance of a steel or composite structure is actually the resistance to fatigue of thestructural members that compose it. Considering the setting of performance requirements over thedesign working life, levels may be set as shown in Table C8.2.1. Fatigue damage is well known to result
from repeatedly applied action such as traﬃc load or wind load. However, depending on the structure
under consideration, other types of repeatedly applied action might be present, so careful attention
must be paid.
Table C8.2.1 Examples of levels of fatigue resistance performance requirements
Level 1
Durability
performance requirement

Fatigue cracking may
not initiate throughout design working
life to maintain service at its startinglevel

Investigation index
Maintenance levelStress range
・periodic inspection

Level 2

Level 3

Fatigue cracking may not Fatigue cracking may
initiate in main members, initiate but after inspecthough it is allowed in sec- tion or management, reondary ones, throughout the pairs or reinforcement
design working life to main- are carried out if retain service at its starting quired
level
Stress range or frequency of repair or reinforcement
・periodic inspection・periodic inspection
・repairing fatigue crack if re- ・repair or reinforcement
quiredif required

8.2.2 Corrosion resistanceSteel and composite structures must maintain the required level of mechanical performance andfunction even if steel corrosion takes place under the expected environmental actions throughout
the design working life. No failure of a steel member is allowed.
【 Commentary 】

The occurrence of corrosion and the factors that cause it to accelerate diﬀer greatly according to
the details of the structure and its location. For example, in a coastal region inﬂuenced by airborne
salt or coat or in a location with bad drainage where water may persist for hours, corrosion accelerates
remarkably (JRA, 2002a). In particular, in the case of steel bridges comprising many members, theduration of wetting caused by rain or dew condensation, the presence of sand-mud sediments, which
are seen as one factor causing corrosion, and the quantity of anti-freeze agent adhering to the structure
diﬀer with each installation. The corrosion resistance of steel is deﬁned as the resistance of the steel
used for the structure against corrosion. From the point view of maintaining performance during thedesign working life, a level of corrosion resistance can be set as a performance requirement, for instanceas seen in Table 8.2.2 (RTRI, 2000).
In the case of a painted steel structure for which a corrosion resistance of performance level I is

123

Chapter 8 Required Durability Performance and Verification

Table C8.2.2 Examples of corrosion resistance performance level
Level 1
Durability performance

Investigation index
Maintenance level

Remarks

Level 2

Level 3

Cross sections may Decrease of cross section
decrease as a result of caused by corrosion durcorrosion during the ing design working pedesign working life riod and of associatedand loading capacity load capacity is allowed.
may also fall, but no Replacing members durreplacement of struc- ing design working petural members or re- riod may be done.
inforcement work is
required.
Amount of decrease in plate thickness, loading capacity
・periodic inspection ・periodic inspection ・periodic inspection・periodic repainting, ・if required: repairs,
・detailed survey if coretc.
painting, etc.
rosion is found to haveprogressed・repairs or reinforcement if required
Applied to temporary
structures
A small decrease incross section is allowed over the design working life but
the loading capacity
must be maintained
unchanged

set as the target, the required performance may be achieved using methods such as regular repainting.
For example, bridges that carry Shinkansen (bullet train) traﬃc are regularly repainted (every 5 to
7 years) after entering service so as to avoid corrosion. For an ordinary steel structure, repainting isoften carried out according to the degree of deterioration; in such cases, the set target is that corrosion
resistance of performance level II should be achieved.
Further, in the case of a non-painted steel structure that is serviced, in a corrosive environment,using weathering steel that is usually in a healthy condition, the target is to maintain a corrosion
resistance of performance level I. However, it cannot be expected that ﬁne rust will be formed on
bridges constructed on the water’s edge or in coastal areas in the particular locations (speciﬁc members
or structural positions) where an anti-freeze agent (sodium chloride or calcium chloride) is applied. In
these cases the target should be to maintain a corrosion resistance of performance level II. Moreover,experience has shown that in the case of non-painted steel structures corrosion does not advance beyond
the point where stable rust is generated. However, recent practice is to assume that corrosion may
occur but corrosion resistance performance is maintained since the progression of corrosion is held
within a ﬁxed limit.
The steel reinforcement inside concrete may corrode as a result of carbonation of the concrete,chloride ion inﬁltration, freeze-thaw action, chemical attack, the alkali-aggregate reaction and others.
The performance of a structure must be assured against such corrosive attack. Reference JSCE, 2001
explains the process of concrete deterioration caused by each of these deterioration factors, the processof corrosion of steel inside the concrete, the grading of a deteriorated structure in terms of appearance,and standards for the deterioration of performance.
As this makes clear, one performance requirement pertaining to the corrosion resistance of steel
and composite structures is that corrosion of the steel used should be inhibited throughout the design
working life.

124Standard Specifications for Steel and Composite Structures [Design]

8.2.3 Resistance to material deterioration
Steel and composite structures must maintain the required performance level with respect tomaterial deterioration throughout the design working life.
【 Commentary 】

Resistance to material deterioration represents performance with respect to durability against of
any concrete used in steel and composite structures. For structural members using concrete, such as
in ﬂoor slabs, this performance requirement must be considered and dealt separately from the steel
material. This is explained in section 14.5.2 ”Resistance to concrete deterioration” in Chapter 14”Slab Design”. The material deterioration of concrete is not considered aﬀected by corrosion of steel
because of freezing damage, chemical erosion, the alkali-aggregate reaction, and so on. Veriﬁcation
indices of performance relating to these deterioration factors are explained in reference JSCE, 2002b.
Time-dependent changes or performance deterioration of concrete-based structures caused by these
deterioration factors are explained in reference JSCE 2001.

8.2.4 Maintainability
Ease of repair must be considered against time-dependent degradation of members due to fatigue,
corrosion, and material deterioration throughout the design working life.
Ease of maintenance, covering repair and inspection, after entry into service must be considered.
【 Commentary 】(1) In addition to fatigue, corrosion and material deterioration as described above, functional deterioration may also be related to repair requirements. For example, there are factors aside
from fatigue, corrosion, and material deterioration that make it necessary to replace expansion
joints, bearing supports, distribution pipes, and other components. Maintainability relates tothe investigation of function deterioration caused by these factors.
For instance, it is must be checked that a suitable number of metal hangers are installed inappropriate places to allow for the setting up of scaﬀold for repainting. The structure must also
be designed to make scraping work easy. Repainting is one of the standard maintenance tasks
for steel and composite structures. And in considering structural details, it must also be ensured
that members such as expansion joints, bearing supports, or ﬂoor slabs can be replaced easily.
(2) At design phase, consideration must be given to the ease of carrying out maintenance operations
such inspections, repairs, maintenance management, and so on. Moreover, the basic position
should be that the investigation, cleaning, and painting of a structure can be carried out easily.

8.3 Verification of Durability
8.3.1 Verification of fatigue resistance
8.3.1.1 Verification of fatigue under repeated loading
The veriﬁcation of fatigue under repeated loading must in principle involve using the following
method. If another adequate veriﬁcation method is available, it may be applied. Veriﬁcation of
fatigue under wind loading shall be in accordance with 8.3.1.2.
(1) It must be conﬁrmed that no welded joints of low fatigue strength or for which quality control
is diﬃcult are used in fabricating steel members.
(2) For steel members, it must be conﬁrmed whether the maximum stress range resulting from

Chapter 8 Required Durability Performance and Verification

125

repetition of expected actions throughout the design working life is less than the fatigue
limit (cut-oﬀ limit).
(3) In a case where the maximum stress range is greater than the fatigue limit (cut-oﬀ limit)
under the expected actions throughout the design working life, it must be conﬁrmed thatthe cumulative fatigue damage is less than the threshold value for fatigue failure.
(4) In verifying the fatigue of concrete members, it must be conﬁrmed that serviceability andmechanical performance are maintained under the expected actions throughout the design
working life.
【 Commentary 】

In the fatigue investigation of steel members in a steel and composite structure, the members must
be conﬁrmed to have the required durability by evaluating the eﬀect of stress ﬂuctuation caused inmembers by actions such as the live load.
(1) When selecting a structure, one with joints exhibiting particularly low fatigue strength or one
previously reported as suﬀering damage due to fatigue should not be chosen. Locations where
fatigue cracking has been reported as occurring to date are the welded joints of sole plates inbearing supports, welded joints at cut-out ﬂange-web intersections with the main girder, gusset
plate welded joints with lateral bracing, welded joints between upper and lower ends of a verticalmember in an arch bridge, connections between ﬂoor beam members, connections between web
sections of transverse ribs and longitudinal ribs in an orthotropic steel deck, and welded beamto-column joints in a steel pier. In designing such welded joints, suﬃcient attention must be paid
to avoid fatigue problems. Typical fatigue damage may be seen in reference JRA, 1997.
For joint members, joint designs with low fatigue strength or whose quality can be maintained
only with diﬃculty, such as welded joints with backing strips, ﬁllet welds in cross-shaped loadcarrying joints, partial penetration welds, lap joints, gusset welded joints penetrating the web ofa main girder, and interruption joints in steel pipes, should be avoided. If it is necessary to use
these types of joint, it must be conﬁrmed that fatigue cracks will not occur throughout design
working life.
(2) Basically, the joints or structures used should be ones in which the required fatigue resistance isassured throughout the design working life by evaluating the eﬀect of stress ﬂuctuations caused
in members by actions such as the live load. For instance, in the case of highway bridges, thecalculated stress range obtained with the fatigue design load is applied movably against lanes
must be conﬁrmed to be below the fatigue limit (cut-oﬀ limit) determined beforehand for eachjoint.
In choosing joint types, welded joint positions, and structural details, it is important to consider
such points as the degree of stress concentration and the secondary stress caused in actual use,which are regarded as diﬃcult to take into account at the design phase. Additionally, for complex
structures where conventional stress investigations are considered diﬃcult, the stress range may
be investigated using analysis methods such as FE.
(3) If the calculated stress range in (2) above is not below the fatigue limit (cut-oﬀ limit), an
investigation based on the linear cumulative damage rule, in which the eﬀect of repeated load
over a period (of almost 100 years) is accounted for in design, must be considered. Same inrailway bridge, after calculating the maximum stress range using the characteristic loading values
determined from the loading frequency and the magnitude of the train load, it must be conﬁrmedthat this value is less than the fatigue limit (cut-oﬀ limit) of each joint. In the case of not, as done
similarly in highway bridge, a linear cumulative damage rule based investigation considering theeﬀect of repeating load throughout the design working period (60 or 70 years) must be considered.
These investigations may be seen in the references Fatigue Design Recommendations for Steel126

Standard Specifications for Steel and Composite Structures [Design]

Structures (JSSC, 1993a), Fatigue Design Recommendations for Steel Highway Bridges (JRA,2002a), and Fatigue Design Recommendations for Steel Railway Bridges (RTRI, 2000).
(4) The same for steel and composite structures, investigations done in (4) must be done. The
investigation of other composite structures between steel and concrete is available in the reference
JSCE, 2002a. Structures such as pre-stressed ﬂoor slabs or composite ﬂoor slabs between steel
and concrete are investigated in section ”14.4.1 Fatigue resistance of slab” of Chapter 14.

8.3.1.2 Verification of fatigue under wind loading
Veriﬁcation of fatigue under wind loading must in principle involve conﬁrming that the windvelocity at which vortex-induced vibrations arise is greater than the design wind velocity or theamplitude of vortex-induced vibrations is less than a threshold value. If another adequate veriﬁcation method is available, it may be applied.
【 Commentary 】

In considering the fatigue of steel structures caused by wind loading, the most important phenomenon in the dynamic wind response is vortex-induced vibration. This type of vibration is a phenomenon that occurs over a limited range of both wind velocity and wind amplitude, but because fatigue occurs at a comparatively low wind velocity, its investigation is very important. Vortex-induced
vibration has been reported as occurring in bridge girders, the main towers or cables of bridges ofsuspended structure or with hanging members, such as Langer bridges, and even in attachments suchas lighting columns and handrails, etc.
With the present level of technology, the most reliable way of predicting the dynamic wind response
phenomena of structures is to use wind tunnel tests. On the other hand, wind tunnel tests are notalways a convenient means of investigation because a wind tunnel is a specialist item of equipment, sothey cost money and time. To simplify investigations aimed at prooﬁng structures against dynamic
wind response, the Wind Resistant Design of Bridge Road Handbook (JRA 1991) provides someestimated formulas that give results on the safe side for structures, mainly bridges, with spans up to
200 m. These formulas, which are based on past tests, can be used to determine whether it is necessary
to investigate the wind velocity at which phenomena occur in more detail and are also used in Standard
Speciﬁcations for Concrete Structures.
If it proves possible to predict the wind velocity that causes vortex-induced vibration of a certain
using these methods, the fatigue investigation can be carried out by conﬁrming that wind velocity
that induces vortex-induced vibration is greater than the assumed velocity and that the amplitudeof vibrations that occur is smaller than the allowed amplitude. Moreover, the investigation of windvelocity and allowed vibration amplitude may be carried out with reference to Wind Resistant Designof Bridge Road Handbook (JRA, 1991).
In general, the wind velocity at which vibration occurs in attachments such as hanging members oreven lighting columns and handrails may be estimated, but it is diﬃcult to predict the amplitude of vibration with high accuracy. Therefore, after conﬁrming whether vibration occurs at the predicted windvelocity or not through careful observations while construction is under way, measures to eﬀectively
control the vibration may be taken if necessary.
Looking at the occurrence of fatigue in steel structures resulting from wind action aside from vortexinduced vibration, consideration may have to be given to gust response and rain vibration, which is aunique vibration phenomenon of cables. Gust response is an irregular vibration phenomenon causedby airﬂow disorder and is characterized by an amplitude that increases gradually as wind velocity
increases. However, gust response is not usually considered a problem except in particularly unusualcases such as suspension bridges of unusual scale and which transform easily or cable-stayed bridges.

Chapter 8 Required Durability Performance and Verification

127

However, the additional eﬀect of gust response is considered in the regulations on wind loadingin the Standard Speciﬁcations for Concrete Structures (JRA, 2002a). Rain vibration is a vibration
phenomenon caused in the cables of cable-stayed bridges during rain or when the wind is strong.
Recently, even in the absence of rain, attention must be paid to cable vibration because some research
results have indicated a dynamic response to wind acting at an angle. However, there have been nocases of fatigue failure caused by rain vibration up to now in the cables used in Japan.

8.3.2 Verification of resistance to steel corrosion
Veriﬁcation for resistance to steel corrosion must in principle involve using the following method.
If another adequate veriﬁcation method is available, it may be applied.
(1) In a case where the corrosion protection method consists of a surface coating such as paint,
it must be conﬁrmed that the speciﬁc coating selected is suitable for the particular corrosive
environment.
(2) In a case the corrosion protection method is anything except natural weathering of the steel
or a surface coating, it must be conﬁrmed that the speciﬁc corrosion protection method
selected is suitable for the particular corrosive environment.
Regarding corrosion of steel reinforcement in concrete, it must be conﬁrmed that the concretecarbonation depth and the chloride ion concentration remain below the threshold values forthe occurrence of steel corrosion.
【 Commentary 】

Methods of corrosion prevention for steel must achieve the required durability against the environmental conditions in which the steel is employed. However, the scale, shape, and other characteristicsof the materials that may be applied with a particular method are limited. These limits and theconditions of each method with respect to workability of repairs and the diﬃculty of carrying out theinspections required to maintain corrosion prevention performance also diﬀer from method to method.
Therefore, in selecting a method of corrosion prevention, it is necessary to consider cost-eﬀectiveness,a maintenance plan for inspection and repair, and environmental conditions along with requirements
related to durability, aesthetics, etc. To prevent steel corrosion, available methods include surface
coating, surface treatment, galvanic corrosion protection, and treatment of the steel itself.
In general, surface coating is able to prevent corrosion or control it below a ﬁxed limit. Because
the performance of coating methods normally deteriorates gradually over time, the ability to maintainperformance above the ﬁxed standard depends on drawing up and implementing a suitable and eﬀective maintenance plan (including inspection, examination, repair, etc.). To achieve this, it is essential
to implement suitable accelerated tests or exposure tests under the environmental conditions of theconstruction site to clarify structure durability and conﬁrm the principle of the chosen corrosion prevention method. Eﬀective inspection, examination, and maintenance is not possible without a clear
plan, so adequate attention must be paid to this when adopting a corrosion prevention method forsteel structures.
Practical results to date indicate that certain representative corrosion prevention methods, suchas surface coating or using weathering steel, zinc plating, or metal thermal sprays, are able to satisfy
the performance requirements in general if design and maintenance are properly implemented. The
principles of these corrosion prevention methods, the manner in which their functionality fails, andrepair methods that can be used to recover functionality are explained in Table C8.3.1 (JRA, 2002a).
(1) The most used method of preventing steel corrosion is to add a protective ﬁlm by surface coating.
Although this method imposes few structural restrictions and oﬀers a large degree of freedom
in selecting the ﬁnish color, factors in the environment do cause the paint ﬁlm to deteriorate so128Standard Specifications for Steel and Composite Structures [Design]

Table C8.3.1 Representative corrosion prevention methods(1) surface coating(2) steel weathering(3) stainless steel(4) hot dip galvanizing(5) metal thermal
spray

Basic principle

Mode of loss of functionality(including unpredicted
deterioration)

Recoverymethodwhen function lost

Isolating from corrosion environment with a paint layer
Controlling corrosion by
generating a fine rust layer
Controlling corrosion bymeans of a oxide layer
passivation film
Protective film of zinc oxideand sacrificial corrosion prevention by zinc
Sacrificial corrosion prevention by spraying witha metal (zinc, aluminum,
pseudo-alloy, etc.) to forma protective film

Deterioration of paint layer

Repainting

Peeling of rust layer. Associated decrease in cross section
Localized corrosion as pits
generated when the film isthin
Decrease of zinc layer thickness

Painting, etc.

Thinning of sprayed metal
layer (zinc, aluminum, zincaluminum pseudo-alloy, etc.)

Thermal spraying
or painting

Painting, etc.

Thermal spraying
or painting

recoating must be carried out periodically in order to maintain functionality. The deterioration
rate of the paint ﬁlm is determined from the relationship between corrosion factors such as
airborne salt in the environment to which the structure is exposed and the characteristics of thepaint ﬁlm itself. As a consequence, the investigation of corrosion resistance entails choosing apaint speciﬁcation (JRA, 1990 and JBA, 1996) and conﬁrming that a suitable repainting cycle isset in consideration of the corrosion environment, which depends on the structure’s conﬁgurationand location. As an example, one method of deciding when to repaint depends on the rusted
area exceeding 0.3(2) The addition of an appropriate quantity of an alloying element (Cu, Cr, Ni, etc.) to steel, to create
weathering steel, will cause ﬁne rust to be formed. This ﬁne rust layer inhibits the developmentof rust and protects the steel surface, reducing the overall corrosion rate as compared withplain steel. In other words, corrosion is gradual and performance deterioration is suppressed.
Nevertheless, there can be problems with the uniformity of the ﬁne rust layer leading to unevencorrosion rates, particularly where there is airborne salt, where an anti-freeze agent is used (orused nearby), where a bridge is readily inﬂuenced by chloride, or where full wetting and drying
cycles are lacking. Consequently, this method should be used only under suitable conditions
according to the type of material (JRA, 2002a).
To give an example, hot-rolled atmospheric corrosion resisting steels for welded structures(SMA) are speciﬁed in JIS G 3114. These are, in principle, for use without painting in regions
where the amount of airborne salt, as measured by a prescribed method, is below 0.5 mdd (NaCl:
mg/100cm2/day); these areas are shown in Fig.C8.3.1 (PWRI, The Kozai Club, and JBA, 1993).
Others like attention at designing or constructing when weathering steel is used in such truss
bridge, arch bridge or rigid frame bridge are given concretely in this reference and should be consulted. Recently, types of weathering steel (Ni-based high corrosion resistance weathering steel)have been developed with improved chloride resistance, improved surface processing to accelerate
the generation of ﬁne rust, and better prevention of ﬂowing rust. These types of weathering steel
have come into use in steel structures, but if they are to be used proper investigations of corrosion resistance must be carried out considering the actual environment and standard of corrosion

Chapter 8 Required Durability Performance and Verification

129

prevention.

Coastal area along
Sea of Japan I

Coastal area along
Sea of Japan II

Coastal area
along Pacific ocean

Okinawa
Coastal area
along SetonaikaiClassification of area
Coastal areas along Sea of JapanI
II

Coastal areas along Pacific ocean
Coastal areas along the Inland Sea (Setonaikai)
Okinawa

Airborne salt measurements not requiredMore than 20 km from the coastline
More than 5 km from the coastline
More than 2 km from the coastline
More than 1 km from the coastline
Always required

Fig.C8.3.1 Classification of areas in which unpainted weathering steel is applicable

In hot dip galvanizing, steel is dipped into molten zinc at around 440 ℃, forming a two-layer
surface ﬁlm consisting of a steel-zinc alloy and pure zinc. Corrosion of the steel is suppressedby the protective eﬀect of this ﬁlm and by sacriﬁcial oxidation of the surface of the ﬁlm. The
long-term durability of zinc plating for a particular structure cannot be well understood until a
tracing survey is carried out, but in some places aﬀected by seawater or sea breezes, the protective
ﬁlm may not form and the zinc layer and alloy layer are gradually consumed. Consequently,
a structure will require painting in the future. Moreover, structural considerations such as
restrictions on the size of members imposed by the size of the zinc plating tank and the possibilityof thermal transformations in the plating tank are required at design phase (JRA, 2002a). In
addition, plating burn and plating cracks must be avoided during the zinc plating process. Details
should be looked up in literature (JSSC, 1996).
Metal thermal spraying is a method in which a shielding layer is created by spraying molten
metal using compressed air onto the steel surface after carrying out some surface processing,such as grinding. Zinc, aluminum, or an alloy of zinc and aluminum can be used for metal
thermal spraying. As a method of forming a metal layer on the steel surface, it diﬀers fromhot dip galvanizing in that application is not restricted by the scale and size of the structure.
Metal thermal spraying provides a surface with a great many concavities and convexities, so
paint adherence is good and it can be used as a foundation for painting (JRA, 2002a).
To ensure that a corrosion prevention method operates optimally, every detail of the structure130Standard Specifications for Steel and Composite Structures [Design]

must be considered thoroughly in consideration of the method being used, with detailing suchas chamfering used where needed. Further, when diﬀerent types of metal come into contact witheach other, as in welding or bolting of parts, the material of lower electric potential experiences
accelerated corrosion corresponding to the diﬀerence in electric potential. In such cases, measures
such as isolation should be implemented (JRA, 2002a).
(3) The steel used in reinforced concrete is protected by a passivation ﬁlm that forms in the highly
alkaline environment. However, even in this environment, the steel may begin to corrode andcorrosion will progress if the concentration of chloride ions exceeds a certain value and causes
the ﬁlm to be unstable. Once corrosion of the steel starts, cracks form comparatively early andthe corrosion process accelerates. On the other hand, concrete undergoes carbonation throughreaction with the carbon dioxide in the air. This relates to the water-tightness (ventilation
ability) of the concrete and elapsed time.
As a general rule, it is necessary to conﬁrm that throughout the design working life the depthof carbonation does not reach the limit at which corrosion of the steel starts and that the chloride
ion concentration at the steel surface remains below the concentration at which corrosion starts(JSCE, 2002b). Surface coating, steel shielding, and other measures (of coating or plating) may
be used to protect the concrete (JCI, 1998). Details of protection methods against corrosion, suchas electrical methods that restrict corrosion progression of the steel, suitable shielding materials
for the steel, and coating materials for the concrete surface, are given in JCI, 1998.
The most common method of predicting the approximate depth of carbonation, based on
historical records, is to treat it as proportional to the square root of service period. At present,
the need for measures against carbonation is investigated by checking that the design valueof carbonation depth, found from the carbonation rate coeﬃcient (calculated using the typeof cement and water-cement ratio) is less than the limit depth (calculated by subtracting theremnant neutral depth from expected value of cover depth) at which the steel starts to corrode.
However, JSCE, 2002b should be consulted about certain cases in which, if the cement being used
and water-cement ratio and the cover depth satisfy some conditions, it is not generally possible
to omit investigations of carbonation.
(4) Speciﬁc details relating to the corrosion protection of steel in concrete can be obtained from theliterature (JSCE, 2002a; JSCE, 2002b; JRA, 2002b). But in some environments, especially whereanti-freeze agents are used, taking certain suitable measures such as to prevent the ingress ofwater with chloride ions into the concrete is recommended (JSCE, 2002b). Additionally, standard
methods for maintenance should be consulted in the literature (JSCE, 2001). Details of repair
and reinforcement methods can also be obtained from the literature (JSCE, 1999 or JCI, 1998).

8.3.3 Verification of resistance to material deterioration
Veriﬁcation of resistance to material deterioration must in principle involve using the following
methods. If another adequate veriﬁcation method is available, it may be applied.
(1) It must be conﬁrmed that concrete has the required frost resistance by determining the
dynamic elastic modulus and mass loss in freezing and thawing tests.
(2) Regarding concrete corrosion due to chemical attack, it must be conﬁrmed through accelerated tests, atmospheric exposure tests, or another adequate veriﬁcation method that concrete
deterioration does reach a tangible level or aﬀect the required level of performance.
(3) It must be conﬁrmed that concrete has the required resistance to the alkali aggregate reaction(ASR).
(4) In a case where a surface coating is applied to concrete, the waterprooﬁng eﬀect of thecoating must be conﬁrmed in consideration of maintenance planning.

Chapter 8 Required Durability Performance and Verification

131【 Commentary 】(1) The main causes of deterioration of concrete itself are freezing, chemical erosion, and the alkaliaggregate reaction. Freezing-induced deterioration may be seen not only in cold climates but
also in mountainous areas. Concrete’s resistance to freezing is inﬂuenced by large number offactors in addition to its overall quality, including how low the temperature falls, the numberof freeze-thaw cycles, the degree of water saturation, etc. Evaluating these factors accurately is
not an easy task. At present, it is speciﬁed that investigating the freeze-thaw performance of astructure should be carried out by performing accelerated freeze-thaw tests and using as indicesthe loss of mass and the relative dynamic Young’s modulus of the concrete (JSCE, 2002b).
Additionally, if the water-cement ratio and air content can be conﬁrmed to satisfy some certain
conditions, the above type of investigation can be replaced by certain conﬁrmations and suchthe upper limit of water cement rate should be considered at mix design phase may be consulted
from the reference (JSCE 2002b), and appendix 1.
(2) Chemical erosion of concrete is multifarious and depends on the power of external deterioration
actions in the environment. As a result, determining the durability performance of concrete
against these external actions is diﬃcult and impractical. Because in oceanic environments orenvironments inﬂuenced by, for example, acid rain erosion actions are relatively moderate as so
the standard required about chemical erosion resistance in concrete should require deteriorationof concrete not become remarkably. In some environments, such as in sewage systems or in
hot-spring facilities, where severe erosion actions are acting, the performance requirement shouldbe that deterioration of the concrete does not aﬀect the required performance of the structure.
These two facts are recommended as the standard for chemical erosion resistance of concrete(JSCE, 2002b). The conﬁrmation items mentioned above and some speciﬁc investigations may
be found in JSCE, 2002b.
(3) No practical prediction formula has yet been established for the alkali-aggregate reaction, so thealternative of conﬁrming resistance to the reaction through an accelerated test on a concrete
test piece is adopted here. An example of a test method is given in JSCE, 2002b. Additionally,using the measures given in a notiﬁcation by MLIT (Controlling measure against alkali-aggregate
reaction) or in Annex 1 and 2 (Regulations) of JIS A 5308, it should be determined whether thealkali-aggregate reaction can be controlled.
(4) The literature (JSCE, 2002a; JSCE, 2002b; JRA, 2002b) should be consulted about considerations related to coating the surface of concrete or for details of preventing deterioration of theconcrete itself. Also, JSCE, 2001 should be consulted for standard methods of maintenance.
Details of repair and reinforcement methods may be found in JSCE, 1999 or JCI, 1998.

8.3.4 Verification of maintainability
Veriﬁcation of maintainability must in principle involve determination at the design stage of easeof maintenance, including inspection and repair, throughout the design working life. If anotheradequate veriﬁcation method is available, it may be applied.
【 Commentary 】

In evaluating the performance of steel and composite structures with respect to the maintenanceplan, the repairs that might become necessary as a result of deterioration may be repainting, expansion
joint repair, bearing support repair, distribution pipe repair, ﬂoor slab replacement, and other steel
member repairs. It should be conﬁrmed that structural details are such that these kinds of repair tasks
are feasible.
For instance, repainting work requires that a scaﬀold can be easily installed and that structural

132

Standard Specifications for Steel and Composite Structures [Design]details make painting and scraping work easier. Also, when jacking up the main girder to replace abearing support, it will be diﬃcult to insert the jack unless there is adequate working space between
bridge and abutment members. That means it is necessary to consider whether adequate work space
is provided during the design phase, and also to ensure that a sole plate is ﬁtted to the ﬂange to takethe jack and that any additional vertical stiﬀeners are provided. The structure of abutments and piersthat carry the reaction force must be considered also. To give an example, in many cases a bracket
is used to suﬀer the jack, to do same in a metal bridge pier, a structural detail in which a bracket
is able to be installed must be considered. In designing a concrete bridge pier, it must be conﬁrmed
during the superstructure design phase that the reinforcing are arranged such that anchor bolts canbe appropriately installed.
The items which such repair and reinforcement works must be conﬁrmed against fatigue may besuch space enough to carry members and equipment or structural detail in which carrying equipment
in is made more easily. Moreover, the presence of suitable manholes for carrying equipment into a steel
girder, cable rack, or distribution pipework and their workability must be conﬁrmed. It should also be
conﬁrmed that suitable ventilation is possible. These structural details and precedents can be foundin JRA, 2002a or JBA, 2002.
References in Chapter 8
Japan Road Association (1990) ：Wind-resistant Design Manual for Highway Bridges ．
Japan Road Association (1991) ：Wind-resistant Design Manual for Highway Bridges.
Public Works Research Institute, the Kozai Club, and Japan Bridge Association (1993) ：Research Committee on Application of weathering Steel to Bridge, Report of Cooperative Research on Application of
weathering Steel to Bridge, XX.
Japanese Society of Steel Construction (1993a) ：Fatigue Design Guideline for Steel Structures and Commentaries.
Japanese Society of Steel Construction (1993b) ：Investigation Manual of Painted Steel Bbridges, JSS IV031993 ．
Japan Bridge Association (1996) ：Paint Guidebook for Bridege Engineers.
Japanese Society of Steel Construction (1996) ：Design and Guide for construction of Hot Dip Galvanizing
Bridge.
Japan Road Association (1997) ：Fatigue of Steel Structures.
Japan Concrete Institute (1998) ：Report of Research Committee on Rehavilitaion of Concrete Structures.
Japan Society of Civil Engineers (1999) ： Reinforment Guideline of Concerete Structutres (Draft), (Concrete
Library, No.95).
Railway Technical Research Institute (2000) ：Fatigue Design Recommendations for Steel Railway Bridges,
Steel and Composite Structures.
Japan Society of Civil Engineers (2001) ：Standard Specifications for Concrete Structures, Maintenance Volume.
Japanese Society of Steel Construction (2001) ：Investigation Research Subcommittee on based design for Steel
Structures, Guideline of Performance based design for Steel Structures, JSSC Technical Report, No.49.
Japan Society of Civil Engineers (2002a) ：Standard Specification for Concrete Structures, Structural Performance Verification Volume.
Japan Society of Civil Engineers (2002b) ：Standard Specification for Concrete Structures, Construction Volume.
S.Nakatani, K.Uchida, K.Nishikawa, M.Kanda, K.Miyazaki, S.Kawama and S.Matsuo (2002) ：Experimental study
on the fatigue durability of highway bridge slab, National Institute for Land and Infrastructure Management, No.28.
Japan Bridge Association (2002) ：Repair and Reinforcement Examples of Steel Bridges.
Japan Road Association (2002a) ：Specifications for Highway Bridges and Commentary, I Common Specifications Volume, II Steel Highway Bridges Volume ．
Japan Road Association (2002b) ：Specifications for Highway Bridges and Commentary, I Common Specifica-Chapter 8 Required Durability Performance and Verification

133

tions Volume, II Concrete Bridges Volume ．
Japan Road Association (2002c) ：Fatigue Design Guideline for Steel Highway Bridges ．
Japanese Society of Steel Construction (2002d) ：Reference on Proof Stress, Durability and Reinforcement forConstructed Steel Bridge Members.
Japan Road Association (2005) ：Handbook of paint and corrosion prevention for steel highway bridges.

134Standard Specifications for Steel and Composite Structures [Design]

Chapter 9 Required Social and Environmental
Compatibility Performance andVerification
9.1 General(1) Steel and composite structures shall maintain their social and environmental compatibility
under the actions speciﬁed in Chapter 2 throughout the construction and in-service periods.
(2) Performance items related to social and environmental compatibility include social compatibility, economic rationality, and environmental compatibility.
(3) Social and environmental compatibility shall be veriﬁed with respect to the limit state established for each performance item by setting a proper performance index representative ofeach performance item. However, in cases where there are diﬃculties in setting and verifying such limit states for social and environmental compatibility, society and environmental
compatibility shall be veriﬁed by optimizing each performance item.

【 Commentary 】

Steel and composite structures should be compatible with social and environmental conditions,meaning that adverse inﬂuences on the surrounding social and natural environments should be minimized.
In this speciﬁcation, performance requirements include verifying social compatibility in consideration of the social importance of the structure, economic rationality (to check economic eﬃciency overthe structure’s life cycle), and environmental compatibility (to check environmental loading from CO2
emissions and harmonization with the structure’s surroundings).
In cases where it is diﬃcult to set limit states for social and environmental compatibility, veriﬁcation
should be by optimizing the performance requirements.

9.2 Required Social and Environmental Compatibility Performance(1) Steel and composite structures shall be designed to provide the functions required according
to their importance.
(2) Steel and composite structures shall be designed to be safe and functional and to minimize
both construction cost and life-cycle cost.
(3) Steel and composite structures shall be designed to avoid adverse eﬀects on the surroundingsocial and natural environments resulting from vibration and noise, to minimize environmental impacts, such as CO2 emissions, throughout their life cycle, and to oﬀer an aesthetic
that does not provoke undesirable psychological reactions in people nearby.

【 Commentary 】

Performance requirements to ensure the social and environmental compatibility of steel and composite structures include social compatibility, economic rationality, and environmental compatibility.
Because steel and composite structures can strongly aﬀect social and economic activity, they should
be designed such that the functionality required according to their importance level is attained. It is
generally unacceptable for steel and composite structures to have excessive safety and compatibility

Chapter 9 Required Social and Environmental Compatibility Performance and Verification

135

with society and the environment. Rather, they should be designed to provide adequate safety andfunctionality while minimizing not only construction cost but also life cycle cost.
In generally, steel and composite structures are expected to have a service life of 50 years and overthis time they can strongly aﬀect the surrounding social and natural environments. They should bedesigned so as to not adversely aﬀect the surrounding social and natural environments with vibrationand noise, to minimize environmental impacts, such as lifetime CO2 emissions, and to avoid undesirable
psychological reactions among those who see them.

9.3 Verification of Social and Environmental Compatibility
9.3.1 Verification of social compatibility
Social compatibility shall be veriﬁed by conﬁrming that the performance index representativeof each performance item satisﬁes the limit-state requirements established for that performance
item in consideration of the importance of the steel or composite structure.
【 Commentary 】

Structural factors can be determined as speciﬁed Chapter 1 section 1.5 in consideration of socialand economic impacts, importance in disasters, and economic factors such as reconstruction and repair
costs at the time when the structure or its members reach their limit states as a result of actions during
the construction and in-service periods. The social compatibility of structures should be veriﬁed using
the appropriate structural factors for safety, serviceability, and durability as deﬁned in Chapters 6, 7,
and 8, while economic rationality and environmental compatibility are speciﬁed in this chapter.
The owners (contracting parties) of structures may determine the values of structural factors because they cannot be logically deﬁned based on reliability theory. However, the values of structural
factors shown in Table C1.5.1 can generally be adopted.

9.3.2 Verification of economic rationality
Economic rationality shall be veriﬁed by conﬁrming that the life-cycle cost （ LCC ）of a steel orcomposite structure is minimized or that the life-cycle utility (LCU), including social, economic,
and cultural utilities, is maximized. However, in a case where it is impossible to satisfy these
conditions, economical rationality shall be veriﬁed by optimizing LCC or LCU.
【 Commentary 】

Since many steel and composite structures form part of the social capital, they are required to oﬀer
eﬀective functionality within limited budgets. For this reason, it is diﬃcult to obtain social consensus
for excessively high levels of safety, serviceability, repairability, durability, constructability, and thesocial and environmental compatibility speciﬁed in this chapter. However, it is extremely diﬃcult toproperly set performance levels for structures. One eﬀective method of dealing with this problem is todetermine each performance level so that the life-cycle cost (LCC) of a structure is minimized. LCC
includes the following costs.
(1) Investigation and project costs(2) Initial construction costs (including land acquisition, etc.)(3) Maintenance and repair costs during in-service period(4) Removal costs(5) Depreciation based on social discount rate(6) Anticipated value of loss (damage and loss of the structure, loss of human life, social, economic,

136Standard Specifications for Steel and Composite Structures [Design]and cultural losses caused by functional failure of the structure, etc.) if the structure reaches alimit state
Costs (1) to (5) can be calculated with relative ease, but further research is needed in order toestimate cost (6). At present, costs (1) to (4) can generally be considered in performance veriﬁcation
by LCC.
Since social capital essentially plays a role in creating a more aﬄuent national life, it may be
insuﬃcient to focus on only the actual cost of a structure. Therefore, both positive and negativeeﬀects (utilities) of a structure should be considered in performance veriﬁcation. For example, thesocial, economic, and cultural utility of the existence of a structure and the service it provides aswell as the recyclability of the structural materials can be quantitatively evaluated as contributing
to positive utility, while construction and maintenance costs can be treated as negative utility. The
life-cycle utility (LCU) of a structure can then be deﬁned as the sum of the positive and negative
utility values. This means that the ideal approach is to determine each performance level so that LCU
is maximized. Although the concept of LCU has been little researched so far, performance veriﬁcationin terms of LCU is also described in this chapter. It is expected that research in this ﬁeld will progressin the near future, leading to greater understanding of the utility and beneﬁt of steel and composite
structures among the general public.

9.3.3 Verification of environmental compatibility
Environmental compatibility shall be veriﬁed by conﬁrming that performance indices for vibration and noise, which might adversely aﬀect the surrounding social and natural environments,
environmental impacts such as CO2 emissions, and landscape are less than the speciﬁed criteria.
However, in a case where it is impossible to satisfy these conditions, environmental compatibility
shall be veriﬁed by optimizing each performance item.
【 Commentary 】

Performance requirements related to environmental compatibility are vibration and noise (which
can adversely aﬀect the nearby social and natural environments), environmental impacts (such as CO2
emissions over the life cycle of the structure), and the appearance of the structure to people nearby.
If there is a possibility that a structure will cause environmentally harmful vibration and noise
during construction and the in-service period, performance levels estimated using numerical analysis
and from previous similar examples should be conﬁrmed to be less than the criteria speciﬁed in theenvironmental quality standards or by ISO. As for noise and vibration from large highways close toresidential areas, the sound pressure level generated by vehicles is generally regulated under the noise
regulation law and the vibration regulation law. The limit of vehicle noise is 45 to 80 dB, depending on
the area classiﬁcation and time of day under the noise regulation law, while traﬃc-induced vibration
is limited to 60∼70 dB depending on the area classiﬁcation and time of day under the vibration regulation law [Japan Society of Civil Engineers, 2002]. In addition, some local governments specify theirown environmental criteria and these limit values can generally be used for performance veriﬁcation.
Methods of estimating the noise and vibration generated by structures can be classiﬁed as analyticalmethods based on techniques reported in the literature and analogies based on measurements taken insimilar structures [Japan Society of Civil Engineers, 2003]. On the other hand, limits on low-frequency
sounds have been deﬁned as ”100% pass level L50 in the range 1∼80 Hz is lower than approximately
60∼90 dB for low-frequency sound in the general environment” [Air Quality Bureau, Environment
Agency, 1984] and alternatively as ”G-weighted sound pressure level in the range 1∼20 Hz is around100 dB for perceptible low-frequency sound” [ISO, 1995]. These values can be taken as the limit
values for low-frequency sound. Further, the impact of vibration and noise on ecosystems, including

Chapter 9 Required Social and Environmental Compatibility Performance and Verification

137

animals and plants, have not necessarily been evaluated quantitatively. Therefore, limit values should
be appropriately determined with reference to research examples consisting of environmental impact
assessments for existing similar structures.
As for environmental impacts, such as lifecycle CO2 emissions, speciﬁc limit values and veriﬁcation
methods have not necessarily been proposed and future research results are awaited. At present, environmental impacts should be reduced as much as possible in consideration of economy and technology.
Universal and quantitative indices for the appearance of structures to people nearby have neverbeen proposed and, as with the environmental impacts discussed above, future research is awaited.
At present, attention should be paid to (1) making the structure mechanically clear, (2) choosing
a suitable structure for the surrounding circumstance, (3) unifying structural types, (4) considering
ancillary structures, and (5) other considerations (distance between bearings, position of bridge piers,etc.) as described in Part II Structure Plan of these speciﬁcations. In outline, a structure’s appearance
should avoid undesirable psychological reactions among people nearby while considering economy andtechnology.
References in Chapter 9
Air Quality Bureau, Environment Agency(1984) ：Reports on Low-Frequency Aerial Vibration
Japan Society of Civil Engineers (2002) ：Guidelines for Performance Verification of Hybrid Structures (tentative) ．
Japan Society of Civil Engineers (2003) ：Towards establishment of performance-based design system for steel
structures ．
ISO(1995) ：ISO7196 Acoustics-frequency Weighting Characteristics for Infrasound Measurements.

138

Standard Specifications for Steel and Composite Structures [Design]

Chapter 10 Structural Members in General
10.1 Structural Members
All members are designed in a simple structure as possible for the convenience of fabrication,transportation, site construction, examination, painting, maintenance, patching etc. The examination of critical stage of members is given in chapter 6.
【 Commentary 】

The choice of a complex design for a structure can lead to various problems in terms of fabrication,transportation, erection, inspection, painting, draining, maintenance, and so on. Each structuralmember should be made as simple as possible, otherwise the design calculation will end up being too
complex and substantial and unexpected secondary stresses may arise. In other words, if a structure
is very diﬃcult to fabricate then one cannot expect good-quality fabrication, while if it is diﬃcult totransport it may end up being damaged during transportation. Defects may also be overlooked if a
section is diﬃcult to inspect or cannot be inspected thoroughly. Similarly, if the structure is diﬃcult topaint, this could be the reason for a poor paint job, which would hasten corrosion of the steel material.
Furthermore, since inspections and repairs are essential if a structure is to be kept functionally soundover a long period, it is also important to consider future maintenance activities such as inspection
and repair during the design stage.

10.2 General
10.2.1 Secondary stress
The secondary stress which is caused by the inﬂuence of member’s eccentricity, node ’s rigidity,
abrupt change in section, ﬂoor girder’s deﬂection, ﬂoor framing deformation involved in the changeof the member length, member deﬂection under empty weight etc... must be designed to become
small as much as possible in structure members.
【 Commentary 】

Secondary stress is stipulated through reference to [Japan Road Association, 2002]. Although acertain amount of secondary stress is unavoidable, the normal practice is to ignore secondary stressduring design calculations and to include its impact within the safety factor. However, eﬀort should
be made to minimize the secondary stress in the design of each structural member. The following
points are raised in the commentary to [Japan Road Association, 2002] as requiring attention in orderto reduce secondary stress as much as possible.
1) Eccentricity of structural member
Eccentricity should be reduced as much as possible when designing the sections of a structure
in detail. Even when eccentricity is inevitable, the design must reduce its impact to a minimum.
2) Rigidity of panel joints
Since the secondary stress rises when the rigidity of a panel joint is too large compared to thatof each member converging at that joint, panel rigidity should accord with the rigidity of themembers. In particular, when designing a truss, secondary bending due to panel joint rigidity

Chapter 10 Structural Members in General139

as well as secondary stress caused by eccentric jointing of secondary members to the panel joints
and loading on the transverse beams should be taken into account. Since many other countries
do not require secondary stress to be checked when the ratio of member height to length, h/l, isless than 1/10, [Japan Road Association, 2002] states that h/l should ideally be less than 1/10
(i.e., the minimum slenderness ratio should be about 30).
3) Deﬂection of deck girder
When the deﬂection of a deck girder is large, depending on the method used to connect theend parts, out-of-plane deformation of the main girder may occur, leading to higher secondarystress. Also, the deck slab is subjected to an additional bending moment due to deﬂection of thedeck girder. For this reason, deﬂection of the deck girder must be kept as small as possible.
4) Deformation of deck system caused by change in member length
In the case of a tied arch with a long span, substantial tensile force is exerted on the ties. If thedeck system is rigidly connected to the ties, it will stretch with the ties and deform unexpectedly.
In such cases, it is best to install an expansion joint in one section of the stringer.
5) Deﬂection of a member caused by its own weight
The height of a structural member such as a truss member, which is designed based only on
longitudinal force, should be greater that its width in order to minimize the bending stress due
to its own weight. However, care must be taken since if it is too high the panel joint will become
too rigid, and secondary stress will increase.
6) Others
Secondary stress due to friction of movable beam ends, settlement of supporting joints, temperature changes, sudden distortion, and stress concentration due to corrosion must also be taken
into consideration, and eﬀort must be made to minimize such stress as much as possible. Extraattention must be paid when high tensile steel is used for a main girder with an exceptionallysmall beam height because deﬂection of the cross beam will be greater as it would be less rigid
than if ordinary steel were used. As a result, secondary stress due to out-of-plane deformationof the main girder in the case of a steel girder through-bridge and out-of-plane bending of the
web member in the case of a truss would be greater. Further, care must be taken when hightensile steel is used for a primary member and mild steel for a secondary member since a variety
of secondary deformations and stresses will occur.

10.2.2 Stress concentration
The stress concentration must be considered in design in case it inﬂuences the member notch
part or structural discontinuity part.
【 Commentary 】

When there is a weakness because of a signiﬁcant local concentration of stress due to a notch,
measures must be implemented to alleviate this stress concentration by altering the shape or reinforcing
with a reinforcing material. Since the impact that stress concentration has on fatigue and brittle failure
diﬀers greatly from the impact on loading strength in terms of design direction, one must thoroughly
study its impact on failure mode beforehand.

10.2.3 Member with alternate stresses
The member which is subjected alternately to a compressive stress and a tensile stress must be
designed safely to each stress.
【 Commentary 】

140Standard Specifications for Steel and Composite Structures [Design]This is stipulated by reference to [Japan Road Association, 2002]. The following is the commentaryfrom that document.
For structural members subject to alternating stress, the necessary cross-sectional area for eachstress must of course be calculated and the largest of the cross-sectional areas should be used. But
at the same time, buckling in response to compressive stress must also be compared. For example,
alternating stress arises around the center of the span in the case of the web member of a truss, so
this part must be designed for safety against various stresses. Structural members whose stress sign
reverses depending on wind direction, such as web members in the transverse groove, are subject toalternating stress; their cross sections must be able to withstand the tensile force due to wind direction
and various compressive stresses.

10.2.4 Minimum plate thickness and corrosion(1) The minimum thickness of the steel plate is assumed to be the one provided not beingtransformed when the plate is processed, transported, constructed in site, and considering
the damage of the section caused by corrosion and wear-out etc.
(2) In the case of the corrosion allowance [margin] set up, the plate thickness in the check tosafety is assumed to be the one decreased by this margin thickness.

【 Commentary 】

The minimum thickness of structural steel is determined based on the way it is handled during
fabrication, transportation, and erection as well as in consideration of corrosion. Generally, the eﬀects
of corrosion are not considered for a structure that has undergone anti-corrosion treatment, such as bypainting or hot dip galvanizing, but it is taken into consideration during the design stage in the caseof underground structures which are in a highly corrosive environment and cannot easily be given ananti-corrosion treatment in the future.
In [Japan Road Association, 2002], the corrosion environment varies according to the anti-rust or
anti-corrosion methods implemented and the location of the structure, while handling and fabrication
conditions diﬀer for each individual bridge. However, the following regulations are given as a generalrule with regard to the minimum thickness of structural steel.
1) Structural steel must be 8mm or more in thickness. However, the thickness of the web of I-section
steel and channel steel may be reduced to 7.5 mm or more. Closed-section longitudinal ribs, as
used as stiﬀeners for steel decks and box girders, may be reduced to 6 mm or more if the corrosion
environment is good or suﬃcient measures have been taken against corrosion.
2) The wall thickness of steel tube to be used as a principal member should be 7.5 mm or greater,while steel tube used as a secondary member must be 6.9 mm or greater in wall thickness.
Material used for guard rails, ﬁller, and pedestrian deck slabs need not follow these regulations.
Refer to ”8.2.2 Resistance to Corrosion” for corrosion measures related to the use of weathering
steel.

10.2.5 Curved members
It is necessary to do a thorough examination about the additional stress by the curve when the
curved member is designed as a straight member.
【 Commentary 】

When ’curved’ structural members such as curved I girders and arch rib are designed as polygonalstraight members, the additional stress that may occur due to bending in the radial direction of the

141

Chapter 10 Structural Members in Generalcurve (because of discrepancies in the angle of longitudinal stress in the members) must be taken
into consideration. If this additional stress is suﬃciently small compared to the design stress, curved
structural members can be designed as multiple straight structural members, as in the case of a curved
box girder of large out-of-plane rigidity and arch ribs of large radius of curvature.

10.2.6 Dynamic wind-resistant design of structural members
Because the vibration caused by wind may occur to the following members except bridge girders,
the necessity of dynamic wind resistant design must be examined.
• Towers of cable-stayed bridges and suspension bridges• Cables of cable-stayed bridges and hangers of suspension bridges• Arch bridges and truss bridges with large slenderness ratios• Pillar-shaped members with especially large slenderness ratios, such as lighting pillars【 Commentary 】

This is stipulated by reference to [Japan Road Association, 2002]. The towers of cable-stayed
bridges and suspension bridges do not generally require dynamic wind resistant design as completed
systems, although it may be necessary to consider dynamic wind resistance during erection. There
have been many cases of vibration occurring in the cables of actual cable-stayed bridges. Vibration
may also occur in the suspenders of Langer bridges and the chord members of trusses with a large
slenderness ratio, as well as in lamp posts.
The reason for vibration in structural members such as these has not been fully understood and,since it also varies depending on the structure’s resistance to wind turbulence, it is diﬃcult to comeup with a speciﬁc check method. For this reason, the ideal approach is to conduct a vibration study
according to [Japan Road Association, 2002] and [Japan Road Association, 1991].

10.3 Frame Members with Axial Tensile Force
10.3.1 Slenderness ratio of members
The maximum slenderness ratio of the tensile member is made to become below the decided
maximum slenderness ratio in consideration of the characteristic of the structure.
【 Commentary 】

In order to ensure that a tensile member has suﬃcient rigidity to withstand damage during trans-

Table C10.3.1 Maximum slenderness ratio of a tensile member
AISC

Standards for Highway Bridge

Standards for Railway Structure[AISC,1978][Japan Road Association, 2002][Railway Technical ResearchStandards for Hydraulic Gate

Institute, 2000]& Penstock Technology[Japan Hydraulic Gate
& Penstock Association, 1981]

Principal
MemberSecondaryMember

240

200

300

240

200
–

142

Standard Specifications for Steel and Composite Structures [Design]

portation and erection as well as to minimize vibration during use, while also ensuring the rigidity of
the whole structure, rules have been established regarding the slenderness ratio of such members basedon the structure’s characteristics and the member’s level of importance.
The maximum slenderness ratio of a tensile member as stipulated by [AISC, 1978, Japan Road Association, 2002, Japan Hydraulic Gate & Penstock Association, 1981, and Railway Technical ResearchInstitute, 2000] is as shown in Table C10.3.1. However, these limits do not apply to eyebars, steel bars,
and wire rope.

10.4 Frame Members with Axial Compression Force
10.4.1 Width-thickness ratio of plate subjected to compressive stressand stiﬀened plate
The maximum width-thickness ratio of plate that is subjected to a compressive stress andstiﬀened plate is assumed to be the one decided in consideration of the steel class, the position of
the plate. The strength of the plate that is subjected to a compressive stress and stiﬀened plateis given in ”Chapter 5 Material Strength”.
【 Commentary 】

The principle regarding the maximum width-thickness ratio of plates and stiﬀeners that are subject
to compressive stress due to axial compressive forces and bending moments is outlined here.
(1) The maximum width-thickness ratio of plates subject to compressive stress as stipulated by[Architectural Institute of Japan, 2002, Architectural Institute of Japan, 1975, Architectural Institute of Japan, 1973, AISC, 1978, ASCE, 1971, Japan Road Association, 2002, Japan HydraulicGate & Penstock Association, 1981, and Railway Technical Research Institute, 2000] is as shownin Table C10.4.1.

Fig.C10.4.1 Extreme ﬁber stress of a plate(2) The stance of [Japan Road Association, 2002] on the width-thickness ratio of a plate supported
at both ends with stiﬀeners (stiﬀening plate) is as follows.
When a stiﬀener that satisﬁes rule (3) has been placed at regular intervals on a plate supported
at both ends and which is subject to compressive stress, the width-thickness ratio of the stiﬀening
plate is expressed by Eq.(C10.4.1). However, the thickness of a plate that is only temporarily
subject to stress during erection needs only to satisfy Eq.(C10.4.2).

where,

Fbt

851f nb≤ √t
F(C10.4.1)b≤ 85f nt

(C10.4.2)：speciﬁed value of material strength (N/mm2 )：total width (mm) of stiﬀening plate (see Fig.C10.4.2)：plate thickness (mm)143

Chapter 10 Structural Members in General

Table C10.4.1 Maximum width-thickness ratio of plate subject to compressive stressType ofStandards

Guidelines

Technical

AISC-

ASCE

Reference

Steelfor Steelfor

Guidelines

Spec.

Plastic

HighwayStandards Standards
forStructure

Plasticity

for High(Part II)

DesignBridgeHydraulic Railwayof Steel

Buildings

Gate &

Structure

for
Structure

Penstock
Technology

b/t of jutted platesuch as H
cross-section
membersb/t of flange plateof box cross-section
membersd/t1) of web plateof columns

d/t of web plate of
beam

SS400
or A36
SM490
or A441
SS400 orA36
SM490
or A441
SS400
or A36
SM490
or A441
SS400
or A36
SM490
or A441

15.5

10.0

9.0

8.5

8.5

12.5
16

12

13.2

8.5

8.5

7.0

7.0

11

47.8

30.0

32.2

31.6

56f2)

40

40.7

26.0

27.5

26.8

48f2)

34

47.8

45.0

43.2

42.8

43.0

40

40.7

39.0

36.8

36.3

36.4

34

71.0

71.0

50.3

68.6

70.0

70

70

70

60.6

61.0

42.9

58.2

59.3

60

60

60

(A36 and others refer to ASTM standard)
NOTE: 1) ”d” is all dimensions of the structural member for those regulations other than ”Standards for Designing Steel
Structure” [Architectural Institute of Japan, 2002], ”Technical Guidelines for High Buildings” [Architectural Instituteof Japan, 1973] and ”Standards for Hydraulic Gate & Penstock Technology” [Japan Hydraulic Gate & Penstock
Association, 1981]. Here, ”all dimensions” refers to the height of the structural member including the thickness ofa flange around the strong axis.
2) f = 0.65φ2 + 0.13φ + 1.0, φ = (σ1 − σ2 )/σ1
σ1 , σ2 ： the extreme fiber stress at both ends of a plate, but the compressive stress is positive andσ1 ≥ σ2 (See Fig.C10.4.1.)nf：number of panels created by vertical stiﬀener (n ≥ 2)
：coeﬃcient depending on stress gradient

 
 2
φ
φ
+ 0.13+ 1.0nnφ：stress gradient ，φ = (σ1 − σ2 )/σ1 (0 ≤ φ ≤ 2)

f = 0.65

σ1 , σ2 ：extreme ﬁber stress at each edge of stiﬀening plate (N/mm2 )However, the compressive stress shall be positive and σ1 ≥ σ2 (see Fig.C10.4.3)

Fig.C10.4.2 Total width of stiﬀening

Fig.C10.4.3 Extreme ﬁber stress ofplate

stiﬀening plate(3) The view of [Japan Road Association, 2002] regarding the stiﬀener designed in (2) for the stiﬀening plate is as follows:
1) The steel of the vertical stiﬀener shall be of to the same type as that of the plate to be144Standard Specifications for Steel and Composite Structures [Design]

reinforced or superior
2) The moment of inertia of cross-section Il (mm4 ) and cross-section area Al (mm2 ) of one
piece of vertical stiﬀener calculated in section 4) shall satisfy Eq.(C10.4.3) and (C10.4.4),
respectively.
bt3
γl,req
11
bt
Al ≥
10n
Il ≥

where,tbnγl,req(C10.4.3)(C10.4.4)：thickness of stiﬀening plate (mm)：total width of stiﬀening plate (mm)：number of panels created by vertical stiﬀener (n≥2)：rigidity required of the vertical stiﬀening plate according to thecalculation in section 3)
3) The rigidity required of the vertical stiﬀening plate is calculated as follows:a) If α ≤ α0 and the moment of inertia of cross-section It (mm4 ) calculated in 4) below
satisﬁes Eq.(C10.4.6), then :
⎫
 2
⎪
t0
(α2 + 1)2
2⎬
(t ≥ t0 ) ⎪γl,req = 4α n
(1 + nδl ) −tn(C10.4.5)⎪(α2 + 1)2⎪2⎭γl,req = 4α n(1 + nδl ) −(t < t0 )n
bt3 1 + nγl,req(C10.4.6)
It ≥
11
4α3
b) In other cases :
⎡
 2
t0
1⎣
2
γl,req =2n(1 + nδl ) − 1nt21  2γl,req =2n (1 + nδl ) − 1 − 1nwhere,

2

⎤
− 1⎦

⎫
⎪
⎪
⎬
(t ≥ t ) ⎪0(C10.4.7)⎪⎪⎪(t < t0 ) ⎭α：longitudinal and transversal dimension ratio of a stiﬀener, α = a/b

α0a：marginal longitudinal and transversal dimension ratio, α0 = 4 1 + nγlδl：cross-section area ratio of one transversal stiﬀener, δl =γl：stiﬀness ratio of transversal stiﬀeners, γl =(see Fig.C10.4.4)

t0
F
f

√

：transversal stiﬀener interval (mm)Il
bt3 /11

Al
bt

√
b F
：plate thickness of stiﬀener, t0 =426f n：speciﬁed value of material strength (N/mm2 )：coeﬃcient depending on stress gradient shown in (2)4) The moment of inertia of the stiﬀener’s cross section is obtained by the following rule:a) If a stiﬀener is located on one edge of the plate to be reinforced, then it is themoment of inertia of the cross section with respect to the surface on the stiﬀener
side of the plate to be stiﬀened.
b) When stiﬀeners are located on both edges of the plate to be reinforced, then it is
the moment of inertia of the cross section with respect to the neutral surface of theplate to be stiﬀened.

Chapter 10 Structural Members in General

145

Fig.C10.4.4 Longitudinal and transversal dimension ratio of stiﬀener

10.4.2 Perforated plate
The minimum plate thickness of the perforated plate that is subjected to a compressive stressis decided in consideration of the distance between welding lines, the width from welding line tothe hole.
【 Commentary 】

It is common to occasionally use structural members with perforations for operational purposes.
In such a case, local buckling may occur if the perforated plate is too thin. [Japan Road Association,
2002] stipulates as follows in such cases.
(1) The minimum plate thickness for perforated plates and the maximum distance between the inner
weld line and the edge of a perforation is as shown in Table C10.4.2:
Table C10.4.2 Perforated plate
Steel type
SS400, SM400, SMA400W
SM490
SM400Y, SM520, SMA490W
SM570, SMA570W

Fig.C10.4.5 Perforated plate

Minimum plate thickness
(mm)
d/50
d/40
d/40
d/35

where, tdeMaximum width between inner weld
line and edge of perforation (mm)
13 t
11 t
11 t
10 t

：thickness of perforated plate (mm)：distance between inner welding lines (mm)：maximum distance between inner weld line

to edge of perforation (mm)(2) The length of perforation measured in the stress direction must be less than double the width of
perforation.
(3) The length of plate between two perforations measured in the stress direction must be greaterthan d. However, the distance from the rim of perforation at the edge and the edge of theperforated plate must be greater than 1.25d.
(4) The radius of curvature of the rim of the perforation must be greater than 40 mm.
Furthermore, in [Railway Technical Research Institute, 2000] it is stated that the minimum
thickness of a perforated plate should be d/50 for a compression member and d/60 for a tension
member based on experience.

146Standard Specifications for Steel and Composite Structures [Design]

10.4.3 Inﬂuence of eccentric bending moment
The inﬂuence of bend moment by eccentric is considered when angle steel, T steel etc is installed
only in one side of the gusset plate.
【 Commentary 】

A compression member comprising an angle or T section should ideally be checked according to”Chapter 6 Necessary Capability and Checking for Safety” as a member that is subject to bending andcompression by calculating the eﬀect of eccentricity on the bending moment. However, to check every
member in this way would make calculation very complicated, so an abbreviated calculation may be
used. The view of [Japan Road Association, 2002] as regards the abbreviated calculation is as follows.
Design can follow Eq.(C10.4.8) when the compression member comprises an angle or T section
whose ﬂange is connected to the gusset plate, as in Fig.C10.4.6.
P ≤ 1.0l/rx
Ag σcug 0.5 +1, 000where, PAglrx(C10.4.8)：axial compressive force (N) with safety factor already taken into consideration：total cross-sectional area of member (mm2 )：eﬀective buckling length (mm)：radius of gyration of area (mm) around the axis passing through the gravity center ofa cross-section and parallel to the gusset surface (x-axis of Fig.C10.4.6)
σcug：compressive strength (N/mm2 ) as calculated using the following equation

using l/rx⎧
1.0F
(λ ≤ 0.2)⎪⎪⎨(1.109−0.545λ)F(0.2 < λ ≤ 1.0)
σcug =⎪
1.0⎪⎩
F(1.0 < λ)(0.777 + λ2 )
1 F lwhere ，λ ：slenderness ratio parameter λ =π E rxF ：speciﬁed value of material strength (N/mm2 )E ：Young’s modulus of steel (N/mm2 )Fig.C10.4.6 Compression member comprising angle or T section

10.4.4 Slenderness ratio of structural members
The slenderness ratio of the compressive member is made to become below the maximum width- thickness ratio in which the characteristic of the structure is considered.

147

Chapter 10 Structural Members in General【 Commentary 】

Table C10.4.3 shows the maximum slenderness ratio of a compression member as stipulated by[AISC, 1978, Architectural Institute of Japan, 2002, Japan Road Association, 2002, Japan HydraulicGate & Penstock Association, 1981, Deutscher Normenausschuss, 1990, BSI, 1980, and Railway Technical Research Institute, 2000].
Table C10.4.3 Maximum slenderness ratio of compression member
SourceAISC
Standards for Steel Structure
Reference for Highway Bridge
Standards for Hydraulic Gate
& Penstock Technology
DIN4114
BS5400Standards for Railway Structure

Maximum allowed
slenderness ratio

Comment

240
300
200
250
120
150
150
250
180
250
100
120

principal member
bracing, secondary member
compression member
compression member
principal member
secondary member
secondary member
compression member
member subject to fixed load
member subject to wind
primary compressive member
primary compressive member

10.5 Frame Members with Bending
10.5.1 Width-thickness ratio of plate subjected to compressive stressand stiﬀened plate
The maximum width-thickness ratio of plate that is subjected to a compressive stress andstiﬀened plate is assumed to be the one decided in consideration of the steel class, the position of
the plate.
【 Commentary 】

This is in accordance with 10.4.1.
10.5.2 Eﬀective section
The bending rigidity in the case of calculating deﬂection, statically indeterminate force etc is
deﬁned in term of the eﬀective section corresponding to the eﬀective width of ﬂanges.
【 Commentary 】

This is stipulated by reference to [Japan Road Association, 2002]. There is no need to consider bolt
holes when looking at the cross-sectional performance of a member in structural analysis, but ﬂexural
rigidity must be calculated by taking the eﬀective width into consideration.

10.5.3 Overlapping ﬂange
In the cover plate which acts as ﬂange made by overlapping steel plates, the detailed structure
which is considered 1) welding propertystress ﬂow, 2) stress distribution of girder, 3) fatigue, etc

148Standard Specifications for Steel and Composite Structures [Design]is adopted.
【 Commentary 】

This is stipulated by reference to [Japan Road Association, 2002]. When the cover plate receives
direct loading or if special attention to fatigue of the cover plate is required, the requirements outlined
by [Railway Technical Research Institute, 2002] should be used.
A cover plate used as a ﬂange by superimposing a steel plate on it should, in principle, consist of
one outer ﬂange whose design is governed by the requirements given below. (Refer to Fig.C10.5.1.)
1) The thickness of the outer ﬂange should be less than 1.5 times the thickness of the inner ﬂange

Fig.C10.5.1 Thickness of outer

Fig.C10.5.2 Welding details of the ends ofﬂange

outer ﬂange

2) The thickness of an outer ﬂange used as a compressive ﬂange should be greater than 1/24 of theouter ﬂange’s width.
3) The thickness of an outer ﬂange used as a tension ﬂange should be greater than 1/32 of theﬂange’s width.
4) The length of the outer ﬂange should be greater than the value obtained by adding 1 m to twice
the depth (m) of the girder.
5) The total length between the ends of the outer ﬂange shall be greater than the theoretical value
by 30 cm, and greater than 1.5 times the width of the outer ﬂange.
6) An outer ﬂange used as a tension ﬂange should be of length such that the stress in the ﬂange
calculated using the sectional area excluding the outer ﬂange is less than 90% of the strength of
the steel member, allowing for a safety factor.
7) The ends of the outer ﬂange should be continuously ﬁllet welded with unequal leg length. Welding
details are shown in Fig.C10.5.2.

10.5.4 Eﬀective section for shear forces
The eﬀective section which bears shear forces is decided appropriately according to the section
shape of the member.
【 Commentary 】

The commentary of [Japan Road Association, 2002] assumes that the ”shear forces in a cross section
caused by bending have a distribution that ﬂows along the center line of each plate in the case of athin-walled beam, thus exact values are given by the so-called shear ﬂow theory”. However, it is also
stated that ”in the case of a general plate girder, the greater part of the shear forces caused by bending
is withstood by web plates, and since little error from the above theory is expected even if one assumes

149

Chapter 10 Structural Members in Generala uniform distribution in the web plates it may be possible to use the simple formula (shear forces
caused by bending)/(total area of cross sections of web plates)”.
The conclusion here is that, regarding whether to apply rigid shear ﬂow theory or the simple method
to calculate the eﬀective section withstanding shear forces, an appropriate judgment is to be made by
the engineer in charge according to the cross-sectional shape of the structural member.

10.6 Steel Pipes
10.6.1 Radial thickness ratio
The maximum radius thickness of steel pipes is decided in consideration of local buckling. The
strength of steel pipe members is given in ”5.5 Steel Pipes Strength”.
【 Commentary 】

The strength characteristics of steel tubes are greatly aﬀected by the diameter to wall-thickness
ratio (D/t). Since local buckling easily occurs in structures with a relatively large D/t, such as steelpiers and pipe arches, stiﬀeners and diaphragms are installed. Meanwhile, stiﬀeners are not normallyused when using small steel tubes with relatively small D/t, such as in oﬀshore jacket structures.
The requirements for tubular steel structures in [Architectural Institute of Japan, 2002 and Architectural Institute of Japan, 1980] are as follows.
23500
D
≤
t
f
where, Dtf(C10.6.1)：nominal external diameter of steel tube (cm)：tube thickness(cm)：speciﬁed value of material strength (N/mm2 )10.6.2 Stiﬀened member
The structure which can prevent a buckling or a local transformation caused by shearing andtorsion is adopted in steel pipe members.
【 Commentary 】

This is stipulated by reference to [Japan Road Association, 2002]. In principle, ring-shaped stiﬀeners
or diaphragms should be ﬁtted into steel tubes to prevent buckling due to shear and torsion, as well
as local deformation. The requirements for stiﬀeners according to [Japan Road Association, 2002] areas follows.
(1) Maximum spacing between reinforcement components: in principle, ring-shaped stiﬀeners or
diaphragms should be ﬁtted into steel tubes with a maximum spacing of three times the outer
diameter of the tube. However, when the tube is within R/t ≤ 30 this can be omitted.
(2) Hardness of ring-stiﬀener: the width and thickness of the ring-stiﬀener’s jutted pillar must eachsatisfy Eq.(C10.6.2).
d
+ 70
20
b
t≥
17

b≥

(C10.6.2)

150Standard Specifications for Steel and Composite Structures [Design]where, bdt：width of ring-stiﬀener’s jutted pillar (mm)：thickness of ring-stiﬀener (mm)：outer diameter of steel tube (mm)Fig.C10.6.1 Ring stiﬀener

Fig.C10.6.2 Diaphragm

10.6.3 Node structure
The node part and shoe parts at which the concentrated load works must be the structure which
prevents a local transformation and transmits the stress smoothly.
【 Commentary 】

This is stipulated by reference to [Japan Road Association, 2002]. Although steel tubes are very
resistant to axial compressive force and torsion, local deformation occurs when they are subjected toconcentrated loading. Therefore, panel and bearing points should, in principle, be reinforced with ringstiﬀeners or diaphragms. In [Japan Road Association, 2002], the requirements regarding the degree of
local deformation when a ring stiﬀener is used are as follows.
(1) The degree of deformation at a panel point must satisfy Eq.(C10.6.3).
δ≤
where, δR

R
500(C10.6.3)：degree of deformation at panel point (mm)：radius of steel tube (mm)Fig.C10.6.3 Shape of ring stiﬀener(2) The degree of deformation at a panel point of a ring stiﬀener must satisfy Eq.(C10.6.4).
When using together with support
When using only ring stiﬀener
where, P
I
E

0.007

P R3
EI

P R3
0.045
EI

：operating load (N)：Ring stiﬀener’s moment of inertia of cross-section (mm2 )：Young’s modulus of the tube (N/mm2 )(C10.6.4)

151

Chapter 10 Structural Members in General(3) The steel tube’s eﬀective width, λ, when calculating the ring stiﬀener’s moment of inertia of crosssection should be according to Eq.(C10.6.5).
√
λ = 0.78 Rt
where, Rt
λ(C10.6.5)：steel tube’s eﬀective width (mm)：thickness of steel tube (mm)：eﬀective width

Fig.C10.6.4 Eﬀective width of steel tube

10.6.4 Curved tube
When the curved tube is used, the safety against additional stress at the curved part and the
local buckling must be determined.
【 Commentary 】

This is stipulated by reference to [Japan Road Association, 2002]. However, when a member iscomposed of a bent tube and the angle of the bend satisﬁes Eq.(C10.16), the tube can be regarded asa straight member in design. In Eq.(C10.6.6) the additional stress due to the bent member has been
set as being less than 2% of the stress of the straight memberθ = 0.04
where, θ
d
L
Ra

d
L

：angle of bend (radian). In the case of a circular arch, θ =：diameter of steel tube (mm)：length of straight member (mm)：diameter of curvature of arch (mm)Fig.C10.6.5 Bent tube

(C10.6.6)
L
Ra

152

Standard Specifications for Steel and Composite Structures [Design]

10.6.5 Steel pipe connections(1) The joint which connects steel pipes should be able to ensure the stress transmission, toprevent a local transformation, and to secure toughness.
(2) When a steel pipe and a steel pipe are axially connected, the direct joint ﬁtted by the hightensile bolt or the welding is used.
However, the demand performance shown in ”Chapter 11 The joint” is satisfactory, ﬂange
joint is acceptable.
(3) When a steel pipe is connected to a member with diﬀerent member axis to each other, gusset
joint and branching joint is used.
【 Commentary 】

This is stipulated by reference to [Japan Road Association, 2002].
(1) Direct connections
In principle, when tube sections are directly joined using high-strength bolts or rivets, thespacing between these high-strength bolts or rivets should be uniform around the circumference,with non-varying line intervals and pitches. Furthermore, the splitting of a restrainer plateshould, in principle, be at less than four points.

Fig.C10.6.6 Example of 4-way splitting of a

Fig.C10.6.7 Flange connection

restrainer plate(2) Flange connections
In principle, ﬂanges should be joined either with double ﬂange connections or ribbed ﬂange
connections. When a rib-less ﬂange connection is used, thorough veriﬁcation of such possibilities
as ﬂange deformation must be carried out.
(3) Gusset connections(a) When a gusset plate is attached to a main tube longitudinally, in principle either a throughgusset should be used or the main tube should be reinforced with ribs (Fig.C10.6.8 (a) (b)).
(b) When either a gusset is to be attached to the tube vertically or a stiﬀener rib is to be ﬁtted
at a panel point with no ring stiﬀener, the attachment width should be such that the center
angle of the steel tube is more than 120 °(Fig.C10.6.8 (b) (c)). Furthermore, in instancessuch as that shown in Fig.C10.6.8 (c), the gusset plate should be reinforced with ribs asneeded. Also, the end of the gusset plate on the side of a branch tube should be ﬁnished toa smooth surface after box welding (Fig.C10.6.8 (a)).

153

Chapter 10 Structural Members in General

(a)

(b)

(c)

Fig.C10.6.8 Gusset connection(4) Branch connections
Branch connection of steel tubes shall meet the following requirements (Fig.C10.6.9)(a) The wall thickness of the main tube must be more than R/30 and, in principle, greater thanthe branch tube’s wall thickness.
(b) The outer diameter of the branch tube should be more than 1/3 of the main tube’s outer
diameter.
(c) The angle between the two tubes should be more than 30 °.

Fig.C10.6.9 Branch connection

Fig.C10.6.10 branch connection with eccentricity(d) There should be no eccentricity in the axis of either tube. However, if this is unavoidable
because the branch tube is a secondary member, eccentricity of up to 1/4 in the directionof the branch tube is allowed (Fig.C10.6.10).
(e) The ends of the branch tube should be cut using an automatic tube cutter.
References in Chapter 10
Architectural Institute of Japan(1973) ：Technical Guidelines for High Buildings.
Architectural Institute of Japan(1975) ：Guidelines for Designing Plasticity of Steel Structure ．
Architectural Institute of Japan(1980) ：Guidelines and Handbook for Designing and Constructing Steel Tube
Structures ．
Japan Hydraulic Gate & Penstock Association(1981) ：Standards for Hydraulic Gate & Penstock Technology ．
Japan Road Association(1991) ：Handbook for Wind Resistant Design of Road Bridges ．
Public Works Research Institute, Ministry of Construction(1994) ：Recommendations for Design and Construction of Unpainted Weather Resistant Bridges (drafted revision) ．
Railway Technical Research Institute(2002) ：Design Standards for Railway Structures and Commentary, Steeland Composite Structures ．
Japan Road Association (2002) ：Specifications for Highway Bridges and Commentary, II Steel Highway Bridges
Volume ．
Architectural Institute of Japan(2002) ：Design Code for Steel Structure.
AISC(1978) ：Specifications for Design, Fabrication and Erection of Structural Steel for Buildings.

154Standard Specifications for Steel and Composite Structures [Design]

ASCE(1971) ：Plastic Design in Steel, ASCE M&R, No.41.
BSI (1980) ：BS5400.
Deutscher Normenausschuss(1990) ：DIN 18800-2.

155

Chapter 11 Joints
11.1 General
Joints shall be of a design that remains safe for all actions anticipated during erection andthroughout the design working life.
【 Commentary 】

Joints are one of the most important components of structures. They link structural members
and structural elements together to build up a structure. Joints should be of a design that meet thevarious performance requirements speciﬁed in this code for all actions anticipated during erection andthroughout the design working life of the structure, just as for the structural members and elements
themselves. In particular, the performance requirements considered in the case of joints are thoserelated to structural safety, such as load-carrying capacity and deformability, public safety, durability,
and so on. One example of a public safety requirement is the dropping out of a high-strength bolt
from underneath a bridge due to delayed fracture. Durability performance, such as fatigue/corrosion
resistance, is also important for joints, but this is dealt with in detail in Chapter 8 deals. Accordingly,
this chapter deals only with the safety of joints.
In the case of road and rail bridges, joints are designed to have adequate strength for general actions.
But where the forces are small, joints are designed to have a strength that is a multiple of that of thejoined members, using a speciﬁc ratio such as 75%. This means that joints are speciﬁcally designed witha strength and rigidity so as not to be weak points in the structure. These days, with developments in
FE analysis and computer technology, research into semi-rigid connections is moving forward, focusing
on the role of joints in providing seismic resistance. Consequently, it is expected that new types ofjoints reﬂecting this work will come into use. Considering this, it is desirable that deformability should
be added as a veriﬁcation requirement for joint safety to complement load-carrying capacity.

11.2 Joint Safety Requirements
Requirements relating to the load-carrying capacity and deformation of joints shall be speciﬁed
adequately so as to ensure the safety of the structure under the inﬂuence of all actions anticipatedduring erection and throughout the design working life.
【 Commentary 】

In specifying the requirements relating to joint load-carrying capacity and deformation, the functionof the joint in the structure should be taken into account so as to ensure safety during erection andthroughout the design working life. If the function of the joint is diﬀerent in the structure, therequirements are properly diﬀerent.
If the joint does not need to undergo large deformation, a strength requirement for the rigidity of
the joint, such as 75% of the strength of the joined members or 50% of the load-carrying capacity of thejoined members, determined using characteristic material values might be substituted for deformation
requirements so as to maintain a certain joint rigidity under earthquake/construction/accidental/secondary forces. It is important to keep a balance of rigidity throughout the whole structure.

156

Standard Speciﬁcations for Steel and Composite Structures [Design]

11.3 Verification of Joint Safety
The safety of joints shall be veriﬁed by means of the following methods to conﬁrm that therequirements of 11.2 are met during erection and throughout the design working life.
(1) Load-carrying capacity
It must be conﬁrmed that the resistance of joints is suﬃciently greater than the actions
applied during erection and throughout the design working life to ensure the required load
carrying capacity.
(2) Deformation
Standard procedure is to conﬁrm that joint deformation during erection and throughout thedesign working life under all anticipated actions is less than the deformation requirements
in consideration of required deformation capacity and also suﬃciently below the safe degreeof deformation.
【 Commentary 】

Joint safety should be veriﬁed by the partial factor method speciﬁed in 6.3 ’Veriﬁcation for Safety’.
But veriﬁcation using other methods may also be applicable if it is ensured that the method is suitablefor veriﬁcation. Some of the other methods available for veriﬁcation are as follows: evaluation of theprobability of exceeding the limit state; methods based on the reliability index; and methods based on
experimental and analytical results.
Generally, joints are designed in full consideration of the novelty of the connection method. Thisclause only speciﬁes the principle of veriﬁcation, so conventional veriﬁcation methods might be adopted.
However, it should be noted that conventional design methods for joints do not allow for large deformation of joint sections.

11.4 General Principles for Joints
11.4.1 Member joints
Structural details of joints between members shall be designed so as to satisfy the following
requirements.
(1) Smooth transfer of load(2) Avoidance of eccentricity(3) Avoidance of undesirable stress concentration(4) Avoidance of undesirable residual stress and secondary stress【 Commentary 】

This clause indicates the principles of joint design in this code.

11.4.2 Mixed welded, high-strength bolted, and bolted connections
Where there is a mix of welded, high-strength bolted, and bolted connections, the propriety ofsuch joints shall be judged in consideration of the load-transfer mechanism.
【 Commentary 】

Because the load-transfer mechanism becomes very complex when welded, high-strength bolted,
and bolted connections are mixed, careful attention should be paid and clauses 11.1 to 11.3 should beChapter 11 Joints

157

followed in using such connections.
The commentaries given in various Japanese design codes are summarized below.
(1) Welded and high-strength bolted friction-type connections
1) Since the relationship between stress and strain at the connection point in a high-strength
bolted friction-type joint is almost the same as that of the connected members, groove
welding and a high-strength bolted friction-type connection can operate together to transfer
the action force. Where a ﬁllet weld in the stress direction is mixed with a high-strength
bolted friction-type connection, both connections can transfer the action force because theslip between splice plate and connected plate in the bolted connection is almost the same asthat of the ﬁlet weld. However, in cases where such a mixed connection is long, the edge gap
becomes large and yielding can begin. In such cases, the stress distribution at the connection
and the load-carrying capacity of the whole joint should be considered suﬃciently.
2) The mixed usage of ﬁllet welding perpendicular to the stress direction and a high-strength
bolted friction-type connection must not be used in principle, since there is not enoughinformation about the load-transfer and deformation mechanisms of this combination.
(2) Welded and high-strength bolted bearing-type connections
Welded and high-strength bolted bearing-type connections must not be used together in principle, since in a bearing-type connection the load is transferred through shear deformation of thebolt, so the relationship between applied force and deformation of the bearing is signiﬁcantly
diﬀerent from that of the weld.
(3) Welded and normal bolted connections
Welded and normal bolted connection must not be used together in principle for the same reason
that the combination of welded and high-strength bolted bearing-type connection is not allowed.
That is, there is a great diﬀerence in load-transfer mechanism between the weld and the bolted
connection.
This combination could be used, however, if the normal bolted connection does not transfer
the action force in design.
(4) High-strength bolted and normal bolted connections
Where high-strength bolted and normal bolted connections are used together, the normal
bolted connection cannot transfer the action force due to the diﬀerence in load-transfer mechanism between the two connection types.

11.5 Welded Connections
11.5.1 Requirements(1) Welded connections that transfer load shall not be subject to failure under all actions anticipated during the design working life and should transfer forces securely and smoothly
between members/elements.
(2) Weldability shall be taken into consideration.

【 Commentary 】(1) This clause gives the requirements for welded connections to ensure that they do not fail under
all actions anticipated during the design working life of the structure.
Some damage might be found at welded connections that transfer load before they reach thedesign limit state with certain welding methods/ conditions. It is important to realize that welded
connections must transfer the forces securely and continuously between members/elements and158Standard Speciﬁcations for Steel and Composite Structures [Design]

should not fail until the design limit state. In general, to prevent failure at welded connections,the strength and elongation characteristics of the welding material used for the connection aresuperior to those of the connected material. However, the heating necessary to create a welded
joint causes a heat-aﬀected zone to form, where material properties may change; in particular,
embrittlement and softening may occur. For this reason, the welding materials and the materials to be joined by welding, the connection type, and the welding method should be selected
appropriately.
A welded connection that transfers load should deform along the design deformation curve
while securely and continuously transferring the load. In cases where a welded connection isdesigned for a nominal applied force, it should be noted that a local stress concentration mightoccur at the welded connection or the welded connection might be a weak point if the structure
is subjected to abnormal applied forces such as in an earthquake or during construction due to
its lower rigidity.
In the design of steel bridge piers, it is now common that deformation capacity is provided
for in order to secure earthquake resistance. In the case of a design which allows for plastic
deformation of welded connections, the connections should be detailed appropriately to assure
adequate fusion. Further, since the balance of strength between the welded materials and theweld itself is also very important, an examination by experiment and FE analysis should be
carried out. Details are given in the Seismic Design section of this code.
(2) Since the performance of a welded connection depends on the welding process, weldability must
be taken into consideration. In order to ensure that welding is carried out appropriately, theconnection details should be designed in consideration of ease of welding. For example, where
there is a welded connection at the corner of a steel bridge pier, extremely thick steel plate has
to be welded and it is diﬃcult to locate defects. That is, the ease of weld quality control must
be taken into consideration.

11.5.2 Safety verification of welded connections(1) The safety veriﬁcation of welded connections that transfer load shall be conﬁrmed such that
their resistance exceeds all actions and does not fall far below the resistance of the weld
material and the member itself.
(2) Veriﬁcation of weldability shall be conﬁrmed through due consideration.

【 Commentary 】(1) The safety veriﬁcation of load-transferring welded connections basically conforms with that forframe members (6.3.1.1) and joints (11.3). In general, the strength of a welded connection ishigher than that of the welded members and there are few cases of weld failure. However,
embrittlement and softening are possible in the heat-aﬀected zone, so it should be conﬁrmed thatmaterials are selected properly, an appropriate connection type is adopted, and that weldability is
1 select suitably
properly considered. For example, regarding embrittlement, it is important to: tough materials to be welded and for the weld itself; and 
2 check for appropriate heat input and
1 consider the chemical compositioninterpass temperature. As for softening, it is important to: and mechanical properties of the materials; 
2 develop connection details with less constraint;
3 prescribe a welding procedure taking into account welding strain. There is a great variety
and 
of welded connections; the safety of chosen methods should be examined through experiments
and weldability tests.
Full penetration groove welds, partial penetration groove welds, and continuous ﬁllet welds
are used for welded connections that transfer load. Discontinuous ﬁllet welds suﬀer from certain

159

Chapter 11 Joints

problems such as blow holes at weld beginnings and ends, weld cracking, stress concentrations at
crater, and diﬃculty in preventing rust. However, discontinuous ﬁlet welding might be used incases where it is conﬁrmed that such problems can be solved. Plug welds and slot welds should
not be used for welded connections that transfer load because it is diﬃcult to ensure adequate
melting and slug inclusion defects tend to occur. However, considering ability and welding strain,some penetration groove welding and ﬁllet welding is suitable.
Veriﬁcation examples using the partial factor design method are given below.
1) Safety veriﬁcation of welded connections subject to axial force/shear force
In the case of a full-penetration groove weld, as the strength can be assumed to be equal tothat of the connected members, veriﬁcation of the members subjected to axial force/shear
force, as given in clause 6.3.1.1.(1), is adequate veriﬁcation of the welded connection. In thecase of ﬁllet welds and partial-penetration welds subjected to axial force/shear force, theshear strength at the throat cross section should be used.
γiwhere ， γi
Psd , Vsd
Prd , Vrd

τud

Psd
Vsd
≤ 1.0 or γi
≤ 1.0
Prd
Vrd

(C11.5.1)：structural factor：design axial force and design shear force of the welded connection：design axial resistance and design shear resitance

(=

τud 
a l)
γb

(a：eﬀective throat thickness of weld ，(l：eﬀective weld length design strength of weld)：design strength of the welded connection2) Safety veriﬁcation of welded connections subjected to bending moment
In the case of a full-penetration groove weld, as the strength can be assumed to be equal tothat of the connected members, veriﬁcation of the members subjected to bending moment,
as given in clause 6.3.1.1.(2), is adequate veriﬁcation of the welded connection. In the caseof a ﬁllet weld, the expanded cross section at the throat, as shown in Fig.C11.5.1, should
be used. Furthermore, in case of partial-penetration welds, the same veriﬁcation as for ﬁllet
welds can be used in practical design.
γiwhere ，

γi
Msd
Mrd
τud
I
Yt

Msd
≤ 1.0
Mrd

(C11.5.2)：structural factor：design bending moment of the welded connection




I τud
：design bending resistance
(=
)
Yt γb
：design strength of the welded connection：moment of inertia at the neutral axis for expanded cross section
for weld connection：distance from neutral axis of expanded cross section for weld connection

Where full-penetration groove welding is used for the ﬂange plate and partial-penetration
groove welding/ﬁllet welding is used for the web plate, the deformability and stress levelat the groove weld connection are diﬀerent from those at the partial-penetration groove
weld/ﬁllet weld connection. Therefore, when full-penetration groove welding is used together
with ﬁllet welding in this way, the ﬁllet weld should be disregarded in the bending moment
veriﬁcation.

160

Standard Speciﬁcations for Steel and Composite Structures [Design](a) Fillet weld(b) expanded throat cross-section(c) example of throat cross section

Fig.C11.5.1 Fillet weld connection subjected to bending moment

3) Safety veriﬁcation of welded connections subjected to axial force, bending moment, andshear force simultaneously
In the case of a full-penetration groove weld connection, the resistance of the connection isassumed to be equal to that of the connected members, so the resistance of the connection
is veriﬁed in accordance with clause of 6.3.1.1(5), which prescribes the combined stressveriﬁcation when a member is subjected to bending moment and shear force simultaneously.
In the case of a ﬁllet weld, resistance is veriﬁed by the shear strength of the throat crosssection. The expression used for veriﬁcation is equation 11.5.3 below. In this equation, thecoeﬃcient φ=1.21(＝ 1.12 ) for the combination of normal stress and shear stress is not taken
into account because only the combination of shear stresses is veriﬁed. This equation may
be applied also to partial penetration welds in practice.

2 
2 
V
P
M
sd
sd
sd
≤ 1.0
(C11.5.3)
γi2
+
+
Prd
Mrd
Vrd
where ， γi ：structural factor
The eﬀective throat thickness and eﬀective length for veriﬁcation of welded may be taken
as in 4) and 5) below.
4) Eﬀective thickness
1 The eﬀective thickness of a weld that transfers load should be the theoretical throat of
weld.
2 The thickness of the theoretical throat of each type of welding connection is shown below.
• The theoretical throat of a full-penetration groove weld is the thickness of the connected
members regardless of the bead ﬁnish (Fig.C11.5.2). When the thickness of the members
is diﬀerent, the thickness of the thinner member is taken as the theoretical throat
thickness.

a : theoretical throat thickness

Fig.C11.5.2 Theoretical throat thickness of full-penetration groove weld

• A partial-penetration weld should be designed so that tensile force is not applied perpendicular to the bead direction. The theoretical throat thickness that resists shear
force is the depth of penetration, as shown in Fig.C11.5.3.
• The theoretical throat thickness of a ﬁllet weld is the distance from the base of the161

Chapter 11 Joints

a : theoretical throat thickness

Fig.C11.5.3 Theoretical throat thickness of partial-penetration weld

the root of weld(a) Equal leg ﬁllet weld(b) Unequal leg ﬁllet weld

Fig.C11.5.4 Theoretical throat thickness of ﬁllet weld

isosceles triangle to the root of the weld, as shown in Fig.C11.5.4.
• The theoretical throat thickness of a partial-penetration weld overlapped by a ﬁllet weld
can be the same as the theoretical throat of the ﬁllet weld.
The theoretical throat thicknesses of a partial-penetration weld is shown in Fig.C11.5.5. The
eﬀective throat thickness has been calculated for a standard groove [Japanese Society of Steel
Construction, 1997]. In that case, the eﬀective throat thickness was the value obtained bysubtracting 3 mm from the theoretical throat for a groove with a small angle, except in
the case of submerged arc welding (SAW). This idea was appropriate and gave a resulton the side of prudence when it was speciﬁed in 1977; arc welding (SMAW) was a popular
welding process at that time. However, shielding gas welding (GMAW), which requires morepenetration than covered arc welding, is more common now. Consequently, it is necessary toreexamine the method of calculating eﬀective throat thickness. The method of calculatingeﬀective throat thickness for shielding gas welding is shown in Japanese Society of Steel
Construction, 1997. The calculation method given in table C11.5.1 might be applicable inthis code taking into consideration of these latest research results.
Table C11.5.1 Calculation method for eﬀective
throat thickness
SMAW

SAW

Te-3mm
Te

Te
Te

≧

D 2･√T(θ=45°～70°)
S=D(secθ-1)
Te=(D･secθ･cos(θ/2))45o ≥ θ ≤ 60o
60o ≥ θ ≤ 70o

GMAW
solid wire
Flux-coredsolid wire
wire
Te
Te-2mm
Te
Te-1mm

Fig.C11.5.5 Theoretical throat
thickness of partial-penetration
weld overlapped with a ﬁllet weld5) The weld should have an eﬀective length as shown in below.
1 The eﬀective weld length should be equal to the theoretical throat thickness. If pen
etration is insuﬃcient because the cross section of the weld metal is imperfect at the162Standard Speciﬁcations for Steel and Composite Structures [Design]

weld start point, as shown in Fig.C11.5.6, it might not be possible to transfer the loadcorrectly. Further, defects such as cracks in the crater at the weld end point easily occur. For this reason, these parts of the weld should be excluded from the determinationof the eﬀective length.
Effective length

beadcrater

Fig.C11.5.6 Eﬀective length of weld
2 The eﬀective length must be the projected length in the stress direction, as shown in
Fig.C11.5.7, when the weld line is not perpendicular to the stress direction in the caseof a full-penetration groove weld. Moreover, the weld end tab should be used for an
important connection that transfer load.

3 Load transfer is not clear when box welding is carried out with ﬁllet welds because
the stress orientation changes at the corners. Additionally, it is diﬃcult to eliminate
the inﬂuence of the start point of the weld/crater. Accordingly, these parts of theweld should be excluded from the determination of the eﬀective length, as shown in
Fig.C11.5.8.
Box weld

Effective length l = li sin aend tabFig.C11.5.7 Eﬀective length of weld

Box weldl = effective length

Fig.C11.5.8 Eﬀective length of weld(2) Various restrictions on fabrication work, such as a need for ﬁeld welding, limited work space,and a limited range of welding positions, mean that a good weld may not be obtained. It is
important to ensure a suitable secure fabrication environment while paying careful attention to
working conditions.
This attention to fabrication is necessary since cracking may occur where a welding takes
place under restricted conditions. A great deal of caution is also needed where discontinuous
ﬁllet welding is used for decorative laminates or metal form welding, since defects can easilyarise.
The means of weld quality assurance must be considered in advance.

11.5.3 Size of fillet welds and geometry and dimensions of welded connections(1) The size and minimum eﬀective length of each ﬁllet weld shall exceed each the required
design value in every case. The size of a ﬁllet weld, taken as the heat-aﬀected zone, shall beminimized.

163

Chapter 11 Joints(2) The geometry and dimensions of welded connections shall be designed in consideration ofsmooth load transfer, avoidance of undesirable secondary stress and deformation, and fatigue.

【 Commentary 】(1) This clause is speciﬁed by reference to the Speciﬁcations for Highway Bridges II 6.2 [Japan Road
Association, 2002]. At the design stage, ﬁllet welds must be of at least the required size toensure that undesirable cracks do not occur. The weld size (shown as S in Fig.C11.5.9(a)) is notnecessarily the length to the end of weld metal. In Fig.C11.5.9(b), size S is shown for a casewhere the shape of the weld is not an isosceles triangle.

S : sizea : throat thicknessc : excessive convexity

Leg length

Leg length(a) Equal leg ﬁllet weld(b) Unequal leg ﬁllet weld

Fig.C11.5.9 Fillet weld size

The standard size of ﬁllet weld, S, is that which satisﬁes Eq.(C11.5.4) and is also greater than
6mm. The upper limit of weld size as calculated by Eq.(C11.5.4) is 8mm. For welds of this size,
appropriate preheating is necessary if steel with a PCM (the weld cracking parameter) exceeding
0.24 is used or if covered arc welding is used.
t1 > S
where ，

S
t1
t2

and

S≥

√
2t2

(C11.5.4)：size(mm)：thickness of thinner plate(mm)：thickness of thicker plate(mm)Oversized welds needlessly increase strain and broaden the area of material whose structureis changed by welding. On the other hand, welds that are too small tend to crack as a resultof rapid cooling. This is the reason for these minimum and maximum values of standard weld
size being speciﬁed. These standard values are the same as those in the Speciﬁcations for SteelHighway Bridges, 1956 as well as in the current speciﬁcations for highway bridges. In this code,
the upper bound of ﬁllet size up to 8mm is added. For instance, 10mm is the upper bound in
the design standards for steel structures [Architectural Institute of Japan, 2004] as the standard
for steel buildings, while 8mm is the upper bound in AASHTO, 1994 as the standard for steel
1
bridges in the USA when the plate thickness exceeds 20mm. According to Minami, et al 2005, √
modern steel materials rarely crack as a result of rapid cooling even if S ≥ 2t is not satisﬁed,
since PCM is low and the content of diﬀusible hydrogen (that aﬀects crack occurrence) is low in
2 the welding of extremely thickthe case of submerged arc welding or shielding gas welding; plate of small area raises the maximum value of Vickers hardness locally, though if the ﬁllet size
is 8mm, the defect might be removed; and 
3 weld cracking might occur if steel with a PCM
exceeding 0.24 is welded using covered arc welding in which diﬀusible hydrogen is high. The
value in this code is speciﬁed in consideration of these ﬁndings.

164Standard Speciﬁcations for Steel and Composite Structures [Design]

As a remarkable point in design, Until now, the shear strength requirement dictated ﬁllet
welds of 6mm or less for the web plate and ﬂange plate of a girder bridge. A stress veriﬁcationof ﬁllet welding was sometimes omitted. However, it is now necessary for the ﬁllet weld size tobe veriﬁed for shear stress, if necessary, because the section details are diﬀerent.
The minimum eﬀective length of a ﬁllet weld should be the length that can be properly welded
without undesirable cracking. Cracking occurs easily due to quick cooling if the heat capacity of
the weld is less than that of the surrounding material. In general, a weld should be at least 10
times the ﬁllet size, or more than 80mm and more.
If welded connections are designed only by considering the forces applied, stress might concentrate locally even if the calculated overall stress of the connections is low. Since the stiﬀnessof the welded connection will decrease signiﬁcantly in this case, the connection might form theweak point of the structure with respect to secondary stress when the applied force is below thestrength of the connected members. In such cases, careful consideration is necessary.
(2) Structural details of the standard butt joint, lap joint, and T-joint, which are typical connection
types used in steel and composite structures, are described in below:
1) Butt joint
Where a butt joint connects members with diﬀerent cross sections along the principal
direction, such as at main girder connections, the cross section should be adjusted appropriately so as to ensure the equal transfer welding heat and reduce stress concentrations asmuch as possible.
According to Speciﬁcations for Highway Bridges II 6.2.10 [Japan Road Association, 2002],
there should be an inclination of 1/5 or less in the length direction.

Fig.C11.5.10 Butt joint of primary members with diﬀerent cross sections

2) Lap joint
1 In the case of a lap joint that transfers load, undesirable stress concentration andsecondary stress must be avoided.
2 A front ﬁllet weld or one/two sided ﬁllet weld should be used because a bending momentacts on the bead and stress concentrations would readily occur if a single ﬁllet weld wereused.

3 A lap joint with a small lap deforms quite easily because it has less resistance to eccentricloading. The lapped amount should be ﬁve or more times the thickness of the thinplates, since rupture strength falls with secondary stress.

4 The speciﬁcation in a case where a side ﬁllet weld only is used for a lap joint subjected
to axial force at the member end is given as follows:• Distance of weld line shall be less than 16 times of the thickness of the thinner platein principle. However, if it is subjected to only tensile force, the value is 20 times.
If this value is exceeded, special measures to prevent the plate lifting need to be
implemented. This is achieved by specifying the maximum bolt spacing, the aim ofwhich is to prevent local buckling or plate lifting and to smooth load transfer.
• Length of side ﬁllet weld should be greater than the distance between weld lines to165

Chapter 11 Joints

smooth load transfer.

l > 5tl > b

l : Lap lengthb < 16t (or 20t)

t : thickness of thinner platel : Lap lengtht : thickness of thinner plate

Fig.C11.5.11 Lap joint by ﬁllet welding3) T-joint
1 In the case of a one-sided ﬁllet weld or partial-penetration groove weld at a T-jointsubjected to external force, the stress concentrates at the root of the weld, which is oneof the weak points of a ﬁllet weld, and resistance to deformation is low. Therefore, thistype of weld may be used only if the connection has a structure that resists deformationin the horizontal direction, such as where sections of the chord member in a truss
structure are joined. However, both sides of the T-joint must be welded in the case ofa single T-joint. The standard of eﬀective length of a ﬁllet weld for primary members
is more than ten times the ﬁllet size.
2 Where the angle of a T-joint is less than 60 °, adequate ﬁllet weld penetration at theroot cannot be achieved. Further, where the angle of a T-joint is greater than 120°, the weld volume increases so as to satisfy the required throat size. In such cases,
full-penetration groove welding should be used in principle.

Fig.C11.5.12 T-joint

Fig.C11.5.13 T-joint with angle under 60 °above 120 °11.6 High-Strength Bolted Connections
11.6.1 Requirements for safety of high-strength bolted connections
The requirements for the safety of high-strength bolted connections shall be speciﬁed such thatthe requirements given in 11.2 are satisﬁed.
【 Commentary 】(1) High-strength bolted connections fall into three categories according to their load-transfer mechanism: 1) friction type, 2) bearing type, and 3) T=tension type.
A friction-type bolted connection is one which transfers the load by the frictional force between

166Standard Speciﬁcations for Steel and Composite Structures [Design]

two plates tightened together with high-strength bolts. A bearing-type bolted connection is one
which transfers the load by the bearing force between the bolt hole and the bolt shank, using theshear resistance of the bolt. This is the same load-transfer mechanism as in a riveted connection.
The performance of a bearing-type connection can be improved by tightening the bolt. A tensiontype bolted connection is one which transfers the load by reducing the contact stress between twoplates tightened together with bolts. A short tension-type connection uses normal high-strength
bolts while a long tension-type connection consists of long high-strength bolts or PC rods andrib plates.
(2) Friction-type connections should be designed so as to be safe against slip at the connection andagainst yielding of the connected plates. Where a gap is found between the two plates, a ﬁller
plate must be ﬁtted in principle, following clause 11.7.7 in order to avoid reduced slip resistance
Bearing-type connections should be designed so as to be safe against shearing
and corrosion.
of the bolt shank and yielding of the bolt and the plates. In recent years, however, bearing-typebolted connections are generally used only as a means of strengthening members with fatigue
cracks and there is little application of this connection type in road bridges. Further research andmore application examples are needed before bearing-type bolted connections can be used more
widely. This code speciﬁes a draft bolt as the standard bolt for bearing-type bolted connections.
There are many problems in using this type of connection, including constructability, plate defects
caused by bolt installation, correction work after fabrication, drill design, and so on. Bearing-typebolted connections must be used only after considerable eﬀort to understand the load-transfer
mechanism, constructability, and suitability with regard to the surrounding environment.
Tension-type bolted connections should be designed so as to be safe against bolt failure andyielding of the connected plates. At the design stage, in particular, it should be noted that axial
force, joint rigidity, and stress occurring at the connection are inﬂuenced greatly by joint details
and by any strengthening of the connected portions. Since this type of connection makes use of
the contact stress between two plates, as with the friction-type connection, bolt axial forces andﬂange plate ﬂatness should be considered. Examples of the application of this type connection
are connections of anchor frames, sole plates for shoes, corner connections in steel rigid-frame
piers, and connections between main and lateral girders.
(3) High-strength bolted connections should not be used for connections that might be submerged,
in principal, because of the danger of reduced slip coeﬃcient, bolt corrosion, and delayed fracture of the bolt. However, such connections might be used after conﬁrming that submergence
will not cause these conditions and that the safety of the joints is maintained. Further, special consideration of bolt corrosion is required for these connections whether or not they aresubmerged.
(4) In any of these connections, the connection location, constructability, and the surface state of theconnected members must be checked to ensure that the required performance of the connection
is satisﬁed.

11.6.2 Safety verification of high-strength bolted connections
The safety of high-strength bolted connections shall be veriﬁed in accordance with 11.3.

【 Commentary 】

The safety of high-strength bolted connections should be veriﬁed with respect to load-carrying
capacity and deformability in accordance with 11.3.
The veriﬁcation of load-carrying capacity should basically conﬁrm that it exceeds the corresponding
force resulting from the action, taking into consideration the load-transfer mechanisms of friction-type,

167

Chapter 11 Joints

bearing-type and tension-type bolted connections, respectively. However, the method of veriﬁcation
given below may be used under the presupposition of the structural details given in 11.7.
An example of the veriﬁcation equations for load-carrying capacity using the partial factors speciﬁedin the Design Standard for Railway Structures is given here.
1) Veriﬁcation of slip resistance of friction-type connections

1 Veriﬁcation for connections subjected to axial force/shear force should be carried out using
the following equation.
γa γb γiwhere ，

Ps
≤ 1.0
Pu

γa
γb
γi
Ps

：structural analysis factorPu：slip resistance of bolts in row i (Pu = nmnmPa：number of bolts used for the shear plate

γm：material factor(C11.6.1)：structural member factor：importance factor：applied force for bolts in row i

Pa
)
γm

：number of friction surfaces：characteristic value of slip resistance of bolt per slip surface(Table C11.6.2)

Fig.C11.6.1

Numer of bolt


2 Veriﬁcation for connections subjected to shear force/bending moment should be done using
the following equations.
Pi
≤ 1.0
Pu

2  2 
Vs
Pi
2
+
≤ 1.0
(γa γb γi )PuiVu

γa γb γiwhere ，

γa
γb
γi
Pi

：structural analysis factor

Pu i：slip resistance of bolts in row i (Pu = ni mnim

：number of bolts in row i (Fig.C11.6.2)(C11.6.2)(C11.6.3)：structural member factor：structural factor：applied force for bolts in row i (Fig.C11.6.2)：number of friction surfaces

Pa
)
γm

168

Standard Speciﬁcations for Steel and Composite Structures [Design]Pa：characteristic value of slip resistance of bolt per slip surface

Vs：shear force applied to the connectionVu：shear slip resistance (Vu = nm

(Table C11.6.2)

n
γm

Pa
)
γm
：number of bolts used for the shear plate：material factor[1st row bolts]gb1 = g 0 + 12
σ +σP1 = 0 1 ⋅ b1t
2[ ith row bolts]

b =
i

P =
i

g −1 + gi2i

σ −1 + σ
i

2

i

⋅

bt
i

whre, t : plate thickness
σ0 : smaller of applied stress or
50 % of design strength

Fig.C11.6.2 Web joint (subjected to moment and shear)
3 Veriﬁcation for horizontal joints of ﬂanges/webs in the bridge axial direction should be
carried out using the equation below.
This equation is good for the case of horizontal connections between web plates subjected
to shear force with bending moment. However, in this case the eﬀect of the torsional moment
should be considered.
γa γb γiwhere ，

Ps
≤ 1.0
Pu

γa
γb
γi

：structural analysis factor

Ps：force applied to the connection (Ps =

Vs
Q
I
p

：shear force applied to the connectionPu：slip resistance of the joint (Pu = nm

n
m
Pa
γm

(C11.6.4)：structural member factor：structural factor

Vs Q
p)
I

：geometrical moment of the outside section from joint line
：moment of inertia of the girder：pitch of boltsPa)γm：number of bolts in the transverse direction of the joint line
：number of friction surfaces：characteristic value of slip resistance of a bolt per slip surface(Table C11.6.2)：material factor

169

Chapter 11 Joints

In the case of connections for a girder with a wide steel deck (as shown in Fig.C11.6.3(b)),
this equation is used if the steel deck and ﬂange are connected in the bridge axial direction.

(a) Geometrical moment of I-shaped girder(b) Girder with steel deck

Figure.C11.6.3 Examples of joints in bridge axial direction
4 Veriﬁcation by total slip resistance method for friction joints subjected to bending moment
In the design method shown in subsections 
1 and 2 , connections between ﬂanges andweb plates are individually designed for bending moment. However, in the case of connections of I-shaped girders subjected to bending moment, for example, the ﬂange and web
together resist the bending moment. Therefore, in Recommendation on Design, Construction, and Maintenance of Friction-type High-strength Bolted Connections (draft) [Japanesesociety of civil engineers, 2006], consistency between the design method and actual behavior
is ensured and the total slip resistance method is recommended. That veriﬁcation method
is described below. Still, here, the reduction in slip resistance due to such circumstances
as the presence of a gap between the slip surfaces can be considered by using a correction
factor, φ1 .
In the veriﬁcation for slip of all friction-type connections subjected to bending moment,
it must be conﬁrmed that the slip resistance (bending moment) is larger than the applied
bending moment.
Considering the combined action of the ﬂange and web plate by applying the total slip
resistance method, the slip resistance (bending moment) MSL is calculated as follows.
MSL =



(φ3 φ1 γi ρi )ρi = ρs × m × n
where ，

γi

ρi
ρs
m
n
φ1
φ3

(C11.6.5)(C11.6.6)：distance to centroid of the position of the i line of bolts from theneutral axis (distance to the plate thickness center, in the case of
a ﬂange)：slip resistance of bolts in row i：slip resistance of a bolt per slip surface (Table C11.6.2)：number of friction surfaces：number of bolts in each row：correction factor for slip resistance：correction factor for slip resistance (bending moment)(for ﬂange: 1.0; for web: 0.8)

2) Safety veriﬁcation of bearing connections
The bearing resistance of butt joints or lap joints subjected to tension, compression, or shear
force is veriﬁed on the basis of Eq.(C11.6.1).

170Standard Speciﬁcations for Steel and Composite Structures [Design]

The resistance of high-strength bolts used in bearing connections may be lower than theshear resistance or bearing resistance of the bolts as calculated based on their diameter. And
the eﬀective bearing area of a bolt is determined as the product of its nominal diameter and thethickness of the steel plates used. However, in calculating the eﬀective bearing area of a ﬂat-headbolt, half of the depth in the head may also be eﬀective. (Fig.C11.6.4).

Fig.C11.6.4 Eﬀective bearing area of ﬂat-head bolt

γa γb γiwhere ，γa
γb
γi
Ps

Ps
≤ 1.0
Pu

：structural analysis factor：structural member factor：structural factor：force applied to the connectionPu：slip resistance of the joint (Pu = n m

n
m
γm
Pa

：number of bolts

τa
σb
As
Ab

(C11.6.7)Pa)γm：number of joint surfaces：material factor：characteristic value of resistance of a bolt as follows:

the smaller of the shear resistance Psa = τa As or
the bearing resistance Pba = σb Ab：characteristic value of shear resistance of a bolt (Table C11.6.3)：characteristic value of bearing resistance of a bolt (Table C11.6.4)：cross-sectional area of bolt shank：eﬀective bearing area of bolt shank (product of thickness of plate and bolt
nominal diameter)

3) Safety veriﬁcation of tension-type bolted connections
Tension-type bolted connections, which transfer the load in the bolt axial direction using thestrength of the bolts, appear very useful. When using this type of joint, the resistance of thebolts, the tightening force, the rigidity of the connection, and the stress state must be suﬃciently
considered.
In some current standards, tension-type bolted connections are forbidden, in principle, forconnections where there is fatigue action. The safety veriﬁcation method for tension-type bolted
connections and the application examples shown in Fig.C11.6.5 are taken from Speciﬁcations for
Highway Bridges [Japan Road Association, 2002] and Design Standard for Railway Structures(Composite Structures of Steel and Concrete) [Railway Technical Research Institute, 2002]. Additionally, Recommendation for Design of High-Strength Tensile Bolted Connections for Steel
Bridges [Japanese Society of Steel Construction, 2004] can be referred to as the latest designChapter 11 Joints

171

standard for bridge structures.
The safety veriﬁcation of tension-type bolted connections using the partial factor method is
described below.

Fig.C11.6.5 Examples of tension-type connections


1 Veriﬁcation of tensile-type connections subjected to tensile force should be carried out using
the following equation.
γa γb γiwhere ，γa
γb
γi
Pt
Rt

Pu
n
Pta
γm

Pt + Rt≤ 1.0
Pu(C11.6.8)：structural analysis factor：structural member factor：structural factor：tensile force applied to the connection：prying force caused by bending of T-ﬂange, which is calculated

considering the thickness of the T-ﬂange, the arrangement of bolts, andthe dimensions of each part of connectionPta：resistance of the connection (Pu = n)γm：material factor：characteristic value of resistance of bolt (Table C11.6.5)：material factor

However, in case of a long connection, the prying force can be ignored, because the rib
plates reduce the local deformation of the connection and the contact stress is concentrated
in the center of the connected member.
2
 Veriﬁcation for shear force of tensile-type connections subjected to tensile force and shear
force simultaneously should be carried out using the following equation.
γa γb γiwhere ，γa
γb
γi
V
Vu

：structural analysis factor：structural member factor：structural factor：shear force applied to the connection：shear resistanceof the connectionnPa nPn − Pt)γmnPa：number of bolts
(Vu =

n

V
≤ 1.0
Vu

(C11.6.9)

172Standard Speciﬁcations for Steel and Composite Structures [Design]Pa：characteristic value of slip resistance of a bolt per slip surface

Pn
Pt
γm

：pre-tension force introduced to bolt

(Table C11.6.2)：tensile force applied to the connection：material factor

4) Veriﬁcation at yield state of friction-type connections and bearing-type connections
Connected plates and splices where friction-type connections and bearing-type connections areused can be veriﬁed at the yield state using the following equation.
γa γb γiwhere ，γa
γb
γi
Ps
Pu

Ps
≤ 1.0
Pu

(C11.6.10)：structural analysis factor：structural member factor：structural factor：force applied to the connected plates/splice：yield strength of the connected plates/splice

In Japan Society of Civil Engineers, 2006, the yield strength of connected plates and splices isrecommended to be calculated diﬀerently according to whether tensile force or compressive force
is acting. In particular, when tensile force acts on the connection, friction is assumed to transmit
part of the applied force through use of a yield resistance correction factor.
The following are the methods recommended in Japan Society of [Civil Engineers, 2006].
(i) Yield strength of friction-type connections subjected to tensile force Pty
Pty = φ2 Pyn
where ，

Pyn

(C11.6.11)：the smaller of the yield strength of the connected plates or spliced

components based on net sectional area.
φ2 ：correction factor for yield strength (φ2 = 1.1)
Yield strength Pty should be smaller than the yield strength of the gross section.
(ii) Yield strength of friction-type connections subjected to compression force Pcy
Pcy = φ2 Pyg
where ，

(C11.6.12)

Pyg：the smaller of the yield strength of the connected plates or spliced

φ2components based on gross sectional area.
：correction factor for yield strength (φ2 = 1.0)

11.6.3 Design characteristic values for verification of connection safety
Design characteristic values for the veriﬁcation of connection safety shall be speciﬁed appropriately in consideration of the load-transfer mechanism and the veriﬁcation method used.
【 Commentary 】

Design characteristic values may be speciﬁed as follows based on past experience and examples.
However, the design characteristic values as follows shall be speciﬁed the requirements given in Table
C11.6.4.
(1) Design characteristic values for the slip resistance of friction-type bolted connections
The design characteristic values for the slip resistance of a bolt per slip surface, Pa , are obtained

173

Chapter 11 Joints

using the following equations.

where ，

μ
N
σy
α
Abe

Pa = μN(C11.6.13)

N = α σy Abe(C11.6.14)：slip coeﬃcient：design axial force on bolt
：yield strength of bolt speciﬁed in JIS B 1186
：ratio of yield strength：eﬀective cross-sectional area of bolt speciﬁed in JIS B 1186

The slip coeﬃcient and design axial force are important in calculating the slip resistance. The
slip coeﬃcient, μ , is speciﬁed as a uniform value of 0.40 in [Japan Road Association, 2002] aswell as in the Design Speciﬁcations for Railway Structures and Commentary (Steel/Composite
Structures) [Railway Technical Research Institute, 2000]. In [Japan Society of Civil Engineers,
2006], the recommended value of slip coeﬃcient depends on conditions at the joint surfaces, as
shown in Table 11.6.1. This is based on design speciﬁcations in other countries and in the ﬁeldof architecture, as well as past experience. Thus, slip coeﬃcient may be decided according toconditions at the joint surface. This guideline (draft) gives the standard testing method for
obtaining the slip coeﬃcient.
Table C11.6.1 Recommended slip coeﬃcients for various conditions
at the joint surface
Slip coeﬃcient μ

Conditions at joint
surface
Ideally rusted surface

0.55

Ideally rusted surface
obtained with chemicals

0.45

Rough surfaces

0.25
0.35(indeﬁnite roughness)

Inorganic zinc-rich
paint

0.40(10μ m> Ra ≥ 5μm)0.45(Ra ≥ 10μm)
0.40(paint thickness ≤ 65μm)
0.50(paint thickness ≥ 65μm)

Organic zinc-rich
paint
Hot-dip galvanized

Decide after conﬁrming theperformance of connections byconducting slip test

Comments
Unpainted clean mill scale with ideal amount of
rust
Ideal amount of rust obtained using chemicals

Rough rust-free surface formed with disk grinder
Rust-free blast-cleaned surface obtained by
shot/grit blastingStandard of paint thickness must be 150μm
Content of dry zinc in paint must be more than80%
∗ Shown as ”tentative slip coeﬃcient” in the guidelines on Design Standards for Steel Structures(Steel Bridges) [Japanese Society of Steel Construction, 2004]

Metallic spray
Surface roughened bymechanical processing

Standards for ratio α of yield strength σy in Eq.(C11.6.14) are 0.85 and 0.75, for F8T and for
F10T bolts, respectively, in [Japan Road Association, 2002], and [Railway Technical ResearchInstitute, 2000]. The slip resistance of a bolt per slip surface, Pa , in the case that the slip
coeﬃcient μ is 0.40 is given in Table 11.6.2.

174Standard Speciﬁcations for Steel and Composite Structures [Design]

Table C11.6.2 Slip resistance of a bolt per slip surface, Pa (kN)
Grade of high-strength
bolt

F8T

F10T
S10T

Nominaldiameter
M16
M20
M22
M24
M16
M20
M22
M24

α

σy
(N/mm2 )

0.85

640

0.75

900

Abe
(mm2 )N(N)

Pa*μ = 0.4

157
245
303
353
157
245
303
353

85,410133,280
164,840
192,040
105,980
165,380
204,800
238,280

34
53
66
77
42
66
82
95

It is known that the slip resistance depends on the clearance and shape of the bolt holes as wellas on the number of bolt rows. The recommendations of JSCE[Japan Society of Civil Engineers,
2006], proposes that the slip resistance be corrected according to the following:• Clearance• Filler plates• Oversized bolt hole
• Multiple arrangement of high-strength bolts• Slip/yield resistance ratio (β)
Moreover, [Railway Technical Research Institute, 2000], gives an equation for reducing the slip
resistance for parts subjected to tensile force. It also requires that care is taken with respect tolocal buckling of the plates.
(2) Characteristic values of shear strength and bearing strength for high-strength bolted connectionsof bearing type
The characteristic values of bolt shear strength and bearing strength of the connected plates
are speciﬁed as follows in [Railway Technical Research Institute, 2000].
In the commentary accompanying the design standard for buildings published in 1983, the√shear strength of a high-strength bolt is speciﬁed as 1/ 3 times its tensile strength, as forallowable stress, and the safety factor is calculated as 1.6 against the lower limit of yield resistanceσy and 3.0 against the lower limit of yield tensile strength σB . In [Railway Technical ResearchInstitute, 2000], the resistance is speciﬁed as 1.6 times the allowable stress mentioned above. The
Speciﬁcations for Highway Bridges and Commentary(II Steel Bridges) [Japan Road Association,
2002] is based on same concept except that the safety factor against yield strength is 1.7 forallowable shear strength. The characteristic value of shear strength of high-strength bolts forbearing-type connections is summarized in Table C11.6.3.
The characteristic value of bearing strength should be 1.5 times the standard yield strength
as well as structural steel as shown in Table C11.6.4. However when this value is greater than
the tensile strength, the tensile strength should be taken as the upper limit.
Table C11.6.3 Characteristic values of shear strength of high-strength bolts
for bearing-type connections, τu (N/mm2 )Grade ofhigh-strength bolt

Yield stress orultimate stress σyTensile strength
σB

σy
1 √
1.6 3

1σ
√B
3 3

B6T
480
600
173
116
B8T
640
800
231
154
B10T
900
1,000
325
192
*Reference value is based on [Railway Technical Research Institute, 2000]√B × 1.6
τu = 13 σ
3

185
245
305*reference value

175

Chapter 11 Joints

Table C11.6.4 Characteristic values of bearing strength of high-strength
bolts for bearing-type connections, τb (N/mm2 )Material

SS400
SM400
SMA400SM490

SM490YSM520
SMA490

SM570
SMA570

Bearing strength

360

480

520

570

(3) Characteristic values of tensile yield strength of high-strength bolts for tension-type connections
The characteristic value of tensile yield strength of high-strength bolts for tension-type connections is speciﬁed as follows in [Japanese Society of Steel Construction, 2004], and [Railway
Technical Research Institute, 2000].
By = σy Abe(C11.6.15)

Table C11.6.5 Characteristic value of tensile yield strength ofhigh-strength bolts for tension-type connections, By (kN)
Grade ofhigh-strength bolt

F10T

S10T

NominaldiameterAbe (mm2 )

M16
M20
M22
M24
M20
M22
M24

157
245
303
353
245
303
353

σy (N/mm2 )

900

900

By (kN)
141
221
273
318
221
273
318

(4) Characteristic values of strength of normal bolts
The allowable stress for normal bolts as speciﬁed in JIS B 1051 is given as follows in [Japan
Road Association, 2002]. The strength of a grade 4.6 bolt is assumed to have strength characteristics equal to those of an SS400 ﬁnish bolt. For grade 8.8 and grade 10.8 bolts, the safety√
factor for standard yield strength is set high, the allowable shear strength is speciﬁed as 1/ 3
times the tensile strength, and the allowable bearing strength is speciﬁed as 1.5 times the tensile
strength, because the yield ratio (σy /σB ) is high. [Railway Technical Research Institute, 2000],
also speciﬁes the strength of normal bolts similarly.
The characteristic values of strength of normal bolts are summarized in Table C11.6.6.
Table C11.6.6 Characteristic values of strength of normal bolts (N/mm2 )Grade as classiﬁed by
JIS B 1051

Yield point or
ultimate stress σy (N/mm2 ))Tensile strengthσB (N/mm2 )Shear strength√
σy / 3

4.6
240
400
140
8.8
660
830
(380)
10.9
940
1,040
(540)
* strength values in ( ) are based on [Railway Technical Research Institute, 2000].

Bearing strengthσy × 1.5360(990)(1,410)(5) Characteristic values of strength of pin and anchor bolts in concrete
The allowable stress of pins, as summarized in Table C11.6.7, is determined as 1.6 times
the allowable stress, which is the value speciﬁed in the Design Standard and Commentary for
Structures published in Japanese National Railways age, 1983, taking into consideration theconvenience of the design given in [Railway Technical Research Institute, 2000]. Moreover, thecharacteristic value of shear strength of an anchor bolt in concrete should be taken as 70% of theshear strength of the pin, considering uncertainties in construction.
The allowable stress of pins and anchor bolts in concrete is determined by the same approachin [Japan Road Association, 2002].

176

Standard Speciﬁcations for Steel and Composite Structures [Design]

Table C11.6.7 Characteristic values of strength of pins
and anchor bolts (N/mm2 )Type of strength value
Shear strength
Pin

Bending strength
Bearing strength

Anchor bolt

Shear strength

SS400

S30CN

S35CN

S45CN

170

190

225

―

（ 160 ）

（ ― ）（ 225 ）

（ 240 ）

320

370

420

―

（ 305 ）

（ ― ）（ 420 ）

（ 465 ）

170

200

225

―

（ 170 ）

（ ― ）（ 225 ）

（ 250 ）

120

135

155

―

（ 110 ）（ ― ）（ 155 ）（ 155 ）

* Upper and lower values in ( ) are those calculated by [Railway Technical ResearchInstitute, 2000], and [Japan Road Association, 2002], respectively.

11.7 Structural Details of High-Strength Bolted Connections
11.7.1 Bolts, nuts, and washers(1) Friction-type connections
Properties of bolt, nut, and washer materials used for friction-type connections shall comply
with those speciﬁed in JIS B 1186 (Japanese Industrial Standards). Further, bolts, nuts, andwashers shall have suﬃcient resistance to delayed fracture. Appropriate axial force shall beapplied at installation and the force shall not decrease signiﬁcantly during the service life.
(2) Bearing-type connections
Standards for bolts, nuts, and washers used for bearing-type connections shall be as speciﬁedin JSS II 01-1981 (Japanese Society of Steel Construction Standards).
(3) Tension-type connections
Properties of the bolt material used for tension-type connections shall comply with thosespeciﬁed in JIS B 1186 (Japanese Industrial Standards). Further, bolts shall have suﬃcientresistance to delayed fracture. The appropriate axial force shall be applied at installationand the force shall not decrease signiﬁcantly during the service life.
【 Commentary 】(1) The delayed-fracture characteristics should be considered as well as the mechanical characteristics
speciﬁed in JIS B 1186. In particular, attention should be paid to tightening the bolts by theyield strength tightening method, in which bolt axial force exceeds the yield strength.
Refer to article 6.3.2 of Speciﬁcations for Highway Bridges o Commentary [Japan Road Association, 2002] for the chemical properties of bolts in consideration of their delayed-fracture
characteristics. Further, the standard torque coeﬃcient for bolt sets should conform to Table
C11.7.1.
In [Japan Road Association, 2002], and [Railway Technical Research Institute, 2000], thestandard bolts used for friction-type connections are M16, M20, M22, and M24 in the ﬁrst andthe second category as given in JIS B 1186. In these speciﬁcations, the standard torshear bolts
used for friction-type connections are the same as in JSS II09-1996. Other bolts, i.e. hot-dip
galvanized bolts, rust-proof bolts, weathering steel bolts, ﬁre-proof bolts, ultra high strength
bolts, stainless steel bolts, or large-diameter bolts, can be used after conﬁrming that article (1)is satisﬁed.
Large diameter bolts over M24 can be used with reference to [Japanese society of civil engineers,
2006].
(2) High-strength bolts for friction-type connections and injection bolts may be used for bearing-type

177

Chapter 11 Joints

connections. Because there is a clearance between the bolt hole and the bolt axis, the connection
may slip before bearing. For this reason, injection bolts should be used in principle, because it
is considered that such deformation is not desirable.
(3) Tension-type connections transfer the load through the contact force obtained by introducing ahigh axial force into high-strength bolts as in friction-type connections. The requirements forhigh-strength bolts used in tension-type connections are basically the same as those for frictiontype connections.
[Steel Construction of Japan, 2004], speciﬁes standard high-strength bolts for tension-typeconnections in consideration of actual usage as follows.
The standard high-strength bolt for short connection types should be a high-strength bolt
for friction-type connections. However, since this type of connection is required to operate very
eﬀectively, high-strength bolts of the ﬁrst category (as given in JIS B 1186) should not be used.
When torshear-type high-strength bolts are used for short connection types, a washer should be
used under the bolt head in principle.
Steel rod with material properties equivalent to those of standard high-strength bolts can beused in place of high-strength bolts for long connection types, since standard high-strength bolts
cannot be expected to be available in these lengths. When threads are cut at the ends of a carbon
alloy steel rod for use in a long connection, the strength grade of the rod is less than 10.9 taking
Whenaccount of delayed fracture/fatigue. The shape of the threads must also be considered.
the same examination is carried out, design guidelines 3.2 or 3.4 of [Steel Construction of Japan,
2004] could be referenced.
Table C11.7.1 Torque coeﬃcients for set of high-strength bolts
Average torque coeﬃcient in shipment of
one lot
Coeﬃcient of variance of torque coeﬃcientin shipment of one lot.
Variation by temperature in shipment of
one lot

0.110∼0.160
Less than 5%Less than 5% of average of torque coeﬃcientin shipment for a temperature change of 20 ℃

11.7.2 Holes for bolts
The size of holes for bolts shall be determined in consideration of the corresponding load-transfer
mechanism for the connection type as well as workability.
【 Commentary 】(1) In friction-type and tension-type connections, the size of the bolt holes must be determined suchthat the required bolt axial force is secured, because these connections transfer the load throughthe contact force resulting from the introduced bolt axial force. The standard size of bolt holes forfriction/tension-type connections is the value obtained by adding 2.5mm to the nominal diameterof the bolt. It is necessary to consider that slip resistance will decrease if the hole is oversized
or if an elongated hole is used for reasons of workability. The maximum allowable hole sizes andtheir inﬂuences on slip resistance can be found in [Japanese society of civil engineers, 2006].
The design size of the hole is the value obtained by subtracting 3mm from the nominal diameterfor the net sectional area of a friction-type connection. However, where the nominal diameter
is16mm, 2mm should be subtracted from the nominal diameter.
(2) Regarding bearing-type connections, it is desirable that there is no clearance between the bolt

178Standard Speciﬁcations for Steel and Composite Structures [Design]

shank and the bolt hole, because load is transferred by the shear resistance of the shank and thebearing between the shank and the wall of the bolt hole. The standard size of the bolt hole forbearing-type connections is the value obtained by adding 1.5mm to the nominal diameter.

11.7.3 Bolt length(1) Bolts must be long enough to deliver ﬁrm contact force between the contact surfaces.
(2) Bolt threads in bearing connections shall not extend into the shear plane.
【 Commentary 】

For bolt lengths, refer to the design data book [Japanese Association of Bridge Construction, 2006],
or similar sources.
(1) The following requirements should be satisﬁed in order to ensure secure tightening of bolts.
1) Bolt threads should be visible at the plane of the nut end after tightening.
2) There should be no incomplete thread turns within the nut after tightening.
(2) The bolt length for bearing-type connections must satisfy the requirements given in this clause.

11.7.4 Bolt spacing
The minimum bolt spacing shall be larger than the spacing required to allow tightening. The
maximum spacing should not exceed the local buckling and corrosion-prevention requirements.
【 Commentary 】(1) If the bolt spacing is too small, the work of tightening the bolts becomes impossible or the plates
being connected might be damaged by tightening. On the other hand, if the bolt spacing is
too large, corrosion/local bucking might occur due to the reduced plate contact. Therefore, thespacing must be carefully considered.
(2) The minimum bolt spacing should follow the standard given in Table C11.7.2 considering theworkability of bolt tightening and past experience. However, it might be possible to reduce thespacing to 3 times the bolt diameter. The minimum bolt spacing in Eurocode [CEN, 1993],
Building Standards of Construction and Water Gate Steel Pipe Technical Standard [Water Gate
Steel Pipe Association 2001] is 2.5 times the bolt diameter as the lower limit.
Table C11.7.2 Minimum bolt spacing (mm)Nominal diameter of bolt
Minimum spacing (mm)
M30
105
M27
95
M24
85
M22
75
M20
65
M16
55
Note) The minimum spacing for M27 and M30 bolts is determinedby referring to the Design Standard for Superstructure[Honshu-Shikoku Bridge Authority, 1995](3) The maximum bolt spacing in the grid arrangement should, as standard, be the smaller value
given in Table C11.7.3 in consideration of local buckling between bolts, contact between connected
plates, and practical experience. The maximum bolt spacing in the struggle arrangement canbe twice that in the grid arrangement in consideration of the ﬁxing eﬀect of the bolt which islocated at the bolt line.
(4) The maximum bolt spacing for matching of tension members should, as standard, be a value that

179

Chapter 11 Joints

Table C11.7.3 Maximum bolt spacing (mm)Nominal bolt diameter

Maximum bolt spacing
p

M30
210
M27
190
12t
M24
170
12t 以下 15t − 3/8g and under 12t
M22150(struggle arrangement)
M20
130
M16
110
Where, t: plate thickness of outside plate or shaped steel (mm)p：bolt spacing along the stress direction (mm)g：bolt spacing perpendicular to stress direction (mm)g
24t
and under 300

Fig.C11.7.1

does not exceed 300mm following the speciﬁcation for the direction perpendicular to the stress.

11.7.5 End and edge distance
The minimum distance from the end or edge of a member to the centre of a bolt hole shall belarger than the value required to ensure that there is no end or edge failure because of tearing
prior to bolt failure. The maximum distance from the end or edge of a member to the centre of abolt hole shall not exceed the corrosion prevention requirements.
【 Commentary 】(1) The distance between the centre of a bolt hole and the edge/end of the plate must be speciﬁedsuch that the plate does not fail at the edge/end. If this distance is too short, failure of the platemight occur at the edge/end; on the other hand, if this distance is too great, contact between
connected plates is not good and corrosion might occur because of water seepage. Both of thesefactors should be taken into account in determining the appropriate distance.
(2) Standard minimum and maximum distances from the end or edge of a member to the centre ofa bolt hole are given in Table C11.7.4. These values have previously been used in the design ofriveted connections to prevent failure at the end or edge of the plates. In this code, the samevalues are also adopted as the minimum distance for a bolt considering past practice.
Since, with improved cutting technology, the quality of automatically gas-cut edges is almost
equal to that of rolled edges and ﬁnished edges, there is no fear of detrimental eﬀects of internal
stress or hardening. The distance for automatically gas-cut edges should be the same as for rollededges or ﬁnished edges. In the case of laser cutting, which is now a normal cutting method, theroughness of the edge is equivalent to that of an automatic gas-cut edge. However hardening of
the material is greater than that of an automatic gas-cut edge, the area of the heat aﬀected zone
is smaller, and fatigue strength does not decrease. Considering these results and past practice,laser-cut edges are considered equivalent to rolled edges or ﬁnished edges.
(3) The minimum distance from the end or edge in the stress direction as given by Table C11.7.4
might be insuﬃcient when the number of bolts in this direction is less than 2, because thejoint strength is greater for a bearing-type connection than a friction-type connection. The

180

Standard Speciﬁcations for Steel and Composite Structures [Design]

Table C11.7.4 Minimum or maximum distances from the end or edgeof a member to the centre of a bolt hole (mm)Nominal bolt
diameter

Minimum distance from end or edge (mm)Sheared edge, Hand- Rolled edge, ﬁnished Maximum distancecontrolled
gas-cut- edge, automatic gas- from end or edge
edge
cut edge, laser-cut
edge
M30
–
55
M27
–
50
M24
42
37
8t
M22
37
32
and under 150
M20
32
28
M16
28
23
Note: M30, M27 is based on superstructure design standard [Honshu-Shikoku Bridge
Authority, 1995]

Speciﬁcations for Highway Bridges [Japan Road Association, 2002] adds a veriﬁcation using
expression C11.7.1.
Single shear
Double shear
where ，

e
a
A
t

⎫
A
⎪
⎬
t
2A ⎪
⎭
e>a
t

e>a

(C11.7.1)：minimum distance from the end or edge in the stress direction (cm)：shear strength ratio of bolt and plates：nominal cross-sectional area calculated from the outside diameterof the thread (cm2 )：thickness of thinner plates in single shear (cm)：thinner value of thickness of connected plates or total thickness of splice
plates in double shear (cm)(4) The maximum distance from the end or edge to the center of a bolt hole where the connected
plates are lapped should be 8 times the thickness of the outside plates. But this value must notexceed 150mm.

11.7.6 Minimum number of bolts
At least two bolts are required per connection. Where a connection is subject to shear force,two rows of bolts, meaning a minimum of 4 bolts in total, are required.
【 Commentary 】(1) The minimum number of bolts is two, considering the possibility of insuﬃcient contact between
members and also the work of making the connection. The number of bolts per connection isshown in Fig.C11.7.2(a).
(2) In the case of a connection subjected to shear force, two rows and two lines of bolts are required
as shown in Fig.C11.7.2(b) in order to prevent rotation of the joint.

Chapter 11 Joints(a) Grouped bolts

181(b) bolt arrangement when subjected to shear force

Fig.C11.7.2 Minimum number of high-strength bolts

11.7.7 Filler plates(1) In the case of friction connections where plates of diﬀerent thicknesses are connected, ﬁller
plates should be installed to ﬁll the design gap.
(2) Where it is impossible to install a ﬁller plate, the slip resistance of the connection shall be
reduced by means of an appropriate method.
(3) In choosing the thickness and material grade of the ﬁller plate, corrosion prevention andprotection from rust shall be considered in addition to the load-transfer mechanism.
【 Commentary 】(1) Required performance cannot be secured with friction-type connections if there is a gap between
the connected plates, since local concentrations of contact force might arise or corrosion mightoccur if rain enters between the plates. Therefore, if there is a diﬀerence between the design
thicknesses of the connected plates, a ﬁller plate shall be installed to ﬁll the gap. The limitationon the thickness of this ﬁller plate is half the thickness of the thicker connected plate.
(2) If a plate with adequate thickness is not available as a ﬁller plate, the resulting reduction in slip
resistance must be estimated by an appropriate method. The eﬀect of a gap on slip resistance issummarized in [Japan Society of Civil Engineers, 2006].
(3) It has been conﬁrmed through slip tests on general structural rolled steel plates that friction-typeconnections with ﬁller plates have adequate slip resistance regardless of the grade of material used
for the ﬁller plates. This means that any general structural steel plate is suitable for use as aﬁller plate. However, if the connected plates are of weather-proof steel, the same material should
be used for a ﬁller plate from the viewpoint of corrosion prevention and protection from rust.

11.7.8 Angled and round washers
In a case where the bolt axis is not perpendicular to the surface of the connected member, or
if the surface of the connected member is not ﬂat, care shall be taken not to impose undesirable
bending stress on bolts and washers.
【 Commentary 】

Since the ﬂanges of steel with an I-section or channel section are not necessarily parallel and the bolt
axis may not be perpendicular to the member surface, bending stress can occur at the bolt. Similarly,
if the surface at the joint is curved, a bending moment will be applied to the washer on the inside of
the curve and cracks may occur. Therefore, care should be taken that harmful stress does not occur
in bolts and washers in such cases. In Speciﬁcations for Highway Bridges II section 6.3.14 [Japan load
association, 2002], it is noted that 1) if the angle between the bolt head or nut surface and the member
surface is more than 1/20, an angled ﬁller or washer should be installed so as to prevent eccentric

182

Standard Speciﬁcations for Steel and Composite Structures [Design]

stress arising and 2) if the joints are curved and the radius of curvature is small, round washers should
be used.
Concerning friction-type connections for longitudinal proﬁle (LP) steel plates, it is reported in[Kamei, et al., 2000], that adhesion between connected plate and splice plate surfaces can be assured
by tightening the high-strength bolts; in this case bending deformation of the splice plates and thebolts does not signiﬁcantly aﬀect the behavior of the connection for taper angles up to 4.8/1000. These
results were obtained in tensile tests for various dimensions of connection. This means that tapered
joints can be used without the need for sections of equal thickness or shaped splice plates.
According to [Japan Road Association, 2002], special attention should be paid to curved connections
where the diameter of curvature is less than about 1.0m.

11.8 Bolted Connections
11.8.1 General(1) Regular bolted connections shall be adopted in cases where there is no need for high-strength
bolted connections.
(2) The standard use of bolted connections is for bearing-type or tension-type connections where
there is no axial force on the bolt.
【 Commentary 】(1) In the Design Standards for Railway Structures and Commerntary (Steel and Composite Structures) [Railway Technical Research Institute, 2000], regular bolts up to M10 are allowed foruse in connections for the attachment of bearing supports, inspection walkways, tension panels,
drainage equipment, etc. That is, these connections in these cases do not require high-strength
bolts. But regular bolts should not be used for connections subjected to cyclic force.
(2) A regular bolted joint is a connection that uses regular bolts. It is diﬀerent from a high-strength
bolted joint in which contact force arises from the bolt axial force. Therefore, regular bolted
joints should be used only for bearing-type and tension-type connections. Regular bolts mustnot be used for friction-type and tension-type connections that rely on bolt axial force.
(3) Stainless steel bolts for corrosion protection, post-construction hitting or resin anchor bolts,
U-bolts, and I-bolts, etc. may be used if this clause is followed.
(4) If there is a possibility that bolts might loosen, protection should be provided by using locking
nuts or similar.

11.8.2 Bolts, nuts, and washers
The standard bolts, nuts, and washers used in bolted connections shall be as speciﬁed in JIS
B1180, JIS B1181, and JIS B1256, respectively.
【 Commentary 】[Railway Technical Research Institute, 2000], speciﬁes using the following types of regular bolts forthe attachment of bearing supports, inspection walkways, tension panels, drainage equipment, etc.:
1) The standard ﬁnish is the middle grade and standard precision threads are the second grade.
2) Bolts should be galvanized in a bath in principle; bolt diameter should be greater than 12mm.
3) Locking nut should be used where there is possibility of loosening due to vibration, etc.

183

Chapter 11 Joints

11.8.3 Structural details
Structural details of bolted connections should be determined appropriately in the same way as
those of high-strength bolted connections.
【 Commentary 】(1) The diameter of holes for regular bolts in tension-type connections should be as given in JIS
B 1001. The standard diameter of holes for regular bolts in bearing-type connections shall be
added a nominal diameter of bolts to 0.5 mm.
(2) The minimum and maximum spacing of regular bolts with nominal diameter greater than M16
may be the same as for high-strength bolted connections. The standard minimum and maximum
spacing in regular bolted connections with M10 and M12 bolts may be as shown in Table C11.8.1,
which was derived from Design Speciﬁcations for Railway Structures and Commentary (Steel andComposite Structures) [Railway Technical Research Institute, 2000]. But if the thickness of thetension panels or steel ﬂoor plates is less than 4.5mm, the maximum spacing should be less than
110mm in consideration of ensuring contact.
Table C11.8.1 Minimum and maximum spacing
for regular M12 and M10 bolts (mm)Nominal bolt
diameter
M12
M10

Minimum distance

Maximum distance40
30

Max 150∼under 110(3) The distance from the edge/end of the plate to the center of a bolt hole for regular bolts greaterthan M16 may be as given in the clause specifying high-strength bolts. The standard distance from the edge/end to the center of a bolt hole for regular M10 and M12 bolts may be as
shown in Table C11.8.2, which was derived from Design Speciﬁcations for Railway Structures
and Commentary (Steel and Composite Structures) [Railway Technical Research Institute, 2000].
However, the maximum distance should be determined in consideration of ensuring plate contact
and should be in agreement with the maximum spacing.
Table C11.8.2 Minimum and maximum distance from edge/end to centerof a bolt hole (mm)Nominal bolt
diameter

M12
M10

Minimum distance from end or edge
Sheared edge, Hand- Rolled edge, ﬁnishedcontrolled
gas-cut- edge, automatic gasedge
cut edge, laser-cut
edge
22
19
20
17

Maximum distancefrom end or edge

8t
and under 150(4) The minimum number of bolts is two.
(5) Structural details for angled and round washers may be as given in the clause specifying highstrength bolted connections.

184

Standard Speciﬁcations for Steel and Composite Structures [Design]

11.9 Pin Connections(1) Structural members joined by pin connections shall not move at the point of connection.
Further, nuts should be secured to prevent pins coming loose. The inﬂuence of wear on
rotation at the pin and pin-hole shall be minimized.
(2) Pin design shall include consideration of wear loss to the pin cross section.
(3) In designing a member with a hole for a pin, the safety of the connection shall be veriﬁed inconsideration of the stress concentration adjacent to the hole.

【 Commentary 】(1) Movement between structural members that are joined by pin connections has a bad inﬂuence on
the vibration and impact of girders and can lead to concerns about the occurrence of secondarystress and joint galling. Accordingly, any movement should be restrained using collars or rings,
etc. An example of a pin connection is shown in Fig.C11.9.1.

Fig.C11.9.1

Pin and nut(2) The Speciﬁcations for Highway Bridges specify the structural details of pin connections in section
6.4 Pin Connections [Japan Road Association, 2002] as follows:
1) The diameter of the pin must be greater than 75mm.
2) The length of the ﬁnished part of the pin should be greater than 6mm. The ends of the pinshould be ﬁtted with a roams nut or regular bolts with washers.
In Design Speciﬁcations for Railway Structures and Commentary section 11.3.11, excepting
for this clause, the thread on the pin should be metric ﬁne thread (with a thread pitch of 4mm)in consideration of the possibility of loosening.
(3) In the Speciﬁcations for Highway Bridges and Commentary, section 6.4 Pin Connections [Japan
Road Association, 2002], structural details of members with pin holes are speciﬁed as follows:
1) The diﬀerence between pin and hold diameter should be 0.5mm as standard for diameters
less than 130mm and 1.0mm as standard for diameters greater than 130 mm.
2) The net lateral sectional area of tensile members with pin holes should be greater than 140%of the calculated necessary net sectional area. And the net sectional area of tensile members
behind pin holes should be greater than 100% of the calculated necessary net sectional area
3) The web thickness of tensile members with pin holes should be 1/8 of the net width. The
same regulation is speciﬁed in Design Speciﬁcations for Railway Structures and Commentary
section 11.3.11 [Railway Technical Research Institute, 2000].
References in Chapter 11
Architectural Institute of Japan(1973) ：Design Code for Steel Structure
Japanese Society of Steel Construction(1977) ：Japanese Society of Steel Construction Standard for GrooveChapter 11 Joints

185

Weld (JSS6-1977), JSSC VOL.13, NO.137
Japan Road Association (1980) ：Speciﬁcations for Highway Bridges and Commentary ．
Japan Society of Civil Engineers(1983) ：Design Standard for National Railway Structures
Toshihiko Momose, Kosuke Horikawa(1991) ：Fatigue Strength of Laser-Cut Steel, Proceedings of the 46th
Annual Conference of the Japan society of Civil Engineers, I-185
Railway Technical Research Institute(2000) ：Design Standards for Railway Structures and Commentary, Steeland Composite Structures 11.12 ．
Railway Technical Research Institute(2000) ：Design Standard for Railway Structures and Commentary, Steeland Composite Structures and Design Standard for Steel Structures 14.7∼14.9
Railway Technical Research Institute(2000) ：Design Standards for Railway Structures and Commentary, Steeland Composite structures ．
Japan Hydraulic Gate and Penstock Association(2001) ：Technical Standard for Hydraulic Gate and Penstock,
The Fourth Revised Edition
Architectural Institute of Japan(2001) ：Design Code for Steel Structure.
Japan Road Association (2002) ：Speciﬁcations for Highway Bridges and Commentary, II Steel Highway Bridges
Volume 6.1.11 ．
Japan Road Association (2002) ：Speciﬁcations for Highway Bridges and Commentary, II Steel Highway Bridges
Volume 6.1.2 ．
Japan Road Association (2002) ：Speciﬁcations for Highway Bridges and Commentary ．
Yoshinori KAMEI, Takashi NAKAMURA, Hisayuki AKIYAMA, Masahide TAKAGI, Nobuo NISHIMURA(2000) ：An experimental study on slip strength of HSFG bolted joints of LP steel plate without uniform
thickness portions, Journal of Structural Engineering, JSCE, Vol.64A, pp.1241-1250
Kuniaki MINAMI, Takeshi MORI, Yoshiyuki NAKANO, Tatsuya YAMANO, Masato KOUSAKA, Yasukazu
SHIMOYAMA, Eiichi YONEMOTO(2002) ：A study on welding connections between cross beam and main
girders in steel bridges, Proceedings of Japan Society of Civil Engineers, No.700/VI-54, pp. 65-70
Japan Society of Civil Engineers(2003) ：Special Subcommittee of Performance Based Design for Steel Structures, Committee of Steel Structures, Recommendation for Performance Based Design for Steel Structures
Japan Society of Civil Engineers(2006) ：Recommendations on Design, Construction and Maintenance for Friction Type of High Strength Bolted Connections
Japanese Society of Steel Construction(2004) ：Recommendation for Design of High Strength Tensile Bolted
Connections for Steel Bridges
Japan Bridge Association(2006) ： Design Date Book
Kuniaki MINAMI, Tadashi KASUYA, Chitoshi MIKI(2005) ：A Study on Standard of Size of Fillet Weld,
Quarterly Journal of the Japan Welding Society, Vol23, No.3
AASHTO(1994) ：AASHTO: LRFD Bridge Design Speciﬁcations (SI Units First Edition).
CEN(2003) ：CEN: EUROCODE 3 Design of Steel Structures prEN 1993-2.

186Standard Specifications for Steel and Composite Structures [Design]

Chapter 12 General Considerations for
Framed Structures
12.1 Scope
This chapter applies to the design of framed structures such as trusses, rigid frames, arches andcable structures.
【 Commentary 】

In general, a truss is a structure in which the structural members are arranged such that the stabilityof the overall structure is achieved only based on the axial stiﬀness of each member. For the analysis oftrusses in general, the axial force can be calculated assuming that the nodes are pinned joints. A rigid
frame is a structure in which the structural members are arranged such that the stability of the overall
structure is achieved based on the bending stiﬀness of each member. Axial forces, bending moment,
and shear forces act on the members.
An arch is a structure in which straight or curved members (arch ribs) are united in a smooth,convex upward form that resists the primary load mainly through axial compression forces. In a longspan arch, attention should be paid to the geometrical nonlinearity that will make displacements or
sectional forces greater than the values obtained by inﬁnitesimal displacement theory.
A suspended structure, which commonly means cable structures such as suspension bridges andcable-stayed bridges, is a structure in which structural members are arranged such that the stability ofthe overall structure is achieved based on the axial stiﬀness of the cables as well as the axial and bending
stiﬀness of the tower and girders, which are the primary structural members. In general, tensile forces
act on the cables, while axial forces, bending moment, and shear forces act on the members comprising
the tower and girders.
The terminology used here is that truss, rigid frame, or arch refers to the entire structure, while
the structural members comprising the structure are called truss members, rigid frame members, andarch members, respectively. A framed structure is a structure in which truss members, rigid frame
members, arch members, and others are combined in three dimensions so as to resist loading in three
dimensions. Assuming that the stability of the entire structure can be achieved, a framed structure
can be analyzed as a plane frame system

12.2 Member Section Design
12.2.1 General
The design of members constituting a framed structure shall be in accordance with Chapter
5∼ Chapter 9 (Strength of Members, and Required Various Performance and Veriﬁcation) and
Chapter 10 (General Provisions Related to Structural Members).

【 Commentary 】

The overall structural stability, eﬀective buckling length, and member composition of a section ina framed structure is prescribed in this chapter.

Chapter 12 General Considerations for Framed Structures

187

12.2.2 Design of truss members
12.2.2.1 Composition of sections(1) Cross section of members shall be such that the centroid of the cross section of the ﬁgure
coincides with the center of the cross section as far as possible, and also coincides with theskeleton line.
(2) The assembly of plates used in the composition of section shall be such that the welds will
be as symmetrical as practicable about the vertical and horizontal axes of the section.
(3) Chords, end posts and diagonal members attached to intermediate supports of continuous
trusses, subject to compressive forces shall have box or π cross section, in principle, andthe slenderness ratio related to radius of gyration about the vertical axis (outside the planeof the truss) shall be smaller than the corresponding ratio to radius of gyration about thehorizontal axis (inside the plane of the truss).
(4) The cross section of plates in a box section arranged parallel to the plane of the truss shallbe greater than 40% of the gross section of the members.
【 Commentary 】

Truss members are constructed from box-section members assembled by welding, I-section members,
steel pipes, shaped steel, members assembled from shaped steel, etc. Special attention needs to be
paid to calculating strength, particularly if angle steel or CT steel is utilized, because eccentric joints
tend to be formed at the nodes.

12.2.2.2 Eﬀective buckling length of compression members(1) In-plane of truss
In principle, the length of the frame shall be taken as the eﬀective buckling length of themember.
(2) Out-of-plane of truss
If the member is eﬀectively supported by supporting members in the out-of-plane directions
or by in-plane supporting members, the distance between the supporting points shall betaken as the eﬀective buckling length of the member.

【 Commentary 】(1) (1) The bending deformation of compression members of a truss, which is subject to the conﬁning
eﬀect of adjoining members, exhibit the characteristics of compression members with elasticallyconﬁned deﬂection angles at both ends when the focus is on a single compression member. The
conﬁning eﬀect of adjoining members depends on the relative stiﬀness of the member in focus, thestress level of the adjoining members, details of the truss frame composition, and other factors, so
it is diﬃcult to prescribe a general eﬀective buckling length factor. In this code, standard eﬀective
buckling length factors that err on the safe are provided by reference to Ultimate Strength and
Design of Steel Structures [Japan Society of Civil Engineers, 1994], which refers to values speciﬁedin the design standards for each country presented in Table C12.2.1. If it is not possible to obtain
the eﬀective buckling length factor using the proper method, it is acceptable to adopt a valuethat is not less than 0.9 times the frame length in the case of a chord member or 0.8 times in thecase of a web member.
If the midpoint of a member is eﬀectively supported by another supporting member, its span
may be used as the eﬀective buckling length. Here, ”eﬀectively supported” means a situation inwhich the diagonal member is connected to the supporting member ﬁrmly enough, as shown in188Standard Specifications for Steel and Composite Structures [Design]

Table C12.2.1 Comparison of eﬀective buckling length factors
with regard to in-plane buckling of a truss
Country/code

Chord member

Web member

USA AISC (1969)
Germany DIN4114 (1978)
Eurocodes 3 (1983)
Japan JSHB (1994)
Netherlands NEN3851 (1974)
Tchecoslovakia CSN (1976)
Belgium NBN B51-001 (1980)
France CM (1966)
Switzerland SIA161 (1979)
Great Britain BS5400 (1980)

1.0
1.0
1.0
1.0
1.0
1.0
0.9
0.9
0.9
0.85

1.0
0.9
0.9
0.8∼1.0
0.7∼1.0
0.5∼1.0
0.9
0.8
0.8
0.7

Fig.C12.2.1 and the supporting member has been designed as a compression secondary member
as deﬁned in Chapter 10. In this case, the strength at the connection point of the diagonal
member and the supporting member must be at least a quarter of the strength at the connection
point of the diagonal member and the chord member.

Fig.C12.2.1 Members of a truss(2) According to Reference and Handbook for Highway Bridges [Japan Road Association, 2002],”eﬀectively supported” means a situation in which it is laterally supported by another memberthat can resist a force equivalent to 1% of the maximum compressive force that acts on themember. In a structure such as a pony truss and a single-chorded truss, in particular, it isnecessary to connect the vertical member with other rigid members in order to prevent thebending stiﬀness of the vertical member from causing lateral buckling of the chord member,to say nothing of the stiﬀness of the vertical member itself. In Reference and Handbook for
Highway Bridges, lateral buckling of the upper chord member is prevented by keeping the radiusof gyration of area around the vertical axis at least 1.5 times as much as around the horizontal
axis.
The out-of-plane eﬀective buckling length of a truss with diﬀerent axial forces, , is given by
the equation below for L in Fig.C12.2.2:
P2
 = 0.75 + 0.25
L
P1

(C12.2.1)

where ，P2 , P1 are the compressive forces(P1 > P2 ) that act between nodes a-b and b-a, respectively.
respectively.

Chapter 12 General Considerations for Framed Structures

189

If axial forces of opposite sign act in a vertical member of a K-truss, as shown in Fig.C12.2.3,
and there is no supporting member outside the truss plane, the eﬀective buckling length for L
can be obtained using the equation below:

⎧ 
P
⎪
⎨ 0.75 + 0.25 2 L,P1 ≥ P2
P1
=(C12.2.2)⎪⎩
0.5L,
P1 < P2
where ，P1 is an absolute value of the compressive force, and P2 is an absolute value ofthe tensile force, with a condition that the section between members a-a is uniform.

Fig.C12.2.2 Out-of-plane eﬀective

Fig.C12.2.3 Out-of-plane eﬀective

buckling length of chord members

buckling length of vertical memberswith diﬀerent axial forces

with diﬀerent axial forces

Eﬀective buckling length factors of the main column members of a steel tower are presented
for diﬀerent frameworks and for diﬀerent sectional compositions in Table C12.2.2.
The eﬀective buckling length at the compressive foot of a steel tower should be studied not
Table C12.2.2 (1) Eﬀective buckling length factors of the main column of a steel tower
mainly subject to compressive force

190Standard Specifications for Steel and Composite Structures [Design]

Table C12.2.2 (2) Eﬀective buckling length factors of the main column of a steel tower
mainly subject to bending compression

only at the nodes but also in terms of global corrugated buckling of the entire foot section andlocal buckling of chord members.
At nodes on the upper member of a pony truss, horizontal displacement is elastically conﬁned
by a lateral rigid frame consisting of vertical members and ﬂoor deck members. In evaluating
the buckling load of an upper chord member, it should be noted that the axial compressive force
that acts on it varies depending on the framework, as shown in Fig.C12.2.4, with the designed
section of the members and the moment of inertia of the section changing accordingly.
The eﬀective buckling length of out-of-plane upper chords in the pony truss shown in Fig.C12.2.4
can be obtained from Eq.(C12.2.3).

λ0 + 1.8
=a,≥a(C12.2.3)
Xv0.4
1a
λ0 =
πr

where ，
a
r
F
E
Xv



F
E

(C12.2.4)：eﬀective buckling length：spacing of U-shaped rigid frames：radius of gyration of upper chord about the vertical axis
：nominal value of material strength (N/mm2 )：nominal value of Young’s modulus (N/mm2 )：parameter for evaluating rigidity of U-shaped rigid frame of the pony truss,

K v a3
EIc
Ic ：moment of inertia of section of central upper chord about the vertical axis of
the chordgiven by Xv =Chapter 12 General Considerations for Framed Structures

191

1
h31
bh22
+
+ f h22
3EIc
2EIh
h1 , h2 ：heights of U-shaped rigid frame as shown in Fig.C12.2.4.
Iv , Ib ：moment of inertia of section of vertical member and ﬂoor beam,
respectively
f ：deﬂection coeﬃcient of part connecting vertical member and ﬂoor beam.
If the connection is made by unstiﬀened end plate or by bolts throughangle steel section, the coeﬃcient is 0.5×10−10rad/Nmm,
if the connection is made by bolts through stiﬀened end plate,this coeﬃcient is 0.2×10−10rad/Nmm,
if the connection is adequately stiﬀened, and connected by welding or bybolts, this coeﬃcient is 0.1×10−10rad/Nmm.
Kv =Fig.C12.2.4 Main structural conﬁguration and cross section of pony truss

12.2.2.3 Built-up compression members
The design of built-up compression members formed by steel shapes shall be in accordance withthe following.
(1) Slenderness ratio of built-up compression member
The slenderness ratio about the stronger axis and weaker axis of built-up compression member shall be calculated using the proper method.
(2) Shear force accompanying buckling of built-up compression member
Each part of the built-up compression member shall be designed assuming that a shear force
acts on the part. During design, this shear force shall be added in addition to compressive
force even in built-up compression members that are subject to only shear force.
(3) Structural details of combined compression materials
Structure details of combined compression materials shall be provided as appropriate.
【 Commentary 】

Recently, there have been fewer cases in which built-up compression members are used as the main
structure of a bridge. Although usage is less frequent, this provision is retained in the code in caseof need related to the maintenance or reinforcement of an old bridge. Furthermore, some built-up
compression members used as parts of steel towers or steel columns used in construction utilize tie
plates, etc.; these may not exactly be truss structures, but they are also included in this section. Since
provisions relating to built-up members were deleted from [Reference and Handbook for Highway
Bridges, February 1980], this section is based on Article 11.6 and its explanation in [Architectural
Institute of Japan, 1980]. However, this does not mean to refute the contents of [Reference andHandbook for Highway Bridges, February 1980]. This commentary is also based on [Architectural
Institute of Japan, 1980], though some terms have been modiﬁed.

192Standard Specifications for Steel and Composite Structures [Design](1) The slenderness ratio of a built-up compression member can be calculated using the following
equations.
1) The slenderness ratio about the stronger axis (x-x axis in Fig.C12.2.5) of a built-up compression member is calculated using Eq.(C12.2.5) assuming the member to be a single member.
λ=where ，kr

kr

(C12.2.5)：Eﬀective buckling length (m)：Radius of gyration about the x-x axis (m)2) The slenderness ratio about the weaker axis (y-y axis in Fig.C12.2.5) of a built-up compression member is calculated by proportionately increasing the slenderness ratio of Eq.(C12.2.5)
for buckling. If the structural details of the built-up compression member are in accordancewith subsection (2) below, the approximation of Eq.(C12.2.6) can be used.
m
λye = λ2y + λ21(C12.2.6)
2
However, when ，λ1 ≤ 20 ，
λye = λy(C12.2.7)

can be considered.
Here ，λy
λyem：slenderness ratio considering the built-up member as an integral member：eﬀective slenderness ratio：number of steel shapes or sets of steel shapes formed by assembling

connecting members (ﬁtting strips, tie plates, lacing bars) (Fig.C12.2.6)
λl can be obtained from the equation given below, according to the type of built-up
compression member.
a) Built-up compression member consisting of ﬁtting strips or tie plates (Fig.C12.2.5)
λ1 =where ，1
r1

1
r1

(C12.2.8)：Pitch of tie plates (m)：Minimum radius of gyration of steel shape (m)b) Built-up compression member consisting of lacing bars (Fig.C12.2.7)
λ1 = πwhere ，2
d
e
A

A 3d
nAd 2 e2(C12.2.9)：Component of length of lacing bar along the axis of the member (m)：Length of lacing bar (m)：Distance between the central axes of the steel shapes (m)：Sum of sectional areas of steel shapes constituting the built-up compression

member (m2 )Ad ：Sectional area of lacing bar; however, in case of double lacing bars,
this is the sum of sectional areas of all lacing bars (m2 )n ：Number of connecting surfaces of connecting members (Fig.C12.2.8)c) Built-up compression member consisting of cover plates with holes (Fig.C12.2.9)
λ1 = 1.7

1 1
p r1

(C12.2.10)

Chapter 12 General Considerations for Framed Structures

Fig.C12.2.5 Built-up compression

193

Fig.C12.2.6 Number of steel shapes

members (tie plates)

Fig.C12.2.7 Built-up compression members formed

Fig.C12.2.8 n for lacing bars

by lacing bars

where ，1p
r1

：Length of hole (m)：Hole pitch (m)：Minimum radius of gyration of built-up compression member at the holeposition (m)Buckling load at the non-solid-spandrel axis (y-y axis) of built-up members as shown in
Fig.C12.2.5 is smaller than in the case where the two steel shapes act as one because of theeﬀect of shearing deformation as built-up compression members. A commonly used equation
to calculate approximately the eﬀective slenderness ratio of such built-up members is given
in Eq.(C12.2.6). Here, m in Eq.(C12.2.6) is the number of steel shapes or steel shape groups,
and is counted as shown in Fig.C12.2.6. For built-up members of lacing bars, although λ1 is
to be calculated by Eq.(C12.2.9) (in Figs.C12.2.7 and C12.2.8), Eq.(C12.2.7) can be applied
because λ1 given by Eq.(C12.2.9) is less than 20 except in the case where the cross sectionof the lacing bar is extremely smaller than that of the steel shape.
Suppose Fig.C12.2.6(f) is a built-up compression member of lacing bars, λ1 for x-x axis
is calculated as a lacing bar type in Eq.(C12.2.9), while λ1 for y-y axis shall be calculated
as a ﬁtting strip type in Eq.(C12.2.8). As for a built-up compression member of coverplates with holes as shown in Fig.C12.2.9, it shall be designed on the assumption that thecross section at the position of holes is the material for the built-up compression member.
Eq.(C12.2.10) is based on the calculation method that is similar to the tie plate type,considering deformation as shown in Fig.C12.2.9(b). That is, the eﬀective slenderness ratio
is given by:

194Standard Specifications for Steel and Composite Structures [Design]

Fig.C12.2.9 Cover plates with holes

λye =

λ2y + 2.77

1
p



1
r1

2
(C12.2.11)

therefore, if the following is assumed:
λ1 = 1.67

1 1
p r1

(C12.2.12)

Eq.(C12.2.12) will take the same form as in Eq.(C12.2.6). However, in a normal case,
Eq.(C12.2.7) can be applied because λ1 given in Eq.(C12.2.9) is less than 20.
(2) There are a variety of ways to deal with shearing force that comes with buckling of built-up
compression members, and provisions are diﬀerent from country to country. One of those isEngesser’s idea that tries to prevent failure of the tie rod until the straight built-up compression
member subject to central compression is buckled and bent and the compressed steel shapereaches a yielding state. According to this idea, the ratio of shearing force Qk to axial force N
in the compression buckling increases along with the slenderness ratio as shown in Fig.C12.2.10.
DIN is based on this idea.
On the other hand, based on the idea that eccentricities in opposite directions occur at bothends of a compression member and the tie rod will stay sound until they reach the bearing force,
Qk /N decreases as the slenderness ratio increases as shown in Fig.C12.2.10. In ”Standards for
Designing Steel Structure”, following AISC (2%) and BS449 (2.5%), Qk /N has been determined
as 2%, regardless of the slenderness ratio.
Due to shearing force Qk caused by buckling, the tie rod and its joint or the steel shape issubject to stress, so the safety measures shall be taken in the design. In this case, assumptions
are made in calculation for grid built-up members, as shown in Fig.C12.2.11.
(3) Structural details of built-up compression member
1) The pitch of high strength bolts or intermittent welds used for assembling the compression
member shall be less than (cm) times the minimum thickness of the constituent members,
and less than 30 cm (where, fk : Nominal value of material strength (N/mm2 )). However,
if high strength bolts are staggered, the pitch on each gauge line shall be less than 1.5 times
the value mentioned above. For the built-up compression member, regular bolts shall not
be used except in unavoidable circumstances in order to ensure its stiﬀness.
2) Since it is clear that just an additional tie plate at the midpoint shown in Fig.C12.2.8 will
not increase the bearing force, the number of spacing into which ﬁtting strips, tie plates orlacing bars are divided shall be greater than three, following DIN. The length of all spacing
shall be taken as equal as possible.

Chapter 12 General Considerations for Framed Structures

Fig.C12.2.10 Ratio of shearing force Qk to

Fig.C12.2.11 Qk of a girder

axial force N

combination member

1953) Since errors in the unsafe side that are given in Eq.(C12.2.6) are not negligible if the slenderness ratio of tie plates exceeds 50, the length of each space shall be taken so that theslenderness ratio of steel shapes of ﬁtting strips and tie plates becomes less than 50. In crossshaped sections, ﬁtting strips shall be arranged alternately perpendicular to each other. In
lacing bars, the length of the section shall be taken such that the slenderness ratio of steel
shapes becomes less than the larger of the slenderness ratios of the two main axes of thebuilt-up member.
4) The slenderness ratio of the lacing bar shall be less than 160. In AISC and BS, it shall beless than 140.
5) The ends of a built-up compression member with large spacing between steel shapes shallbe connected by gusset plates or tie plates with adequate rigidity using more than 3 highstrength bolts, or by welds that oﬀer stronger connections than with high strength bolts.
The pitch of high strength bolts used in this part shall be less than four times the diameter of the bolts. In case of welds, continuous welds shall be used. Since, as shownin Fig.C12.2.6(c)∼(f), this is for the purpose of preventing a gap between steel shapes
at the end of the member with large spacing between steel shapes, structures shown in
Fig.C12.2.6(a) and (b) are excluded.
6) In cover plates with holes, the length of the hole shall be less than twice its width. The
distance between inside edges of adjacent holes shall be greater than the distance between
adjacent high strength bolts or distance between adjacent weld lines of the built-up member.
A radius of corner-part of holes shall be greater than 50 mm.

12.2.2.4 Member with direct load
When a load acts to the place besides nodes, bending moment will happen except axial force inthe member. This is valued appropriately in consideration of itself.

【 Commentary 】

If direct external forces act between panel points of a chord member of truss, bending momentand shear force will act on the chord member in addition to the axial force. To deal with these indesigning, it is necessary to consider, for example, the sectional forces which act on the chord member

196Standard Specifications for Steel and Composite Structures [Design]

as multi-span continuous girders that are supported in a vertical member. This type of structure
includes upper chord member of a deck type truss which directly supports the deck and steel shell
Caisson-type ring frame truss which is subject to hydraulic pressure.

12.2.3 Design of rigid frame members
12.2.3.1 Eﬀective buckling length
The out-of-plane and in-plane eﬀective buckling lengths of frame members shall be computedby a suitable method.
12.2.3.2 Members with axial compression forces and bending moments
The method of safety examination for members subjected to combined axial compression forces
and bending moments is given in Chapter 6.
12.2.3.3 Examination of composition of bending, axial forces, and shear forces
The method of safety examination for members subjected to bending, axial forces, and shear
forces is given in Chapter 6.
12.2.3.4 Inﬂuence of foundation structure
The inﬂuence of rotation and relative movement of the foundation must be considered in thedesign.
【 Commentary 】(1) Out-of-plane buckling
The eﬀective buckling length of column members against in-plane buckling of rigid frame may
be calculated using Eq.(C12.2.13).
 = Khwhere ，hK

(C12.2.13)：Height of column in rigid frame (m)：Eﬀective buckling length coeﬃcient, obtained from Eq.(C12.2.14)or (C12.2.15)(1-1) Sway buckling (Refer to Fig.C12.2.12(a))
K=
(1-2)

1.6 + 2.4(ξ1 + ξ2 ) + 1.1ξ1 ξ2
ξ1 + ξ2 + 5.5ξ1 ξ2(C12.2.14)

Non-sway buckling (Refer to Fig.C12.2.12(b))
K=

3 − 1.6(ξ1 + ξ2 ) + 0.84ξ1 ξ2
3 − (ξ1 + ξ2 ) + 0.28ξ1 ξ2(C12.2.15)

where ，⎫
1⎪⎪
1 + Gt ⎬
⎪
1
⎪
⎭
ξ2 =
1 + Gb

(C12.2.16)(Ic /h)(XIb /L)(C12.2.17)

ξ1 =

G=

where ，Ic , Ib

：Moment of inertia of section of column and beam (m4 ). Average value used

Chapter 12 General Considerations for Framed Structures

L

X

197

if the cross section of the member is variable：Length of beam (m)：Indicates summation of the members that are assembled at the upper andlower ends of the column：Value given in Table C12.2.3 according to the connecting conditions on
the other end of the beam
Table C12.2.3 Value of X
Beam and condition

Hinged

Rigid

Fixed

Sway buckling
Non-sway buckling

0.5
1.5

1.0
1.0

0.667
2.000

Depending on the boundary conditions of the column, the values of Gb to be used shall be as
follows:
Bottom end hinged：Gb = ∞ ， Bottom end ﬁxed：Gb = 0(a) Sway buckling(b) Non-sway buckling

Fig.C12.2.12 Buckling of multi-storey framework(2) Out-of-plane buckling
The eﬀective buckling length for out-of-plane buckling of rigid frame of almost equal sections
may be taken as twice the total height of the frame. In a rigid frame where the cross section
varies considerably, or where the rigid frame is of special structure, the eﬀective buckling length
shall be determined separately as given in paragraph 12.2.5.
While the calculation formula provided in many design standards is based on the stiﬀness
ratio of the column to the beam, G = (Ic /h)/(Ib /L), it has been pointed out that the evaluation
may be too much on the safe side in the range of K < 0.5 which is actually utilized for rigid
frame structure. Hence, a calculation method based on approximation of eﬀective buckling length
factors has been adopted [Japan Society of Civil Engineers, 1994]. This method is to be applied
if symmetric rigid frame is subject to symmetric loads. For special structure types, complex
loading conditions, or changing cross sections, eigenvalue analysis in subsection 12.2.5 can beutilized to calculate the eﬀective buckling length.

12.2.4 Design of arch members
12.2.4.1 Eﬀective buckling length
The eﬀective in-plane and out-of-plane buckling length of arch members shall be calculated using
the proper method.

198

Standard Specifications for Steel and Composite Structures [Design]【 Commentary 】

Since there are arch structures of various types, it is diﬃcult to deﬁne uniquely an eﬀective buckling
length for both member buckling and global buckling. In out-of-plane buckling, in particular, member
buckling and global buckling often occur independently of each other; hence, the eﬀective buckling
length of members is deﬁned as below on condition that global buckling will be checked in accordancewith the later subsection 12.2.4.
(1) In-plane buckling
The eﬀective buckling length for the in-plane buckling of arch members in an arch structure
where no axial forces act on the stiﬀening girders and the unstiﬀened arch may be calculatedusing Eq.(C12.2.18). The eﬀective buckling length of arch members in an arch structure where
axial forces do act on the stiﬀening girders should be taken as the panel length.
πLe = √
αγ
where ，L

(C12.2.18)：eﬀective span of arch

γ

：γ =

f
α

：rise of arch

1+4

 2
f
L

：in-plane buckling coeﬃcient of arch given in Table C12.2.4
Table C12.2.4 In-plane buckling coeﬃcientaλ=Lwhere ，a
L
Ia
Ig



Ia
1+
Ig

(C12.2.19)：side span length of stiﬀening girder (m)：eﬀective span of arch (m)：average value of moment of inertia of arch member on one side of the archagainst in-plane bending of arch (m4 )：average value of moment of inertia of section of stiﬀening girder on one side of
the arch (m4 )If the value of f /L and λ falls between the values given in Table C12.2.4, then α must be
calculated by linear interpolation.
Eq.(C12.2.18) calculates eﬀective buckling length based on the section at L/4 assuming a nearly
uniform section in the axial direction of the member; thus, it is considered as the representativevalue for the whole arch structure. In the case of arch bridges, the eﬀective buckling lengthChapter 12 General Considerations for Framed Structures

199√
factor π/ αγ takes a value between 0.12 (for ﬁxed arch with f /L = 0.1) and 0.23 (for 2-hinged
arch with f /L = 0.3) [Japan Road Association 2002], Reference and Handbook for Highway
Bridges). In some cases it is larger than the interval between nodes (around 0.1∼0.2L) of aregular arch bridge. In designing the section of a member, the eﬀective buckling length obtainedby eigenvalue analysis at each section would be the most suitable value to use, but this equation
may be utilized because it gives a good approximation in an explicit form without the need foreigenvalue analysis when the member section is uniform in the axial direction. General design ispossible for section if a beam or a column with this eﬀective buckling length is assumed.
Since the in-plane load-carrying capacity of the overall structure will greatly decrease if loading
is uneven in the axial direction of the member, overall buckling should be veriﬁed, as explainedlater in Section 12.4, for the case of an unstiﬀened arch bridge or an arch structure where no
axial force acts on the stiﬀening girder. In the case of an arch where axial force acts on thestiﬀening girder, the in-plane load-carrying capacity of the overall structure is great enough thatlittle problem arises, but the buckling of a member between nodes becomes dominant; hence, thepanel length is taken as the buckling length.
(2) Out-of-plane buckling
The eﬀective buckling length for out-of-plane buckling of an arch member should be taken as
the panel length. However, if the arch is supported in the transverse direction by adequately
stiﬀened members with the purpose of restraining it in the transverse direction, the distance
between supports may be considered as the eﬀective buckling length.

12.2.4.2 Veriﬁcation of in-plane load carrying capacity of arches
Arch members shall be designed as members subject to axial compressive forces and bending
moments.
【 Commentary 】

The design of an arch rib consists of verifying overall safety in terms of overall buckling and also
verifying the member in terms of buckling between panel points. The latter type of buckling tends tooccur more often as axial force becomes more dominant and the slenderness ratio of the arch member
increases; further, it tends to occur at the end panel point close the support point.
In designing an arch member between the panel points, the length of the member (length between
nodes) is considered the eﬀective buckling length for the sectional forces in the structure system as awhole and veriﬁcation is based on the provisions of Chapters 6 to 9. The panel points here are thoseof the arch rib eﬀectively supported by the support member in the buckling direction. However, for astructure in which the arch ribs are supported by cable, such as in the case of a Nielsen Bridge, theeﬀective buckling length must be specially veriﬁed through elastic eigenvalue analysis as described insubsection 12.2.5.
Structures such as circular arches, which are subject to distributed loading such as centripetalloads, and parabolic arches, which are subject to uniformly distributed loading per unit length in the
span direction, may, as an approximation, be analyzed assuming that only axial compressive forces
act. Even for other regular arches, the axial compressive forces become the dominant member force if
the arch rise ratio is small and the slenderness ratio of the member is large. In such cases, an axial
force member may be assumed in design.
For details, refer to the provisions of Chapter 13 of Reference and Handbook for Highway Bridges[Japan Road Association, 2002]. In addition, equations for verifying the in-plane load-carrying capacityof an arch structure as a whole are proposed in Ultimate Strength and Design of Steel Structures [Japan
Society of Civil Engineers, 1994].

200Standard Specifications for Steel and Composite Structures [Design]

12.2.4.3 Veriﬁcation of out-of-plane buckling of arch
Out-of-plane buckling of arches shall be veriﬁed using the proper method.
(1) The safety against out-of-plane buckling of arches formed by one main arch structure andthe safety of out-of-plane buckling of arches in which the spacing of two main arch structures
is small compared to the eﬀective span, shall be veriﬁed.
(2) Out-of-plane buckling of arches shall be veriﬁed against the most critical loading conditions.
(3) Lateral bracings and sway bracings of arch shall be designed in accordance with section 12.4.
【 Commentary 】

The following methods are available for the veriﬁcation of out-of-plane buckling of arches.
(1) (1) If two or more main arch structures, the sections of which have been determined in consideration of safety against the buckling of members between panel points, are stiﬀened with lateralbraces and sway bracing as directed in the provisions of section 12.4 and if the ratio of span tothe distance between the outermost main structures is 20 or less, it is generally not necessary toverify out-of-plane buckling in the complete system. This is applicable also to so-called baskethandle Nielsen Lohse girder bridges where the surfaces of the two arch structures are slanted withrespect to each other, even though the provisions of section 12.4 indicate that it is not applicable.
For other cases, veriﬁcation is prescribed because there is a risk of lateral buckling in theout-of-plane direction of the arch when the entire structure system is considered.
If three-dimensional eigenvalue analysis is not conducted, the eﬀective buckling length factor
can be calculated as an explicit function by deﬁning λ as in the following equation.
1
λ=πwhere ，ry
Iy

Ke

Kβ

β

α
μ

b



F Ke Kβ K Kg S
E
ry

(C12.2.20)


Iy /A：moment of inertia of section around the vertical axis of an arch rib (mm4 ); in thecase of variable section, it is the average over the length Iy = Iyi Li /L,
L = Li：eﬀective buckling length factor to take into account the conﬁning eﬀect of the support
point; it is 0.5 if out-of-plane bending gyration of the arch rib at the supporting
the support point is restrained and 1.0 otherwise.
：eﬀective buckling length factor to take into account the eﬀect of stiﬀening
by lateral braces,√
Kβ = 1 − β + {2ry (0.5 + 0.94 u)/(aKe )}β：ratio of the length of the arch part stiﬀened by lateral braces to the total lengthof the arch rib; for through-arch bridges (Fig.C12.2.13) it is the ratio of the length ofthe part of the arch stiﬀened by lateral braces to the total length of the arch rib,
while for half-through arch bridges (Fig.C12.2.14) it is calculated in a similar way byregarding the upper part (above the base of the portals) as a through-type bridge.
For deck-type arch bridges (Fig.C12.2.15), β = 1.0 because the entire arch is usuallystiﬀened by lateral braces.
：distance between axes of the two arch ribs (mm)：factor representing shearing
deﬂection of the lateral bracings,
 
3/2







2
2
a
A
1 a
2Ad
a
μ=
+
1+
2 L
b
2Ad
b
Ab
：

：panel length of the lateral braces (mm); if variable, the average should be taken.

Chapter 12 General Considerations for Framed Structures

201

Fig.C12.2.13 Through type arch
L
L0

f0

f

l0

l

Fig.C12.2.14 Half-through type arch
Fig.C12.2.15 Deck-type arch

Ad
Ab
K

Igy
Iay
hg
f

：sectional area of the diagonal members of lateral braces (mm2 )：sectional area of the struts of lateral braces (mm2 )：eﬀective buckling length factor to be considered if the loading direction does notremain vertical; it is 1.0 if loading is always vertical. For through-arch bridges
and half-through arch bridges,
⎧

1/4
⎪
Igy
Igy
⎪
⎪
≤1
⎨ 1 − 0.35
Iay
Iay
K =
⎪
Igy
⎪
⎪
⎩ 0.65>1
Iay
For deck-type arch bridges,

0.25
Iay
hg Iay+ 0.01K = 1.45 + 0.05
Igy
f Igy
：moment of inertia of section in terms of horizontal lateral bending of the sectionof the structure including girders and ﬂoor system, if any (mm4 )：moment of inertia of section in terms of out-of-plane bending of the section of thestructure including the two arch ribs that are connected by lateral braces (mm4 )：vertical distance between the center line of the stiﬀening girder and the arch crown(center) in the case of a deck-type arch bridge (mm) (Fig.C12.2.15)：arch rise (mm)202Standard Specifications for Steel and Composite Structures [Design]

Kg

S

σcul

：eﬀective length factor to take into account the eﬀect of conﬁnement of out-of-plane

displacement of the arch by stiﬀening girders; if Kg = 1.0, it is on the safe side forall cases. In the case of through-arch bridges and half-through arch bridges, Kg = 1.0
is usually assumed. In the case of deck-type arch bridges, if the arch ribs and stiﬀening
girders are rigidly connected at the arch crown and an increase in strength is considered,
the calculation may be based on the following equation:
1.48
Kg = 0.5 + 2Igy+ 1.72Iay： total axis length of arch (cm); in the case of through-arch bridges and deck-type arch bridges,
it is the total axis length L of the arch, while in the case of half-through arch bridges it is
the axis length L0 of the arch from the base of one portal to the base of the other portal(Fig.C12.2.14)：local buckling strength of the plates composing the section (N/mm2 )For an arch where the arch axes are in the vertical plane, the arch shapes are symmetricalparabolas or circular arcs, the structural members of the arches are almost the same height, andthe structure as well as the sway bracing are designed in accordance with subparagraph 12.2.4.3,
then out-of-plane buckling of the arch may be veriﬁed using the following equation:
γiwhere ，Nsd

Pcu
A

fud
σcug

λ

Nsd
≤ 1.0
Pcud

(C12.2.21)：design axial force on supports calculated from ﬁrst-order elastic theory for loads(uniformly distributed loads) acting on the structure; in the case of a half-througharch bridge, this is the axial force on the arch ribs at the point of intersectionof the arch with the stiﬀening girder (N)：design resistance in compression:
Aσcug σcul
Pcud =
γb fud：cross-sectional area of one arch rib; in case of a variable cross section,：the average value of sectional area along the length
A = Ai Li /L, L = Li
：speciﬁed design strength (N/mm2 ),fyd /γm：axial compressive strength without considering local buckling; can beobtained from the equation below (N/mm2 )⎧fud(λ ≤ 0.2)
⎪
⎪
⎨
(0.2
< λ ≤ 1.0)
{1.0−
0.545(λ−0.2)}fud
σcug =⎪
1⎪⎩fud(1.0 < λ)(0.773 + λ2 )：Slenderness ratio parameter
As fykAs fykλ==κNs
Ncr
As ： cross-sectional area of arch rib at support
κ：minimum eigenvalue for out-of-plane buckling obtained from paragraph12.2.5
Ncr ：critical buckling load at the support• ” In terms of gyration about the horizontal axis at the support point of the arch rib (whether
it is hinged within the plane of the arch or ﬁxed), its eﬀect on out-of-plane buckling strengthis small.
• ” As to how to deal with coupled buckling along with local buckling of the plates composing

Chapter 12 General Considerations for Framed Structures203the cross section, this is handled as for straight columns.
• ” Axial compressive strength around the vertical axis, if local buckling is not considered,can be calculated by substituting the slenderness ratio parameter obtained for the arch
structure into the equation for axial strength of a straight member.
Lateral braces and sway braces should be designed for the arch in accordance with section
12.4. However, if the forces in the diagonal members of the end lateral bracing are calculatedusing the conventional simpliﬁed method, the slenderness ratio must be made less than 60.
(2) Out-of-plane buckling of arches must be veriﬁed against the most critical loading conditions withthe maximum axial force. Concentrated loads are generally small and therefore can be omitted.
In principle, the loading condition shown in Fig.C12.2.16 should be veriﬁed. If the ratio of thisload to the uniformly distributed load is large, calculation of axial forces at the support points
should be considered.

Fig.C12.2.16 Loading condition used for verifying out-of-plane buckling loads of arch

In the veriﬁcation, the following points may be considered:• ” In terms of gyration about the horizontal axis at the support point of the arch rib (whether
it is hinged within the plane of the arch or ﬁxed), its eﬀect on out-of-plane buckling strengthis small.
• ” As to how to deal with coupled buckling along with local buckling of the plates composing
the cross section, this is handled as for straight columns.
• ” Axial compressive strength around the vertical axis, if local buckling is not considered,can be calculated by substituting the slenderness ratio parameter obtained for the arch
structure into the equation for axial strength of a straight member.
(3) Lateral braces and sway braces are usually designed in consideration of the horizontal lateralloads (which act out of the plane of the arch) caused by earthquakes or wind. Hence, lateralbracing members are designed independently of out-of-plane buckling of the arch; and bucklingof the members may occur before the entire structure system reaches the ultimate state. In
addition, it is evident that excessive axial forces that cannot be calculated using conventional
methods will act on diagonal members of the end lateral bracing. For these reasons, the following
prescription is given.
If the forces in the diagonal members of the end lateral bracing are calculated using theconventional simpliﬁed method, the slenderness ratio must be set at less than 60. Although
this maximum slenderness ratio of 60 is not a value that has been obtained theoretically, it is
conﬁrmed in Ultimate Strength and Design of Steel Structures [Japan Society of Civil Engineers,
1994] that the safety of this design method has been veriﬁed through numerical experiments withvariable parameters. Though it is true that a more rational way of design is to calculate member
forces separately using a more rigorous method, the situation is conveniently expressed in termsof the slenderness ratio in order to avoid design complication.
Arch bridges that do not meet the conditions stipulated above must be separately veriﬁed. To
do this, veriﬁcation of strength through three-dimensional ﬁnite element elasto-plastic analysis is thedesirable method.
If the support points of the arch undergo rotation as out-of-plane bending and torsion occur, the204Standard Specifications for Steel and Composite Structures [Design]

out-of-plane buckling strength will be signiﬁcantly lower; if out-of-plane bending and torsion is tobe restrained, little play and looseness should be allowed in the structure and construction requires
adequate care.

12.2.5 Calculation of eﬀective buckling length by eigenvalue analysis
For structures which are diﬃcult to calculate the eﬀective buckling length from equations given
in subparagraphs 12.2.2.2, 12.2.3.1, and 12.2.4.1, the eﬀective buckling length of each section canbe calculated by eigenvalue elastic analysis of the entire structure using eq.(12.2.2).
|KE + κKG (Ni )| = 0

ei = π
Here,

KE
KG
κ
ei
(EI)i
Ni

(EI)i
κNi

(12.2.1)(12.2.2)：Elastic stiﬀness matrix of the micro-displacement theory.
：Geometric stiﬀness matrix in the standard state：Eigenvalue：Eﬀective buckling length of cross section i (m)：Flexural stiﬀness of cross section i (kNm2 )：Design axial force of cross section i obtained from structural analysis basedon the design loads (kN)

【 Commentary 】

The eﬀective buckling length of a structural member varies according to loading conditions andsupport conditions, so it is very diﬃcult to uniquely determine the eﬀective buckling length of acomplex structural system with varying cross sections. In the existing design standards [Japan Road
Association, 2002; Railway Technical Research Institute, 2000; and Japan Society of Civil Engineers,
1987], eﬀective buckling length is deﬁned in an explicit form in terms of representative structures andboundary conditions; there is no clear prescription for any arbitrary structural system. Therefore, in
actual design, there are cases where the eﬀective buckling length is an approximate value determinedat the discretion of the design engineer. This may lead to a situation in which safety against buckling
is not adequate. Taking the above into consideration, this code provides methods for determining theeﬀective buckling length of a member section not only by the deterministic method of subparagraphs
12.2.2.2, 12.2.3.1, and 12.2.4.1 but also by elastic eigenvalue analysis of the total structural system
based on the loading provisions of Chapter 2. Now that computers have come into use for everyday
practical design work, elastic eigenvalue analysis is no longer a burden when designing a complex
steel structure. Although the calculations are more complicated than the conventional method, theeﬀective buckling length can be calculated for any arbitrary framed structure that is subject to certain
loads. Furthermore, by setting nodes at points where the section changes, eﬀective buckling length
can be deﬁned for the section between the nodes, thus making possible enhanced design precision andreliability.
If, for all structural members, the stiﬀness, boundary conditions, and loading conditions are given,
the eﬀective buckling length given by Eq.(12.2.2), which is obtained through eigenvalue analysis inEq.(12.2.1), is generally more precise compared with the eﬀective buckling length determined using
the conventional method based on the stiﬀness of adjoining members. However, from the viewpointof practical design, an enormous numbers of eigenvalue analyses would be needed to ﬁnd the mostdisadvantageous loading condition for each targeted member, while dealing with eﬀective buckling

Chapter 12 General Considerations for Framed Structures

205

length would become complicated because the eﬀective buckling length varies with member crosssection where it is not constant.
Furthermore, in certain structural systems, such as those with microscopic axial compressive forces,
those with member cross sections that vary signiﬁcantly, and so on, the eﬀective buckling length of amember takes an unrealistically large value with an extremely big slenderness ratio. In some cases,
the value is so extreme as to make design impossible [Japan Society of Civil Engineers, Ultimate
Strength and Design of Steel Structures, 1994] [Nishino, et al., Bridge and Fundamentals, 1981].
Certain countermeasures are currently available for this, such as a method involving the introductionof an additional axial compressive force to a section subject to microscopic axial compressive forces, amethod of evaluating a higher-order buckling mode in which only the focused member reaches buckling,a method that avoids reliance on loading, and so on; however, none has become the accepted standard
method. Hence, it is necessary to properly evaluate the eﬀective buckling length while comparing
various analysis methods and making an evaluation on the safe side with respect to eigenvalue analysis.

12.3 Verification of Entire Structure
In framed structures such as truss, rigid frame, arch, and cable structure, not only the safety ofeach member and joint but also the safety of the entire structure shall be veriﬁed.
【 Commentary 】(1) Trusses
In trusses where the spacing of the main truss structures is very close compared to the total
length of the truss, or in pony trusses with small transverse rigidity, overall buckling must be
veriﬁed using appropriate methods. If truss girders with a pseudo-box section consisting of amain structure with upper and lower lateral braces have a ratio of span to distance between main
structures that exceeds 30, the transverse rigidity and torsional rigidity will be small and may
cause overall lateral buckling. For veriﬁcation methods in these cases, it is recommended to refer
to Guidelines for Design against Buckling [Japan Society of Civil Engineers, 2005], Handbook
for Design of Steel Road Bridges [Japan Road Association, 1980], etc.
In pony trusses, the lateral buckling strength of the upper chord member must be calculated anddesigned by properly considering the rigidity of the U-frame comprising the vertical members,
diagonal members, and cross beams that support the upper chord member. If the ratio of span
to distance between main structures exceeds 10, it is desirable to conduct an elastic buckling
analysis for the entire structural system to verify safety.
(2) Rigid frames
Generally, if a rigid frame is designed in accordance with section 12.2, it is not necessary
to verify total buckling of the frame; however, if a non-standard frame type is used, separate
detailed calculations are necessary to verify total buckling of the frame. For non-standard typesof rigid frame, elastic buckling analysis of the entire structure must be conducted to verify total
buckling and to calculate the eﬀective buckling length of members.
(3) Arches
The overall arrangement of the structure, its shape, and the cross sections of its members
should be selected so that total in-plane and total out-of-plane buckling of the arch does notoccur. For an unstiﬀened arch in which eccentric loads act in the axial direction and for anarch structure in which the stiﬀening girder is subject to no axial force, care must be taken withregard to total in-plane buckling. In addition, in an arch structure where there is a possibilityof lateral buckling in the out-of-plane direction, total buckling must be veriﬁed. In this case, it206Standard Specifications for Steel and Composite Structures [Design]

is desirable to verify the strength through elasto-plastic ﬁnite displacement analysis. For detailsof the method, refer to section 12.2.
(4) Cable structure
Generally, if the cross section is designed according to section 12.2, it is not necessary toverify total buckling of the cable structure. However, the loading capacity of the cross sectionsof towers, girders, and cables of the main structural components of large suspension bridges
and cable-stayed bridges must be veriﬁed to conﬁrm safety using three-dimensional models of
the entire structural system. The various loads that act on the upper structure of a typicalsuspension bridge or cable-stayed bridge are transmitted to the tower via cables and then to
the foundation. Therefore, this veriﬁcation of the safety of main girders, cables, and towers isextremely important. For large suspension bridges, in particular, safety must be veriﬁed not only
through speciﬁcation of required safety performance and its veriﬁcation as explained in Chapter
6, but also through elastic ﬁnite displacement analysis and elasto-plastic ﬁnite displacement
analysis using a three-dimensional model of the entire structure. In investigating the bucklingof towers and stiﬀening girders in suspension bridges and cable-stayed bridges and also the load
carrying capacity of the entire structural system, Guidelines for Design against Buckling [Japan
Society of Civil Engineers, 2005] can be referred to.
Attention shall be paid to fewer steel girder bridges because recent studies have concluded thatveriﬁcation of total buckling is necessary in construction.
Attention shall be paid to fewer steel girder bridges because recent studies have concluded thatveriﬁcation of total buckling is necessary in construction.

12.4 Constraint in the Transverse Direction
In trusses or arch structures, lateral bracings and sway bracings adequately stiﬀened in thetransverse direction shall be provided for insuring structural functions in three dimensions. If
such measures are not provided, the structure shall be calculated separately as a three-dimensionalframework and safety shall be veriﬁed.
【 Commentary 】

In designing truss and arch members for a bridge, the eﬀective buckling length with respect toout-of-plane buckling of compressive members is calculated on the premise that the panel points of themain structure are suﬃciently supported by lateral braces, sway braces, portal braces, etc. The designof these lateral braces, struts, sway braces, and portal braces is based on section 12.5 of Reference andHandbook for Highway Bridges [Japan Road Association, 2002].
In order to obtain precise values of the forces acting on the diagonal members in the lateral bracingof an arch, while it is desirable to conduct (elastic) ﬁnite displacement analysis for the arch system andthe lateral bracings as a three-dimensional framework, an alternative method is available as follows.
For horizontal lateral loading, assuming that the arch system and the lateral braces form a planeframework, ﬁnite displacement analysis is conducted by setting an arch axial force from the in-plane
design loads imposed by earthquakes or storms along with the horizontal lateral load multiplied bya coeﬃcient. For vertical in-plane loading, assuming a three-dimensional framework of arch ribs andlateral braces, microscopic displacement analysis is conducted using the vertical design load multiplied
by a coeﬃcient. Of the two member forces calculated for each load, the larger one is selected anddesign is carried out assuming a straight column.

Chapter 12 General Considerations for Framed Structures

207

12.5 Camber
In structures where the ﬁnished shape must be maintained, a manufacturing camber shall be
provided, in principle.
【 Commentary 】

While it is common to provide a manufacturing camber to account for the dead load (ﬁxed load),in a composite structure or composite girder of steel or concrete a manufacturing camber should also
be provided for hard dry shrinkage and creep as well as deﬂection due to concrete pre-stressing.
In Standards and Handbook for Designing Railway Structures - Steel/Composite Structures (SI unit
version) [Railway Technical Research Institute, 2000], the rule is to provide a manufacturing camber
for the purpose of avoiding unfavorable eﬀects in terms of ride comfort and safety and preventing sagof the bridge girders due external dead loads. In the case of plate girders, it is a rule to provide amanufacturing camber for a bridge girder with a span over 30 m to deal with the deﬂection causedby the dead load of the main girder; in some cases it is better to provide a camber also for a bridge
girder with a span of less than 30 m if deﬂection resulting from the dead loads is particularly large. In
addition, part of the train load should be considered in the case of an open deck bridge girder carryinga railway. In the case of composite girders, it is a rule to provide a camber for the steel girder againstdeﬂection caused by the dead load regardless of span.
On the other hand, in Reference and Handbook for Highway Bridges [Japan Road Association,
2002], there are no provisions as to the span length.

12.6 Members Considered as SubstructureMembers considered to possess properties of a substructure, such as the base of a column in arigid frame, shall be designed carefully with a view to points such as selection of design loads, rustprevention, and transmission of loads to the foundation.
【 Commentary 】

This clause is speciﬁed by reference to sections 15.2, 15.3, 15.12, and 15.13 of Reference and Handbook for Highway Bridges [Japan Road Association, 2002] and Standards and Handbook for Designing
Railway Structures - Steel/Composite Structures (SI unit version) [Railway Technical Research Institute, 2000. Any part of the column base of a rigid frame structure that is under the ground or in watermust be protected with reinforced concrete, corrosion resistant plating, corrosion resistant paint, etc.
In general, a rigid frame structure is designed on the premise that the column base is completely
ﬁxed or completely hinged. Hence, the quality of the anchor design has a great inﬂuence on thequality of the entire rigid frame structure. Since speciﬁc design methods are not provided in Referenceand Handbook for Highway Bridges, individual design standards have been drawn up by each of
the former public corporations that construct many rigid frame structures [Metropolitan Expressway
Corporation, 2003, Hanshin Expressway Corporation, 2000, Nagoya Expressway Public Corporation,
2003, Fukuoka-Kitakyushu Expressway Corporation, 2002].
1
Regarding types of anchor structure, there are four basic designs as presented in Table C12.6.1: bearing plate, 
2 reinforced concrete, 
3 direct ﬁxing, and 
4 piling. The type of structure adopted anddetails of veriﬁcation diﬀer among the former public corporations. In the case of Hanshin Expressway
Co., Ltd. (the former Hanshin Expressway Corporation), though it has a long track record in the208Standard Specifications for Steel and Composite Structures [Design]

construction of bearing plates of composite reinforced anchor frame type, it has been omitted because
the design standards are under review. In Ultimate Strength and Design of Steel Structures (Japan
Society of Civil Engineers, 1994), essential details for the design of reinforced concrete anchors for rigid
frames are given along with proposals for implementing the limit state design method. Meanwhile,
Study Report on Evaluation Method for Critical Strength of Structures (Japan Society of Civil Engineers, 2002) gives a method of evaluating the bearing force at the anchor and presents the results of astudy of the method based on Reference and Handbook for Highway Bridges.
Table C12.6.1 Structural type of anchor part in each former public corporation

Furthermore, in Standards for Designing Steel Structures [Architectural Institute of Japan, 1973]
and Guidelines and Handbook for Designing Limit State of Steel Structures [Architectural Instituteof Japan, 2002], there are provisions with respect to designing the column base. An outline of thesefollows.
(1) Sections 17.1 and 17.2 of Standards for Designing Steel Structures [Architectural Institute ofJapan, 1973] stipulate that the design must be in accordance with the following (Fig.C12.6.1).

Fig.C12.6.1 Anchor parta) If the column base is assumed to be ﬁxed:
1) Wing plates and ribs should be used to prevent deformation of the base plate. In addition,
joints with the main column member should be completed or combined with the foundation

Chapter 12 General Considerations for Framed Structures

209

by coating with reinforced concrete.
2) The bottom surface of the base plate and the upper surface of the foundation must be
ﬁrmly connected. In this case, the area of the base plate and the sectional area of theanchor bolts may be calculated by regarding the structure as a reinforced concrete column
with a cross section that takes the form of the base plate and with reinforcement consistingof the tensile anchor bolts. The thickness of the base plate can be calculated by assumingthat the additional reactive forces acting on the base plate will be added to the rectangularplate divided by stiﬀeners.
3) If the shear force at the column base is assumed to be transmitted via the frictional force
between the bottom surface of the base plate and the concrete, the friction factor should be
set at 0.4.
b) If the column base is assumed to be a pin and is subject to a tensile force, anchor bolts mustcarry the shear force of the column base and a combination of the tensile force and the shear
force must be considered.
(2) In Guidelines and Handbook for Designing Limit State of Steel Structures [Architectural Institute1 exposed column, 
2 reinforcedof Japan, 2002], column bases are classiﬁed into three types: column, and 
3 embedded column. For design, it is also stipulated that, by considering structuraldivision of the designed structure framework, the overall plastic bearing force or the yield bearing
force must exceed the bearing forces in the ultimate limit state and in the service limit state.

12.7 Considerations of Torsion Acting on Steel Towers
Power transmission towers and columns are subject to torsional loads due to non-uniform tension
in the cables. In this case, the sectional forces shall be calculated and the safety of the structure
veriﬁed.
【 Commentary 】

While this chapter can be used in the design of truss-type power transmission towers and steel
columns, as shown in Fig.C12.7.1, attention should be paid to situations in which one or more of thesuspended cables is severed by a phenomenon such as snowfall or wind, causing the steel tower or steel
column to be subject to non-uniform tension. This provision is made in accordance with Explanation
33 in section 3.1 of [Institute of Electrical Engineers of Japan, 1979]. In general, the calculation of these

Fig.C12.7.2 Cross section of a steel
Fig.C12.7.1 Power transmission tower

tower/column

210Standard Specifications for Steel and Composite Structures [Design]

torsional forces (torsional moment) is very complicated because they are represented by a high-orderindeterminate equation; however, stress may be calculated using the following simpliﬁed equations.
⎫
P
⎪
⎪
p=
⎪
⎪
2
⎪
⎪
⎬
ba

(C12.7.1)
q = 2
P
B + b2 ⎪
⎪
⎪
⎪
⎪
Ba
⎪
⎭
q= 2
P
B + b2As shown in Fig.C12.7.2, by dividing the non-uniform tension P into two forces p in the same
direction and torsion consisting of a combination of q and q  , the stress of each member can becalculated based on the individual horizontal forces.
References in Chapter 12
Architectural Institute of Japan (1973) ：Design Code for Steel Structure.
Institute of Electrical Engineers of Japan (1979) ：Standards for Designing Supporting Objects for ElectricTransmission ．
Architectural Institute of Japan (1980) ：Guidelines and Handbook for Designing Tower-shaped Steel Structures ．
Japan Road Association (1980) ：Specifications for Highway Bridges and Commentary.
Fumio Nishino, Chitoshi Miki, and Atsushi Suzuki (1981) ：Bridge and fundamentals, background and practice for revising reference and handbook for highway II, Chapter 13 Rigid frame structure ．
Japan Society of Civil Engineers (1997) ：Design Code for Steel Structures, PART A; Structures in General,
PART B; Composite Structures.
Japan Society of Civil Engineers (1994) ：Ultimate Strength and Design of Steel Structures, Steel Structure
Series 6 ．
Railway Technical Research Institute(2000) ：Design Standards for Railway Structures and Commentary, Steeland Composite Structures ．
Hanshin Expressway Corporation (2000) ：Design Standards, Part 2, Standards for Designing Structure (Bridges) ．
Japan Society of Civil Engineers (2002) ：Study Report on Evaluation Method for Critical Strength of Structure ．
Architectural Institute of Japan (2002) ：Guidelines and Handbook for Designing Limit State of Steel Structure(SI Unit Version) ．
Japan Road Association (2002) ：Specifications for Highway Bridges and Commentary, I Common Specifications Volume, II Steel Highway Bridges Volume.
Fukuoka-Kitakyushu Expressway Corporation (2002) ：Design Standards, Part 2, Standards for Designing
Structure (Bridges) ．
Metropolitan Expressway Corporation (2003) ：Recommendations for Design of Bridge Structures of Metropolitan Expressway Bridges ．
Nagoya Expressway Public Corporation (2003) ：Standards for Designing Steel Structure ．
Japan Society of Civil Engineers (2005) ：Guidelines for Designing against Buckling, Second Revision (Version2005) ．

211

Chapter 13 Plate Structures
13.1 General(1) This chapter applies to the design of plate structures. Plate elements and stiﬀened plateelements should be designed according to Chapters 6 and 10. A structure that can beconsidered a frame structure shall be designed according to Chapter 12.
(2) The structural analysis of special structures to which this chapter does not apply shall be
carried out under rational loading and support conditions.
(3) Structural details and both of loading and support conditions for structural analysis should
be followed design engineer.

【 Commentary 】

Most steel structures consist of plate elements. This chapter is applicable to steel structures forwhich buckling behavior is a signiﬁcant determinant of performance.
(1) (1) The structural characteristics of plate structures, as covered in this chapter, can be seen as
aggregates of ﬂat plate elements with clear static performance, such as steel girders, steel deckplates, steel piers, and so on. Therefore, this chapter is applicable to the following structuresconsisting of plate elements:- steel deck plate,- steel girder subjected to the bending moment,- beam-to-column section of rigid frame structure,- sections under concentrated loading, such as diaphragms or panel points of truss members, andso on.
The design of plate elements under compression, however, should follow the prescriptions
given in section 6.3.1. In cases where the local deformation of the elements is small and thecharacteristics of structure as a whole can be understood as those of a rigid frame member, thedesign of the structure is outside the scope of this chapter and should follow section 10.3.1.
These provisions may be applied correspondingly to members such as curved plate elements,
including the web plate of a curved girder or a corrugated steel plate, by replacing the curved
plate element with an equivalent element. Structural analysis for structural design of the plate
structure should be carried out with a suitable numerical model that simulates the static role ofeach element.
A steel deck plate, which is an example of a plate structure subjected to out-of-plane loading,the distributed load acts directly on the deck plate, while rib plates work with nearby parts of thedeck plate to transmit the forces to the steel girder or beam. In this situation, the componentsof stress for the steel deck plate can be estimated using plate bending theory while those for the
rib plates can be estimated using beam theory with eﬀective width.
(2) When structural analysis of a plate structure is carried out using plate theory, a rational approach should be applied with attention paid both to loading and support conditions. Typicalconsiderations are stress in the plate element, local stress concentrations, and elastic buckling
stress. Because of the simple shape of a plate element these can be obtained from the chart where
both the displacement and force boundary conditions are clear. However, in other cases where
the stress of a non-standard plate structure is estimated by a numerical analysis method such as

212Standard Specifications of steel and composite structures[Design]

the ﬁnite element method, the ﬁnite elements should be set up using a mesh arrangement that
does not result in reduced precision. Furthermore, the following requirements must be met:
1) The loading system to which a plate element is subjected can be divided into the direct loadon the plate and the transmitted load that takes the form of stress at the boundary of theplate. It is necessary to carry out numerical analysis using a structural system that includes
structural members with clear loading conditions or, if the load factor and distributionof loading are not clear, that sets the most disadvantageous loading conditions for eachelement.
2) Where a partial structural model is extracted from the whole structure, it is necessary
to apply reasonable support conditions. Using spring supports is recommended as a way
to model imperfect boundary supports. However, if the spring constant is uncertain, themost disadvantageous boundary condition should be set by the spring constant in numericalanalysis.
3) Given that the responsible engineer has the authority to ﬁnd that global load capacity is notinﬂuenced by local stress concentrations nor by local buckling of each element, this decision
could compromise the safety level of the whole structure. Careful attention is necessary
to the initial deformation and residual stress because they may reduce the strength of theplate structure.

13.2 Eﬀective Width
The stress and the ﬂexural stiﬀness of girders and beams subjected to the bending moment shallbe calculated with considering the inﬂuence of the shear lag by using eﬀective width.
【 Commentary 】

The longitudinal stress acting on the ﬂange plate of a ribbed steel girder or a steel deck plate has
an uneven distribution in the transverse direction if a bending moment is acting the girder or deck.
This phenomenon is known as shear lag. Complex calculations of displacement and girder stress are
required to model shear lag. Therefore, eﬀective width and constant eﬀective stress can be deﬁned
corresponding to uneven longitudinal stress, and ﬂexural resistance and maximum stress should be
estimated by using the above eﬀective width and the eﬀective stress.
Japan Speciﬁcations for Highway Bridges (II Steel Bridges) [Japan Road Association, 2002a] regulate the eﬀective width in section 8.4.4 and section 10.3.5, while Design Standard for Railway Structures(Composite Steel Structures) [General Railway Technology Institute, 2000] follows the these speciﬁcations.

13.3 Steel Girder Web
The post-buckling strength can be expected in the steel girder web which is subjected to both ofin-plane bending and shear loadings. The inﬂuence of welding distortion, stress in the manufacture,transportation and construction should be considered in the design of the steel girder web.
【 Commentary 】

Refer to [Japan Road Association, 2002a and General Railway Technology Institute, 2000] forstiﬀening of the web plates of a steel girder.
One solution for reducing the cost of public works is to shift the general concept of construction

Chapter 13 Plate Structures

213

work from minimum process to minimum weight. This can lead to greater web thickness as the numberof horizontal and vertical stiﬀeners is reduced. The aspect ratio is limited to less than 1.5 in [Japan
Road Association, 2002a], but experimental results have shown that the aspect ratio can be extended
up to 3.0 [Ogaki, 1998][Nara, 1997]. Japan Highway Corporation has adopted a design code that allows
reduction in the number of vertical stiﬀeners for the web plate of a continuous composite 2-main girder
bridge with a pre-stressed concrete slab. Over 30 bridges have been constructed according to this codein the past 10 years. However, the code requires that the following conditions should be satisﬁed:• shear stress can be evaluated small and positive bending moment are aﬀected,• stress gradient of bottom ﬂange can be calculate less than -1.2, and so on.

13.4 Plate Structure Subjected to Out-Plane Loadingor Combined Out-Plane and In-Plane Loadings(1) In case of stiﬀening of steel plate subjected to out-plane loading, the arrangement and thestiﬀness of stiﬀeners should be deﬁned as both the deﬂection and the stress not to exceed
the limit value, and veriﬁed the safety for load performance of the stiﬀeners themselves.
(2) In case of stiﬀening of steel plate subjected to combine out-plane and in-plane loadings, thesafety for load performance of the stiﬀened plate shall be veriﬁed against each loading andboth loadings.

【 Commentary 】

Where a steel plate subjected to out-of-plane loading is to be stiﬀened, it is common to determine
the spacing, location, and stiﬀness of the stiﬀeners so as to ensure the safety of the plate element.
Furthermore, the safety of the stiﬀeners should be veriﬁed, since they may be aﬀected by bending
moment or shear force from the steel plate.
The limit state of the steel plate should be veriﬁed in consideration of both stresses that is related
to plate bending and that is related girder behavior with eﬀective width and their stiﬀener. However,
evaluation of plate bending stress should be entrusted to the responsible engineer.

13.5 Other Plate Structures
The rectangle plate structure with uniform shape and thickness should be designed by chapter
6. The plate structures other than the above-mentioned shall be designed with paying many
attentions to their mechanical characteristics.
【 Commentary 】

Corrugated steel plates and longitudinally proﬁled steel plates (LP plates) are examples of rectangular plate element with varying shape or thickness. Corrugated steel plate is used to form the web
plate of pre-stressed concrete bridges in expectation that its geometry will have an eﬀect on improving
shear buckling resistance. A simple estimating method for the load capacity of the corrugated steel
web of a steel-concrete composite girder is proposed in [Taniguchi et al., 2003 and Kato et al., 2002].
A method of estimating the buckling strength of LP plate, which follows the method of evaluating
the buckling strength of a plate of uniform thickness by taking into account the equivalent thickness,is proposed in [Murakami et al., 1997 and Hotta et al., 1997].

214Standard Specifications of steel and composite structures[Design]

13.6 Load Concentrate Point
The load concentrate point, such as the supports, shall be designed with verifying the safety
against concentrate loading.
【 Commentary 】

The safety of points of load concentration, such as supports and attachments between a girder andribs or braces, should be ensured by means of vertical stiﬀeners, diaphragms, or similar. In the designof load concentration points, refer to the following design codes: [Japan Road Association, 2002a,
Japanese Society of Civil Engineers, 1994, and Metropolitan Highway Corporation, 2003].
Details of connections between superstructure and isolating supports should be designed such thatthe reaction force due to the dead load and the live load is transmitted smoothly to the bearing support.
Furthermore, an isolating support should able to transmit the inertial force of the superstructure to
the bearing support during earthquakes and should be designed such that no local deformation occurs.
An isolating support consists of the girder web, vertical stiﬀeners and diaphragms on the support itself,
ribs, and other components. The design of the vertical stiﬀeners and diaphragms for the support iscarried out as for a steel bearing support. Ribs should be designed such that the bearing stress is
distributed equally, while the stress due to rotational displacement of the superstructure should also
be distributed uniformly. Vertical stiﬀeners on the support should be extended until the edge of arubber bearing to ensure that stress is properly transmitted because the plane geometry of a rubber
bearing is larger than that of a steel bearing.

13.7 Beam-to-Column Connection
At the beam-to-column connection, the stress between the beam members and the column
members shall be smoothly transmitted. In addition, the beam-to-column connection shall be
designed with paying many attentions to the stress concentration in local area.
【 Commentary 】

For the design of a beam-to-column connection without a haunch or with a linear or circular
haunch, refer to [Japan Highway Corporation, 1998, Metropolitan Highway corporation, 2003, andNagoya Highway Corporation, 2003]. On the other hand, beam-to-column connections with othergeometries can be designed by ﬁnite element analysis or following the three design codes referenced.
In recent years, fatigue failures in the beam-to-column connections of steel rigid frame piers havebeen reported [Miki et al., 2003]. In order to avoid fatigue failure, suﬃcient attention must be paid to
welding in the design, manufacture, and construction of beam-to-column connections. [Metropolitan
Highway Corporation, 2003] recommends beam-to-column connections with ﬁllets.

13.8 Panel Connection
Panel connection should be a simple structure as much as possible to smoothly transmit membrane forces each other. In addition, structural details of panel connection should be considered
to be easy connect of each member, to enable easy maintenance work, such as inspection, drain,cleaning and so on.

Chapter 13 Plate Structures

215【 Commentary 】

For the panel connections of a truss structure, provisions for the thickness of the gusset plate are
given in [Japan Road Association, 2002a, Institute of Railway Technology, 2000, and Japan Societyof Civil Engineers, 1976]. Where the panel connection is particularly aﬀected by high loading or
secondary stress, refer to [Japan Society of Civil Engineers, 1976].
When connecting a suspension member or the supporting column of an arch structure with astiﬀened girder or arch rib, it is must be ensured that no defects arise as a result of stress concentrations
and secondary stress in the panel connection. [Japan Bridge Association, 2002] gives some information
about the structural details of such panel connections. Where a tubular member is used for theconnection, refer to section 10.5.

13.9 Cross Beam, Cross Frame, Lateral Bracing and Diaphragms
13.9.1 General(1) Structural details of steel girder should be enable to maintain the shape and the stiﬀness ofthe structure, to transmit lateral loading to the support.
(2) Details of load concentration point of steel girder and truss structure should be enable tomaintain the shape and transmit concentration load.
(3) Geometrical properties of cross-frame and lateral bracing should be considered both of thestructural rigidity and the construction.
(4) All the followings are satisﬁed, slenderness parameter of the member can be applied thecriterion in chapter 10,– bridge structure is considered as a plane structure that pays attention to main girder
or main structure,– cross-frame or lateral bracing without performing as a principal member,– cross-frame or lateral bracing is installed as a truss member.
【 Commentary 】(1) Cross-beams, cross frames, lateral braces, and diaphragms are member that help maintain sectional form, ensure stiﬀness, transmit lateral loadings smoothly to the supports, and help satisfy
the spatial functions of a structure. This article prescribes that such members should, in principle, be ﬁtted to steel girders, such as in [Japan Road Association, 2002a and Institute of Railway
Technology, 2000].
In the case of a bridge with two narrow I-shaped girders, it is necessary to pay careful attention
to global lateral buckling of the whole structure when the number of lateral braces is reduced.
[Japan Road Association, 2002a] prescribes the following requirements with regard to this typeof failure:1) The safety against lateral buckling of a two main girder bridge should be veriﬁed in the casethat the moment of inertia with respect to the horizontal axis is less than that with respect
to the vertical axis and the ratio of span to web interval exceeds 18.0.
2) 2) The torsional stiﬀness of a curved girder should be increased by way of installing lateralbracing.
In recent years, it has become possible to reduce the number of lateral braces, cross beams,
and cross frames or simplify them for the purpose of structural simpliﬁcation. When this isdone, the structural system must complement the function of the lateral braces and crossframes in order to ensure resistance to lateral loading of the steel girder and the stability of
the whole structure.

216

Standard Specifications of steel and composite structures[Design](2) Where eccentric loading aﬀects a box-girder or where wheel loading directly aﬀects the ﬂange
plate, [Railway Technology Research Institute, 2000] requires that diaphragms have suﬃcient
stiﬀness against shear buckling and prescribes detailing in accordance with [Japan Road Association, 2002a].
(3) Since the stress aﬀecting cross frames and lateral braces is small, their cross-section is dominatedby the slenderness ratio. However, the minimum size of L-angles is regulated in principal to
avoid the installation of narrow members as cross frames and lateral braces from the viewpointof stability.

13.9.2 Cross beam
In case that the slab is supported with several main girders, the cross beam on support or the
cross beam for load distribution should be installed between each main girder.
【 Commentary 】[Japan Road Association, 2002a] recommends that cross beams for load distribution should beinstalled at intervals that do not exceed 20 m so as not to violate the assumptions made in the designof the concrete slab if the span of each girder exceeds 10 m. These cross beams for load distribution
should have suﬃcient stiﬀness to overcome the inﬂuence of relative deﬂection between each girder andthe concrete slab.
Filled cross beams are recommended for curved girders. Connections between the main girder andthe cross beams should be designed in consideration of the load transmission mechanism.

13.9.3 Cross frame(1) At the support of deck bridge, the end cross-frame should be installed between each main
girder or each main structure.
(2) The cross-frame which takes charge of load distribution should be designed as the principal
member.
(3) The cross-frame of the skew bridge should be placed with paying attention to the analyticalprocedure, production and construction process.
(4) All the followings are satisﬁed, cross-frame can be reduced,– structural rigidity is ensured as whole structure such as reduced main girder bridge,– responsibility design engineer verify the structural safety.
【 Commentary 】

Since reaction forces arise if a member is damaged or if there is uncertainty about a member, cross
beams should be installed between each girder of an upper deck bridge.

13.9.4 Lateral bracing(1) Structural details of steel girder should be enable to transmit lateral loading to the support.
(2) All the followings are satisﬁed, upper lateral bracing can be reduced,– bridge type is the deck bridge,– the orthotropic deck or concrete slab is connected with main girder,– horizontal motion of main girder is restrained.

【 Commentary 】

Chapter 13 Plate Structures

217(1) In order to ensure the stiﬀness of the main girder, [Japan Road Association, 2002a] requires thatlateral bracing is installed at the top and bottom of the main girder.
(2) Lateral bracing can be omitted in a case where the ﬂoor system and the main girder are connected
tightly to each other with a concrete slab or steel deck plate. However, lateral bracing may also
help prevent deformation of the structure during construction so it may be better not omit thelateral bracing depending on the erection method. [Japan Road Association, 2002a] allows thebottom lateral bracing to be omitted as long as the span is less than 25mm and strong crossframing is installed. Omitting the lateral bracing in a curved girder may lead to a decrease in
the torsion resistance of the whole structure, so [Japan Road Association, 2002a] prescribes thatlateral girders must be present in the case of a curved girder.

13.9.5 Diaphragms(1) Diaphragm should be placed as followings in standard,– an angle of skew direction in the supporting part of the skew girder bridge,– a right angle to main girder in the intermediate part of the skew girder bridge,– a normal direction to main girder in the curved girder bridge.
(2) An opening, or a manhole, should be installed in the diaphragm if necessary.
【 Commentary 】(1) Generally, a diaphragm should be installed at a right angle to the main girder, except in the caseof a skew bridge; this increases the stiﬀness of the diaphragm itself and simpliﬁes manufacture.
A few examples of provisions relating to diaphragm spacing are given below:[Metropolitan Highway Corporation, 2003]: intervals of about 6m are recommended,[Japan Highway Corporation, 2000]: interval not to exceed 6m,[Nagoya Highway Corporation, 2003]: spandrel-ﬁlled diaphragms can be installed at intervals oless than 6m; sub-diaphragms are required if the interval is over 6m.
(2) [Japan Road Association, 1980] proposed characteristic values of stiﬀness parameter, K, according
to the shape of the opening and the opening ratio, ρ, as follows:ρ < 0.4: ﬁlled spandrel type,ρ > 0.8: rigid frame type,other : cross frame type.
References in Chapter 13
JSCE (1976) ：Research Report on the Honshu-Shikoku Connecting Bridge Superstructure Steel.
Japan Road Association (1980) ：Manual on Steel Bridge Design
Japan Society of Civil Engineers (1994) ：Ultimate Strength and Design of Steel Structures, Steel Structure
Series 6 ．
Nara Takashi, Ogura Tsutomu (1995) ：Shear strength and vertical stiﬀener of the steel girder web plate panel,
Japanese Society of Steel Construction, Structural Steel Collection Annual Report Volume 3 dissertation.
Tada Hiroyuki (1996) ：Design and construction of bridge deck pavement.
Japan Society of Civil Engineers (1997) ：Design Code for Steel Structures, PART A; Structures in General.
Nara Takashi, Ogura Tsutomu (1997) ：Evaluation of ultimate shear strength of web plate panel considering
the vertical stiﬀener, J. Steel Constr. Eng., JSSC, Vol.5.
Hotta Takashi, Nishimura Nobuo, Murakami Shigeyuki, Taki Hideaki (1997) ：Using the design method TEPAPURETO I digit local buckling of the section, the paper’s annual steel structure Album Report, Vol.5,
pp.239-246.
Murakami Shigeyuki, Nishimura Nobuo, T. Horita (1997) ：TEPAPURETO compressive strength of the prominent freedom, Journal of Structural Engineering, Vol.43A, pp.107-116.

218

Standard Specifications of steel and composite structures[Design]

Japan Highway Public Corporation (1998) ：Design Guide Vol.2.
Kazuo Ogaki, Hee Kawaguti, Isoe Akira, Takahashi Akikazu, Kawashiri Katsutoshi, Nagai Masatugudashi(1998) ：Two real synthesis for design of stiﬀened steel main girder bridge main girder Research experience,
Journal of Structural Engineering, Vol.44A, pp.1229-1239.
Railway Technical Research Institute(2000) ：Design Standards for Railway Structures and Commentary, Steeland Composite structures ．
JSCE (2002) ：Report of international standards for structural steel research and analysis.
Japan Road Association (2002a) ：Speciﬁcations for Highway Bridges and Commentary, II Steel Highway
Bridges Volume.
Japan Road Association (2002b) ：Fatigue Design Guideline for Steel Highway Bridges ．
Japan Highway Public Corporation (Japan) Expressway Technology Center) (2002) ：PC ﬂoor slab two continuous composite steel beam bridge design and construction documentation.
Katou Hisato, Takashi Kawabata Atsushi, Nishimura Nobuo (2002) ：Practical use of force and displacementof the bridge cross-section steel-concrete composite structure with a corrugated steel web Calculus,
Journal of the Japan Society of Civil Engineers, No.703/I-59, pp.293-300.
Metropolitan Expressway Public Corporation (2003) ：Design Guide for Highway Bridge Structures Capital.
Nagoya Expressway Public Corporation (2003) ：Design Guide for Steel Structures.
Yoda Teruhiko Tanikuti Nozomi (2003) ：Study of simple bending analysis of composite girder with corrugatedsteel web, Journal of the Japan Society of Civil Engineers, No.577/I-41, pp.107-120.
Miki Tizu, Akira Hiroshi Hirabayashi, Tokita Hideo Hiroshi Konishi Taku, Yaginuma Toshiyasu (2003) ： Fatigue cleavage mode of the plate pair conﬁguration and angle of the steel pier, construction of Journalof the Association, No.745/I-65, pp.105-119.
DASt-Richtlinie 012 (1978) ：Deutscher Ausschuss for Stahlbau.
AASHTO (2003) ：AASHTO LRFD Bridge Design Speciﬁcations- S.I. Units 2003 Interim Revisions.
CEN (2003a) ：prEN 1993-1-1 : Eurocode 3 : Design of Steel Structures, Part 1-1 : General Rules and Rules
for Buildings, Stage 49 draft.
CEN (2003b) ：prEN 1993-2 : Eurocode 3 : Design of Steel Structures, Part 2 : Steel Bridges, Stage 34 draft.
CEN (2003c) ：prEN 1993-1-5 : Eurocode 3 : Design of Steel Structures, Part 1.5 : Plated Structural Elements,
Stage 34 draft.

219

Chapter 14 Slab Design
14.1 General
14.1.1 Structural scopeThis chapter applies mainly to designed slabs under out-of-plane actions.
【 Commentary 】

The slab of a road bridge is often subjected to out-of-plane loading through the pavement. Where
this is the case, the eﬀect of pavement rigidity on the out-of-plane rigidity of the slab should bedisregarded because the physical properties of the pavement are signiﬁcantly aﬀected by temperature.
It is generally accepted that the pavement has the eﬀect of distributing this loading over the thicknessof the slab. Further, the entry of water into a concrete slab may cause the strength of the slab todecrease under cyclic loading while steel members may corrode badly. For this reason, the surface ofthe slab should be protected with a waterproof layer.

14.1.2 Design action
The design actions as stipulated in Chapter 2 shall be considered in the design of a slab to copewith variable actions such as a live load.
【 Commentary 】

A slab is a member that directly supports the load and is subjected to variable actions, including live
and impact loads. The eﬀects of these variable actions should be fully taken into account in determining
the actions on the slab used in design. Road and railway bridges are designed in accordance with thespeciﬁcations [Japan Road Association, 2002a; Railway Technical Research Institute, 2000]. If actualloads diﬀerent from design actions are expected, the eﬀects of these actual loads need to be taken
into account. Although the available reference data on variable actions acting on slabs is limited, thedistribution of axle loads can be estimated from the assumed traﬃc volume and the ratio of large
vehicles by consulting the literature (such as Technical Note No. 2700 of the Public Works ResearchInstitute).

14.1.3 Analytical procedure(1) The analytical model shall be developed through the choice of an appropriate modeling range
under appropriate boundary conditions.
(2) In principle, the slab part shall be extracted as a board structure in the analysis. Dependingon the purpose of the veriﬁcation, the slab shall be modeled as having a large inﬂuence on
the stress state at the veriﬁcation point.
(3) In modeling each structural member, an appropriate element shall be chosen in considerationof its structural characteristics.
(4) The value of each material physical property shall be made an appropriate value reﬂecting
its behavior.
(5) The evaluation of the analytical results shall be based on the modeling conditions as appropriate.

220Standard Specifications for Steel and Composite Structures [Design]【 Commentary 】(1) Although it is desirable to model the entire structure, it may be modeled in part as long as
this has no eﬀect on the stress state at a veriﬁcation point. Taking the unidirectional slab of astraight steel bridge as an example, the full width of the slab and about twice the width of theslab need, as a rule, to be modeled in the transverse and longitudinal directions, respectively.
For slabs other than unidirectional ones as well as the slabs of horizontally curved bridges andthose with a signiﬁcant longitudinal gradient, the extent of the model needs to be studied.
As regards the support conditions of a slab supported on steel I girders, the assumption can bemade that the slab is simply supported at the location of the girder webs. For a slab supported
on a box girder, the support conditions at the top face of the upper ﬂange of the box girdershould be modeled appropriately.
(2) When using FEM analysis in design, the slab is essentially regarded as a plate structure anddesign member forces and deﬂections are calculated according to the rigidity and anisotropyof the slab, its span, the layout of girders, the skew angle, and other factors. For a concreteslab, only the concrete portion is modeled in general, while any steel plates, rebars, prestressing
tendons, studs, and other components should be modeled as appropriate in consideration of
their eﬀects on the slab at the point of veriﬁcation [Sakamoto et al., 2002; Honma et al., 2002].
Further, in modeling a pavement whose toughness falls in high-temperature environments, suchas an asphalt pavement, only the slab’s load distribution action is taken into account, while theﬂexural rigidity of the slab should be left out of consideration.
When the purpose of analysis is not to calculate design member forces or deﬂections but tocalculate local stresses, to check the load bearing capacity, or to understand the vibration characteristics, cracking properties of concrete, thermal stresses of concrete, and prestressing forces
introduced in a prestressed concrete (PC) slab, the recommendation is to model the structuralmembers in addition to the slab as determined necessary after consulting past cases [Miki et al.,2005; Nagayama et al., 1998; Kawabata et al., 2004a; Japan Bridge Association, 2004; Yasumatsu
et al., 2003].
(3) The use of plate elements to check the overall behavior of a slab and calculate design member
forces and deﬂections is an eﬃcient method. However, when the anisotropy of the slab is verylarge or the degree of deterioration of a reinforced concrete (RC) slab is taken into account, it isrecommended to use elements capable of taking into account the anisotropy [Matsui et al., 1995;
Sato et al., 1998; Honma et al., 2002]. When taking into account the orthotropy of a steel slab,
analysis using the ﬁnite strip method, which takes into consideration a dynamic model composedof strips and lateral ribs, is also eﬀective [Tada, 1971]. In determining the distribution of stresses
in the direction of thickness or calculating the local stresses in members inside the slab, it isrecommended to use solid, plate, beam, and other elements in combination for modeling.
When solid elements are used for modeling, it is necessary to consider how the mesh is set
in the direction of slab thickness or plate thickness so as to avoid shear locking. Further, inconnecting elements having diﬀerent degrees of freedom, it is necessary to deal appropriately
with the degrees of freedom. When using higher-order elements, the eﬀects of the characteristicsof the elements on the results of the analysis need to be understood. And when taking into
consideration steel girders in the modeling of the slab, the eccentricity caused by the thicknessof the slab should be factored in.
(4) In calculating the design member forces and deﬂections for road bridges, steel members aredealt with as linear elastic bodies using the physical properties speciﬁed in the Speciﬁcations for
Highway Bridges (the Speciﬁcations) [Japan Road Association, 2002] or obtained as test results.
Concrete members are assumed to be linear elastic bodies, with cracks neglected when the elastic
deﬂections of girders under loading are not more than about L/500 (L/300 for cantilevers), usingChapter 14 Slab Design

221

the physical properties speciﬁed in the Speciﬁcations. In addition, when checking load-bearing
capacity, the nonlinearity and cracking of concrete need to be taken into consideration, but
appropriate modeling of these characteristics is a subject for future study. In carrying out
the thermal stress analysis of slab concrete, the material nonlinearity speciﬁed in the Standard
Speciﬁcations for Concrete Structures [JSCE, 2002a] is taken into consideration [Japan Bridge
Association, 2004.] For steel and other non-concrete materials, the physical properties of thematerials are clariﬁed and the nonlinearity of the materials is taken into account as needed.
(5) If the structure is modeled appropriately, the structural analysis factor, γ=1.0, for analysis results
can be taken as 1.0, except for the case where assumptions in modeling are unclear or the analysis
is nonlinear.
In evaluating the results of analysis, it should be borne in mind that the results may varydepending on the type, shape, and size of the ﬁnite elements used. The preferred shape of ﬁnite
elements in the vicinity of a point of interest is a square or cube. As a guide, ﬁnite elements
should be about 50 mm in size when calculating design member forces; element sizing needs tobe studied separately when calculating local stresses. There are some cases where excessively
large values are derived by analysis at interSections of plate elements, at points where nodesof elements with large diﬀerent rigidities are shared, in elements directly below loads, and inelements in restrained sections. In these cases, analysis values of adjacent ﬁnite elements areused for evaluation. Further, adequate attention needs to be paid to the relationship between
the assumed element coordinate system and the global coordinate system.

14.2 Safety
14.2.1 Safety of slab
(1) The slab shall be able to carry the load safely and directly, transmitting it to the supports.
(2) The slab shall be designed so as to secure safety with respect to the two performance items
that follow.

1 Safety in carrying the load directly
2 Safety as the main structural member【 Commentary 】(1) A slab is subject to cyclic loading in addition to the dead load. As one of the ﬂoor framing
members, the slab must transmit these loads safely to the girders as well as supporting them.
Particularly when a slab is subjected to large cyclic loads, it is necessary to conﬁrm that it issuﬃciently safe even toward the end of its design service life.
(2) The safety of the slab, as the plate member that directly supports the loads, needs to be ensured
for its particular conditions of shape and support. Adequate safety must be ensured at the
supports of the slab as well as for the slab in general. Further, the safety of the slab should
be conﬁrmed as needed during its transportation and/or construction until full completion. If
the slab and girders are integrated into the main structural members or if the slab is subjectedto large loads, such as earthquake and wind loading, in the in-plane direction, adequate safety
needs to be ensured under these conditions also.

14.2.2 Out-of-plane shear(1) Under out-of-plane shear, the slab shall be completely safe against punching shear at theloading point.

222

Standard Specifications for Steel and Composite Structures [Design](2) Under out-of-plane shear, the slab shall be safe against shear at the supports.
(3) In the case of change of stress transmission mechanism, the safety of slab shall be considered
under the inﬂuence of cyclic loading.
【 Commentary 】(1) The slab that bears the load directly is subjected to an out-of-plane punching shear force thatacts directly below the load point. The safety of the slab under the action of this force is veriﬁed
based on the assumption that the force is distributed at an angle of 45 °from the point at which
the load acts. In this case, the eﬀect of any eccentricity or unevenness of the loading near theloads point, if any, needs to be taken into consideration. The Speciﬁcations prescribe a minimum
slab thickness to assure adequate safety under these forces. The safety of concrete members canbe veriﬁed in accordance with the Standard Speciﬁcations for Concrete Structures [JSCE, 2002a.](2) A slab supporting out-of-plane loads is subjected to a large shear force in the vicinity of its
supports. It should be veriﬁed that the slab is safe at the load point where the maximum shear
force is induced. The magnitude of the shear force used for the veriﬁcation of safety at the
supports should be determined, as a general rule, through analysis or tests. The Speciﬁcations[Japan Road Association, 2002b] assure the safety of the slab at the supports of the slab under
the action of this shear force by prescribing a minimum thickness for the slab and installing
haunches at the supports.
(3) There are cases where an irreversible change in the force transmission mechanism results fromtensile stresses, such as when cracking occurs, in a concrete slab. In a case where the slab is
subject to cyclic loading, its safety needs to be considered in consideration of the eﬀect of suchchanges in the force transmission mechanism. In practical terms, anisotropy due to cracking
should be taken into account in calculating member forces and concrete in the tensile stress area
should be neglected in conducting veriﬁcations.

14.2.3 Out-of-plane bending(1) Under out-of-plane bending, the slab shall be completely safe against the appropriate calculated out-of-plane bending.
(2) In the case of according to proposed out-of-plane bending equation, it shall be necessary tonote the coverage, the analytical condition, and accuracy and to carry out an appropriate
correction if necessary.

【 Commentary 】(1) A slab that supports out-of-plane loads needs have adequate safety against the out-of-planebending moment. The out-of-plane bending moment is determined from analysis or tests byassuming the most disadvantageous loading condition at the point of interest and taking into
account uneven settlement at the slab supports, as well as the eﬀects of support conditions thataﬀect the direction in which the out-of-plane bending moment is induced.
(2) The Speciﬁcations [Japan Road Association, 2002b] prescribe an equation for the out-of-planebending moment induced by the live load. This equation should be used with a clear understanding of the assumed loading conditions, the scope of application including the span of theslab, the support conditions of the slab, the presence/absence of anisotropy, the accuracy of theequation, and the safety factor in the equation.

Chapter 14 Slab Design223

14.2.4 In-plane forces(1) Under in-plane forces, the slab shall be safe with respect to functioning as part of the main
structure. It shall also be safe against earthquake, wind, and temperature changes.
(2) When under in-plane forces caused by deformation of the slab supporting girder, the safetyof the slab shall be considered of its inﬂuence.
【 Commentary 】(1) In a composite structure consisting of a slab and girders and also in the case of a steel slab, there
are additional forces as well as the out-of-plane load acting on the member because of its role aspart of the main structure. The safety of the slab should be conﬁrmed under these additional
member forces as well as under the member forces arising because of its role as the ﬂoor framingthat directly supports the load as well as combinations of the two. In combining the actions of
the main structure and the ﬂoor framing, the safety factor can be set by taking into account of
the circumstances under which combined member forces are induced. The Speciﬁcations evaluate
the safety of the slab under combined member forces by increasing the allowable stress by 40%.
(2) If the girder supporting the slab undergoes signiﬁcant deformation, in-plane forces in addition
to the in-plane bending moment may act on the slab. In this case, the slab needs to be designed
to ensure its safety under these in-plane forces.

14.2.5 Safety verification of slab
The safety of the slab shall be veriﬁed in consideration of pre-determined factors. At minimum,
the veriﬁcation of slab safety should be evaluated as follows.
(1) General Part
(2) Overhanging part (Support point and Base of handrail)(3) Girder end(4) Opening【 Commentary 】

In order to verify safety, a number of factors need to be determined in an appropriate manner. In
particular, if there is concern that the slab thickness may be insuﬃcient, a large safety factor needs
to be adopted, because any construction errors, including errors in slab thickness, can have a large
eﬀect slab strength. The bending moment equation speciﬁed in the Speciﬁcations gives results with a10∼20% safety margin as compared with theoretical values in consideration of the eﬀects of structural
analysis and construction errors.
In addition to a general veriﬁcation, slab safety should be veriﬁed in the areas speciﬁed in thissection. Further, aside from the areas mentioned above, other areas requiring consideration are where
the cross section changes, at construction joints, at anchorages for prestressing tendons, and at points
where prestressing tendons deﬂect. In these locations, the strength of members and the slab supportconditions change. As structurally weak points, they should be provided with adequate reinforcement.

14.3 Serviceability
14.3.1 Serviceability of slab
The serviceability of the slab shall be veriﬁed using three performance items as follows.
(1) Deformation of slab

224Standard Specifications for Steel and Composite Structures [Design]

From the point of view of users, the slab shall perform without deformation so as to provide
safety and comfort for pedestrians and traﬃc.
(2) Vibration of slab
The slab shall perform without improper vibration under cyclic loading.
(3) Drainage of slab
The slab shall drain quickly, without water pooling on the slab surface.
【 Commentary 】(1) The slab is used by vehicles and pedestrians crossing the bridge. To ensure safe and comfortablecrossing of the bridge, the roadway surface needs to be maintained as a continuous and evenpavement.
It is important, for drivers and pedestrians, that the road surface is free of irregularities anddoes not pool water. Irregularities and water pooling on a paved road surface are phenomenathat arise because of the condition of the pavement or the waterproof layer. Compaction during
construction and deformation of the slab under the pavement while the structure is in service
have a great eﬀect on the performance of the pavement and the waterproof layer. Accordingly,
the slab needs should be rigid enough that concrete does not crack and impair constructability
during paving work or cause failure of the waterproof layer.
(2) The slab vibrates and causes noise as vehicles cross the bridge. Occasional noise does not pose
any major problem but noise can sometimes have a major eﬀect on residents near a bridge
depending on its level. In particular, the slab needs to be rigid enough that low-frequency noise
is not generated.
(3) One of the factors that aﬀects the serviceability of a bridge roadway is the drainage performance ofthe road surface. Rainwater falling on the road surface ﬂows down the longitudinal and transverse
slopes of the roadway and into storm drains. In recent years, high-functionality pavements witha porous surface layer have been used to reduce vehicle noise and rapidly drain water from thesurface. When this type of surface is used, the base course comprises an impermeable bed that is
supported directly on the slab. The performance of the pavement has a direct eﬀect on drainage
performance and the ﬁnished surface of the slab becomes an important factor. It is necessary tocontrol the surface ﬁnish of the slab and the slab needs enough rigidity that harmful cracks do
not form. Additionally, rainwater ﬂowing into the storm drains need to ﬂow smoothly into thestorm drainage system.
To verify the serviceability of concrete parts of the structure, it is necessary to study cracking
because if cracks develop to widths larger than the allowable size or chloride ion concentrations
at the depth of the steel increase to the critical concentration or higher, steel corrosion will takeplace and reduce the durability of the structure. The consequent degradation in watertightness
and outward appearance impairs the serviceability of the structure. Cracking has the eﬀect ofdegrading the durability of concrete mainly by promoting corrosion of the steel; this is coveredin Section 14.5 ”Corrosion Resistance and Resistance to Material Deterioration.”

14.3.2 Serviceability verification of slab
According to section 7.3 ”Veriﬁcation of Serviceability”, the serviceability of a slab should beveriﬁed using the following performance items.
(1) Deformation of slab
Deﬂection under live load and condition of the slab surface shall be within limits.
(2) Vibration of slab
The slab shall not resonate at the frequency of passing trucks.

225

Chapter 14 Slab Design(3) Drainage of slab
The slab shall drain quickly without water pooling on the slab surface.
【 Commentary 】(1) The concrete slab of a road bridge is considered problem free in use if its deﬂection under live
loading is not more than 1/2000 of the slab span. Further, the slab surface is regarded as being
rigid enough to resist deformation if any cracks are no wider than the limit value set during thedesign phase and if cracking is controlled below the target control value during construction.
(2) The physical measures used to assess vibration characteristics include deﬂection, natural frequency, and acceleration. In the design of the superstructure, a limit value is set on resonancefrequency for footbridges and on deﬂection under live loading for road bridges. The Report on
Research Study of Vibration Phenomena Speciﬁc to Slabs [JSCE, 2004a] presents the relationshipbetween the span and natural frequency of RC and PC slabs for steel road bridges, as shown in
Figs.C14.3.1 and C14.3.2, respectively. The results of this survey of vibration and low-frequency
problems (Table C14.3.1) indicate a high likelihood of low-frequency damage occurring when thenatural frequency of the slab is about 10 Hz.This results from the fact that 10 Hz corresponds
approximately to the frequency of the unsprung weight of large trucks [Kawabata et al., 2004a].

Fig.C14.3.1 Relationship between span and

Fig.C14.3.2 Relationship between span andnatural frequency of a slab (RC slab)

natural frequency of a slab (PC slab)[JSCE, 2004a][JSCE, 2004a]

Table C14.3.1 Results of survey of vibration and low-frequency problems [JSCE, 2004a]
Researchers
Yamada et al.
［ Noises and Vibrations 1978 ］
Shimizu et al.
［ Noises and Vibrations 1982 ］
Yasuo Kajikawa［ Prestressed Concrete 2003 ］
Itsuo Murai［ Noise Control 1982 ］
Uchida et al.
［ Nagano research Institute for Healthand Pollution Report 1979 ］
Ishii et al.
［ Chiba Prefectural Research Institutefor Environmental Pollution Report 1981]
Shozo Yamaga［ Japan Highway Public Corporation
Research Institute Report 1977 ］

Results of survey
The frequency of the unsprung weight of large trucks
is 8∼20Hz.
The dominant frequency of noise emitted from joints
is 10∼50Hz.
The dominant frequency of body sensory vibrations isabout 14.5 Hz.
The dominant frequency of noise emitted from the joints ofelevated bridges is 10∼30Hz.
The peak appears at 12.5Hz.

The peak appears at 12 Hz.

Truss bridges: The peak appears at 10∼14Hz.
Steel girder bridges: The peak appears at 10-18 Hz.

226

Standard Specifications for Steel and Composite Structures [Design](3) The slab of a road bridge is regarded as satisfying the drainage performance requirement if thedrainage system is constructed in accordance with the Road Earthworks: Guidelines for Drainage
Works [Japan Road Association, 1987].

14.4 Fatigue Resistance
14.4.1 Fatigue resistance of slab
(1) The slab fatigue resistance under cyclic loading (live load and wind load) shall be assured
for the whole of the design working life.
(2) The veriﬁcation of slab fatigue resistance shall clarify the failure mechanism and examine
the respective inﬂuence of out-of-plane shear and out-of-plane bending.
(3) The veriﬁcation of slab fatigue resistance shall be based on the appropriate speciﬁcations forfatigue strength.

【 Commentary 】

This section covers slabs of concrete construction, including RC, PC, and steel-concrete composite
slabs.
(1) The fatigue resistance of the slab refers to the resistance of the slab to fatigue failure when cyclicloads (live or others) above a certain level act on it. The most important action that inﬂuences
the performance of a road bridge slab is the wheel loading. Wheel loading acts directly on theslab and the slab is subject to very severe conditions as a result of this repeated action. The
requirements for fatigue resistance are that, under repeated wheel loading, the slab retains thesafety factor set for each limit state during the design phase over the design service life and thatthe slab does not suﬀer damage that results in the safety or serviceability of the slab falling
below the allowable level. There are few cases where fatigue other than that caused by moving
vehicles presents a problem with the slab. However, if large sound absorbing barriers are ﬁtted
to the concrete barrier parapets, cantilevered sections of the slab may be subject to relatively
large action caused by wind loading and this may cause speciﬁc vibrations. In this case, it isnecessary to study the fatigue resistance of the slab under cyclic wind loading, depending on themagnitude of the stresses induced in the slab, as well as under other speciﬁc vibrations during
the design service life of the slab. That is, the resistance of the slab to all cyclic actions, not only
wind loading and vibration, needs to be ensured.
(2) The mechanism of fatigue failure varies with the type of slab, so it is important to clarify themechanism in the fatigue design of the slab. Once the failure mechanism has been clariﬁed, it
is possible to determine the fatigue strength as well as verify the fatigue resistance of the slab
under cyclic loading over the design service life. An RC slab subjected to cyclic loading during
the design service period needs to be resistant to fatigue caused by the ﬂexural stress induced in
the rebars and the slab concrete (ﬂexural fatigue durability), by the shear force induced in the
cross section of the slab (shear fatigue durability), and by the punching shear force induced in
the cross section of the slab (punching shear fatigue durability). For a PC slab, the resistanceof prestressing tendons and anchorages to fatigue, in addition to the fatigue resistance requiredof the RC slab, needs to be ensured. In the case of a steel-concrete composite slab, the fatigue
resistance of steel members, such as bottom steel plates, frame members, and rebars, concrete
members, and the joints between steel and concrete members need to be veriﬁed.
(3) In the evaluation of fatigue strength, it is important to clarify the intensity of loads acting on
the slab and the frequency of loading, and to use an appropriate evaluation method. To set

Chapter 14 Slab Design

227

values for the cyclic action of traﬃc loading, an assumption needs to be made as to the traﬃc
to be carried over the design service life of the slab. To be more precise, the magnitude andcumulative frequency distribution of the wheel loading need to be set. Although it is extremely
diﬃcult to correctly assess the cumulative sum of cyclic action imposed by wheel loading because
vehicular traﬃc patterns vary with the social situation and the development of surrounding roads,
it is necessary to set this cumulative sum by predicting, as accurately as possible, future traﬃcvolumes based on measured traﬃc on in-service roads similar to that carried by the bridge [Bridge
Research Laboratory, Department of Structures and Bridges, Public Works Research Institute,
Ministry of Construction, 1988; Pavement Research Laboratory, Department of Roads, Public
Works Research Institute, Ministry of Construction, 1995; Miki et al., 1985; Mori et al., 1995].
The following methods of evaluation the cumulative sum are proposed: evaluation of fatigue
strength based on the S-N curve determined from the results of a moving wheel load test; amethod based on the relative fatigue strength; and a method based on the equivalent load andfatigue safety factor. Further, in a case where the eﬀects of other cyclic actions such as windloading might be expected, the magnitude and cumulative frequency distribution of such actions
need to be set and appropriately evaluated to determine the cumulative sum of the actions during
the design service life of the slab. Incidentally, concrete slabs are currently regarded as satisfying
the predetermined level of safety if they meets the provisions of the Speciﬁcations because it
is known that their fatigue strength is signiﬁcantly improved as compared with conventional
concrete slabs.
Slab fatigue also includes out-of-plane ﬂexural and shear fatigue and out-of-plane punching
shear fatigue. In the case of ﬂexural fatigue in a steel-concrete composite slab, it is generally
the case that the steel fails in fatigue. In the case of the punching shear fatigue of a composite
slab under live loading, it is the concrete that fails in fatigue, as in the fatigue failure pattern of
RC slabs used for existing multiple girder bridges. To verify the resistance of the slab to fatigue,
appropriate tests and analysis techniques capable of reproducing the failure mechanism of theslab should be used.

14.4.2 Fatigue due to out-of-plane shear(1) The slab shall exhibit durability against out-of-plane punching shear fatigue caused by wheelloading.
(2) The slab shall exhibit durability against out-of-plane shear fatigue around it’s the supports.

【 Commentary 】(1) The slab that directly bears the load is subjected to an out-of-plane punching shear force thatact directly below the load point. The slab may fail in fatigue under these punching shear forces.
As a method of evaluating the resistance of the slab to fatigue under punching shear forces, afatigue test using a wheel-loading test machine is available. This is a method of testing the slab
by driving a steel wheel or a rubber tire simulating the wheel of a vehicle over the slab such thatit exerts the wheel load on the slab. It has been veriﬁed that the fatigue failure of RS slabs usedin actual bridges can be reproduced by this test.
Various investigations have been carried out on punching shear failure after an RC slab has
cracked transversely into multiple beam-like forms, and S-N curves based on the results of a moving wheel load test have been proposed [Matsui, 1987; Matsui, 1991; Yasumatsu et al., 1998].
However, the proposed S-N curves are represented by a single logarithmic function with an extremely gentle gradient (m=1/11 to 4/11). Variations in materials and construction work as wellas variations in the intensity of loading due to diﬀerences in loading patterns are extremely large

228Standard Specifications for Steel and Composite Structures [Design]

as compared with a change in the number of cycles of loading, N, on the time axis. Accordingly,
it is diﬃcult to judge the resistance of the slab to fatigue using the concept of the fatigue safety
factor over the service life as compared with using the design service life.

Fig.C14.4.1 Typical S-N curve (Osaka University) [JSCE, 2004b]

S=P= −0.07166 log N + 0.7292
Ps(C 14.4.1)

To avoid this, a proposition is made to express the assumed loads during the required design
service life in the form of representative load and the number of cycles and deﬁne the safety
factor for the resistance of the concrete slab to fatigue as the ratio of the failure load on the S-N
curve to the representative load [Kawabata et al. 2004b.]

Fig.C14.4.2 Typical evaluation of fatigue durability by safety factor [Kawabata et al. 2004b]


log Nef f Vpcd
1−
14
k
P
ν=
Pmax
P =

where ，Nef f

(C 14.4.2)(C 14.4.3)：equivalent number of cycles that is converted in such a manner that the fatigue

damage from the maximum wheel load, Pmax , becomes equivalentChapter 14 Slab Design

Vpcd
k

229

：design punching shear capacity：= (2a + b)/(a + b)

factor for the surface on which wheel load actsa : width of the surface on which the load acts,b : length of the surface on which the load acts

(2) Attention should also be given to the shear fatigue failure in the vicinity of the supports of theslab on which the reaction of the loads acting on the slab acts, in addition to the parts on which
the wheel loads directly act.

14.4.3 Fatigue due to out-of-plane bending(1) The slab shall exhibit durability against out-of-plane bending.
(2) Slab connection components shall exhibit durability against stress caused by out-of-planebending.

【 Commentary 】(1) The slab subjected to out-of-plane loads should be safe against the fatigue caused by out-of-planebending moment. The most common failure pattern in the case of concrete slabs is punching
shear fatigue. For PC slabs, there has been no report on the fatigue failure of the slabs with
their slab thicknesses increased by the large span of the slabs. It is presumed that the fatigue
failure of rebars or prestressing tendons due to bending rather than the punching shear failure
is dominant [Yasumatsu et al. 1998; Hase et al. 1999; Honma et al. 1999.] The same goes forsteel-concrete composite slabs.
The wheel-loading test that is conducted as a method of conﬁrming the resistance of the slab
to fatigue in some cases exerts a smaller bending moment on the slab than occurs in an actual
bridge, primarily due to the limited size of the specimen (the short span of the slab). The ﬂexural
fatigue durability of the slab should be veriﬁed by an appropriate method, such as a fatigue testin which a load acts at a ﬁxed point on a beam-shaped specimen simulating the cross section in
the longitudinal or transverse direction of the bridge.
(2) Members used to connect the components of a slab include shear connectors, which hold theconcrete to the steel plate in a steel-concrete composite slab, and prestressing tendon anchorages
in a PC slab. Shear connectors are generally of welded construction, so attention should be paid
to the fatigue durability of the welds. To verify the fatigue durability of the steel portion ofa steel-concrete composite slab, two methods are available: static testing or FEM analysis todetermine the range in which stresses are induced in the steel portion and then to verify thefatigue durability of the steel based on standard fatigue strength classes. Because there may becases where the stress at the point of interest is aﬀected by alternating loading as wheels passover, the point at which the load acts and the method of applying the load need to be carefully
studied.

14.4.4 Influence of water(1) A waterproof layer should be used to protect against inﬁltration of water from the slab
surface, which could damage the fatigue resistance of the slab.
(2) If a waterproof -layer is not used, the slab fatigue resistance shall be veriﬁed in considerationof the inﬂuence of water on the slab.
【 Commentary 】

230Standard Specifications for Steel and Composite Structures [Design](1) It is known from water-immersion wheel-loading tests that the fatigue durability of a slab significantly decreases when there is standing water on its top surface. To prevent water penetrating
the road surface and collecting on the top of the slab, a waterproof layer should be installed.
(2) If no waterproof layer is installed, the eﬀect on fatigue resistance of water standing on the slab
surface needs to be taken into account.

14.5 Corrosion Resistance and Resistance to Material Deterioration
The materials used for the slab of a steel or composite structure shall exhibit suﬃcient corrosion
resistance and resistance to material deterioration.
14.5.1 Resistance to steel corrosion
Steel components of the slab shall exhibit corrosion resistance.
(1) steel corrosion(2) corrosion of steel used in the concrete【 Commentary 】

This section speciﬁes, of the durability performance requirements for a slab, the basic performancewith respect to changes in the materials used for the slab over time. The slab should not suﬀer harmfuldegradation or damage, leading to a decline in safety and serviceability, as a result of actions on thecomponents of the slab over the design service life of the slab. Although the slab should be provided
with a waterproof layer, as described in Section 14.4, the slab should be highly resistant to material
corrosion and degradation under the action of carbon dioxide, rainwater, and chemical components
entering from the sides and bottom of the slab even if there is no waterproof layer or it fails to function.
The width of cracks in the concrete has a very great eﬀect on the corrosion resistance of the steel
reinforcement used in the concrete. Where the concrete contains steel, the allowable crack width needs
to be determined by taking into account local environmental conditions, the type of steel used, and theconcrete cover depth. The Standard Speciﬁcations for Concrete Structures [JSCE, 2002b] specify theallowable crack width in relation to steel corrosion according to environmental conditions and the typeof steel. This allowable crack width relates to the minimum restriction on crack width that shouldbe imposed so as to avoid corrosion. In a corrosive environment or a particularly severe corrosive
environment, it is to be noted that crack widths should be controlled to below this allowable crack
width and, at the same time, the requirement for chloride ion concentration at the depth of the steelneeds to be satisﬁed. The allowable crack width in relation to watertightness is determined according
to the required degree of watertightness and the dominant member forces acting on the slab by taking
account of how the structure is to be used and the characteristics of loads acting on the structure.
Cracks caused by the thermal stress arising from the heat of hydration of cement during curing aredetailed in Report on Evaluation and Study of Eﬀectiveness of Expansive Additives for Cast-in-situ
PC Slabs [Japan Bridge Association, 2004]. The allowable crack width in relation to watertightness
as addressed in past research as well as overseas speciﬁcations regarding allowable crack width aredetailed in the Guidelines for Survey, Repair and Reinforcement of Cracks in Concrete 2003 [Japan
Concrete Institute, 2003].
(1) For requirements related to the resistance to corrosion of steel exposed to the outside air, suchas the bottom steel plates of a steel slab or a composite slab, the recommendation is to refer
to Section 8.2.2 Corrosion Resistance, because the requirements are similar to those for the
resistance to corrosion of steel members in general. For veriﬁcation, it is recommended to refer
to Section 8.3.2 Veriﬁcation of Corrosion Resistance.
(2) Major factors causing the corrosion of reinforcing steel in concrete are carbonation and salt dam-Chapter 14 Slab Design

231

age. For requirements related to resistance to steel corrosion due to carbonation of the concrete,
it is recommended to refer to Section 8.2.2 Corrosion Resistance, because the requirements are
similar to those for the resistance the corrosion of concrete members in general. For veriﬁcation,
it is recommended to refer to Section 8.3.2 Veriﬁcation of Corrosion Resistance.
Leading causes of salt damage are salt, carried by sea spray and onshore winds, being depositedon the concrete surface and moving into the concrete, where it corrodes the steel, and anti-freeze
agents such as calcium chloride that are applied to roads in cold climates. For requirements
related to the former, it is recommended to refer to Section 8.2.2 Corrosion Resistance, because
the requirements are considered similar to those for the resistance of concrete members in general.
For veriﬁcation, reference should be made to the approximation formula for calculating chloride
ion concentration in concrete in the section titled ”Concrete Subjected to the Actions of the Sea
Water” of the Japanese Architectural Standard Speciﬁcations [Architectural Institute of Japan,
2003] in addition to Section 8.3.2 Veriﬁcation of Corrosion Resistance.
In the case of the latter, where water containing an anti-freeze agent is applied above the topof the slab, it is considered eﬀective to protect the slab using a waterproof layer. To protect
the slab from salt damage resulting from the use of an anti-freeze agent, requirements for andveriﬁcation of the waterprooﬁng system are applicable and detailed in Report on Evaluation of
Durability of Highly-functional Waterproof System [Highly-Functional Waterproof Committee,
2004].

14.5.2 Resistance to concrete deterioration
Concrete components of the slab shall exhibit suﬃcient resistance to material deterioration.
(1) Damage due to alkali-aggregate reaction(2) Damage due to frost(3) Damage due to Chemical action【 Commentary 】(1) For requirements for the protection of concrete damage due to the alkali-silica reaction, it isrecommended to refer to Section 8.2.3 Resistance of Materials to Degradation, because the requirements are considered similar to those for the protection of concrete members in general. For
veriﬁcation, it is recommended to refer to Section 8.3.3 Veriﬁcation of Resistance of Materials to
Degradation.
(2) For requirements for the protection of concrete from frost damage, it is recommended to refer to
Section 8.2.3 Resistance of Materials to Degradation, because the requirements are consideredsimilar to those for protection of concrete members in general against frost damage. For veriﬁcation, it is recommended to refer to Section 8.3.3 Veriﬁcation of Resistance of Materials to
Degradation.
(3) For requirements for the protection of concrete from damage due to chemical action, it is recommended to refer to Section 8.2.3 Resistance of Materials to Degradation, because the requirements
are considered similar to those for the protection of concrete members in general. For veriﬁcation,
it is recommended to refer to Section 8.3.3 Veriﬁcation of Resistance of Materials to Degradation.

14.6 Slabs of Various Types
A slab shall be appropriately designed and then constructed in the ﬁeld so as to perform as
required with respect to each performance item.

232Standard Specifications for Steel and Composite Structures [Design]【 Commentary 】

The materials used to construct slabs include steel and concrete. For RC slabs, which have along track record, steel slabs, PC, which have recently found wide application, and composite slabs,
structural details are available for various slab types that have been determined from experience andin consideration of constructability. In many cases, similar structures are realized by sticking closely
to these details. This section describes typical structural details of slabs of various types that have along track record of use for road bridges.

14.6.1 Reinforced concrete slab
An RC slab shall be designed such that it satisﬁes each performance item. Performance shallbe considered as satisﬁed through the observing of appropriate structural details.
(1) Slab thickness(2) Connection to main girder(3) Execution precision(4) Reinforcement at girder end【 Commentary 】

RC slabs have found many applications in road bridges. The speciﬁcations for such slabs are prescribed in the Speciﬁcations [Japan Road Association, 2002b]. The Speciﬁcations have been updated
when necessary based on the results of investigations of damage, if found. The contents of the Speciﬁcations are very persuasive even though they are not theoretically based. This section describes typicalstructural details of RC slabs as prescribed in the latest Speciﬁcations.
(1) Thickness of RC slab
The Speciﬁcations deﬁne the thickness of the RC slab. In the general, where the main steel
reinforcement is arranged in the transverse direction, the basic slab thickness, t(mm), is given
as 40L + 110 for two-girder slabs and 30L + 110 for multi-girder slabs (and not less than 160
mm in both cases), where L is the span of the slab (m). In actual design, the slab thickness isincreased by multiplying the basic slab thickness by a factor derived from the volume of largesized vehicle traﬃc (thickness increased by 25% at maximum) and a factor derived from theadditional bending moment caused by diﬀerences in the rigidity of the girders. Speciﬁcations arealso given for cases where the slab has a cantilever section and where the span of the slab is in
the direction of vehicle ﬂow.
The above equations for slab thickness are applicable to slabs of span L up to 4 m; they are
not applicable to slabs beyond this maximum.
(2) Slab to main girder connections
The Speciﬁcations prescribe that the slab should, as a general rule, be provided with reinforced haunches for connection to the support girders. Haunches eﬀectively prevent cracks fromoccurring by reducing tensile stresses induced by the action of the slab in the vicinity of themain girders as well as distributing local stresses induced in the shear connector connecting slab
to girder. The Speciﬁcations prescribe that additional reinforcing bars (haunch bars) should be
provided for haunches that are 80 mm or more in depth.
(3) Assurance of construction accuracy
The Speciﬁcations prescribe that rebars of size D13, D16, D19, or D22 should be used as a
general rule and that, having selected a suitable diameter that is not too large, they should bearranged at an appropriate spacing so as to distribute cracks, control crack width, and minimize
rebar deﬂection and bending during construction. This ensures that errors in the cover depth
and alignment of rebars due to deformation of the bars during construction are a minimum.

Chapter 14 Slab Design

233(4) Reinforcement of the slab at girder ends
At girder ends, the slab loses continuity and is subjected to impulsive loads caused by level
diﬀerences at the expansion joints. These loads induce large bending moments in the directionof the main reinforcement and, consequently, the slab is prone to damage. To avoid this, theSpeciﬁcations prescribe that, at girder ends, the slab should be able to resist these loads byintroducing cross girders or brackets at the girder end points, increasing the slab thickness, orarranging additional rebars.

14.6.2 Pre-stressed concrete slab
A PC slab shall be designed such that it satisﬁes each performance item taking into accountconstruction by pre-casting or post-casting. Performance shall be considered as satisﬁed throughthe observing of appropriate structural details.
(1) Slab thickness(2) Connection to main girder(3) Connection between slabs(4) Reinforcement at girder end【 Commentary 】

The speciﬁcations for PC slabs are prescribed in the Speciﬁcations, as is the case with RC slabs.
For RC slabs, the span direction is aligned with the orientation of the main reinforcement. For PC
slabs, the span direction is in some cases diﬀerent from the direction in which the prestressing forces
are introduced. The Speciﬁcations prescribe the slab thickness in each case. This section deals withtypical structural details in the most common case where the span direction of the slab and the
direction in which the prestressing forces are introduced are perpendicular to the direction in which
vehicles operate.
(1) Minimum thickness of PC slab
The Speciﬁcations prescribe that the minimum thickness of the PC slab under the abovementioned conditions should be 0.9 times the thickness of an RC slab: that is, (40L + 110) × 0.9(mm) for two-girder slabs and (30L+110)×0.9 (mm) for multi-girder slabs. The required increasein thickness for traﬃc volume and uneven settlement is the same as for RC slabs. The PC slab
can be made thinner than the RC slab because, when prestressing forces are introduced in the
direction of the span, the bending moment induced under loading in the direction perpendicular
to the span is smaller in the PC slab than in the RC slab. (See 5.4.2 Commentary of Part III
Concrete Bridges of the Speciﬁcations.)
The maximum span was set at 4 m (with 1.5 m cantilevered sections) for RC slabs and is
6 m (with 3 m cantilever sections) for PC slabs. However, RC slabs with large spans haverecently been designed; taking the Warashinagawa Bridge on the Second Tomei Expressway as
an example, slabs with a span of 11 m and a thickness of 360 mm at the center of the span (530mm on the girders) are adopted.
(2) Slab to girder connections
A post-tensioned PC slab is usually connected to the girders with stud shear connectors, asis the case with an RC slab. At the connection points, a PC slab is generally provided withhaunches, as with an RC slab. Taking the Warashinagawa Bridge as an example, the haunches
take the form of a large arch extending from the girder support to the center of the span.
A pre-tensioned PC slab is connected to the girders by the same method as a post-tensioned
PC slab, i.e. with shear connectors. Because the size of the openings in a precast slab at thegirders is limited, thick or screwed shear connectors are in some cases used in consideration of

234Standard Specifications for Steel and Composite Structures [Design]transportability and constructability. High-performance concrete has been used reliably to ﬁll
the space between girders and a precast slab.
(3) Connections between slabs
A standard joint (called a loop joint) is used to connect precast PC slabs together. For
reference, a sectional view of a loop joint is shown in Fig.C14.6.1.
Needless to say, this joint is of RC structure, and is adopted as a general joint for PC slabs
after loading tests have been carried out.

Fig.C14.6.1 Loop joint(4) Reinforcement of slab end
At girder ends, concrete needs to be cast down to the expansion joints and girder end cross girders even when a pre-tensioned PC slab is used. For this reason, the structure of a post-tensioned
PC slab or RC slab is, in many cases, adopted at girder ends. The concept of reinforcement
design for RC slabs, including the doubling of the design bending moment at the girder ends,
applies correspondingly to PC slabs.
The Manual for Design and Construction of PC Slab Steel Continuous Composite Two-Girder
Bridges [Expressway Technology Center, March 2002] points out that it is necessary to fully
conﬁrm that the predetermined prestress is introduced into the slab in the vicinity of cross girders
and expansion joints at the slab end. As regards the member forces induced by prestressing, thethis manual describes the following design concept:
1 Lay out prestressing tendons and introduce prestressing forces so as not to induce tensilestress in the PC slab under the dead load.
2 Lay out prestressing tendons and introduce prestressing forces so as not to cause cracks inthe PC slab under the dead load and live load.
The concept of allowing tensile stress to be induced and cracks to form in prestressed reinforced
concrete (PRC) depending on the combination of loads is also described in the manual.

14.6.3 Steel-concrete composite slab
A steel-concrete composite slab shall be designed such that it satisﬁes each performance item.
Performance shall be considered as satisﬁed through the observing of appropriate structural details.
(1) Slab thickness(2) Shear connector(3) Reinforcement at girder end【 Commentary 】

Most steel-concrete composite slabs are of relatively new structure. Although in basic form they
comprise steel and concrete, there is an extremely wide variety of structure types: for example, thereChapter 14 Slab Design235

are composite slabs consisting of steel plate or sectional steel and concrete in which ﬂat bars, shear
connectors, or bent truss rebars transmit the shear forces; and there are composite slabs of sandwich
structure with superplasticized concrete placed between upper and lower steel plates or sectional steel.
This section describes the structural details of a typical composite slab called the Robinson type.
This is a composite slab in which shear connectors are provided on the bottom steel plate, rebars arelaid over the top of the steel plate, and then concrete is placed.
(1) Thickness of steel-concrete composite slab The Guidelines for Design of Steel Structures - Part
B [JSCE, 1997] include an equation for calculating the minimum thickness of the concrete partof a steel-concrete composite slab Eq.(C14.6.1).
hc = 25L + 100 (mm)(not less than 150 mm)(C14.6.1)

where, L=span of the slab (m)This equation is applicable to slabs subjected to a bending moment where the maximum span,L, is 8 m. Comparing the minimum thickness of the composite slab with that of the PC slab,
there is no need to secure a concrete cover depth from the bottom steel plate of the composite
slab, and these guidelines adopt a value that yields a composite slab thinner than the PC slab
by an amount approximately equal to the lower concrete cover depth. When the bottom steel
plate is included in the calculation of the composite cross section (note that there is a type ofcomposite slab in which the bottom steel plate is a non-strengthening member), the standard
thickness of the steel plate is about 8 mm.
The equation also applies to composite slabs that use other types of steel bottom plate.
(2) Shear connectors
The above guidelines specify that shear connectors of well-tested design be used and that theyshould be designed so as to fully distribute the forces acting on the slab. The standard sizes of theshear connectors are speciﬁed as φ16 and φ19 mm so as not to cause harmful deformation of a slabthat has a relatively thin bottom plate. The shear connectors should be evenly spaced 250 mm
apart at maximum and 100 mm apart at minimum. The length of the shear connectors should
be designed so that the top of a connector under positive bending moment is in compression.
Based on test results, these guidelines specify that the shear stress, taking into account thefatigue acting on the shear connectors, should be limited to not more than 500 kgf/mm2 (49N/mm2 ).
(3) Reinforcement of slab at girder ends
Since a composite slab loses continuity at the girder ends and is subject to impulsive loading
caused by level diﬀerences at the expansion joints, the slab is designed with increased thickness
at girder ends, as in the case of RC slabs. In the case of a skew bridge, additional rebars areprovided in a skew direction, as in the case of RC slabs.
To reinforce the bottom steel plate in the vicinity of the girder ends, the number of rebars isincreased or additional rebars are arranged in the skew direction.
Recently, composite slabs this thickening at girder ends have been introduced to reduce the
man-hours needed to machine the slab. In this case, a structural analysis is carried out to conﬁrm
that the bending moment induced in the slab, with concrete placed down to and enveloping theend cross girders, remains small enough that it presents no structural problems at the girder
ends where the continuity is lost and the slab is subjected to impulsive loading.

14.6.4 Orthotropic steel deck
An orthotropic steel deck shall be designed such that it satisﬁes each performance item. Performance shall be considered as satisﬁed through the observing of appropriate structural details.

236Standard Specifications for Steel and Composite Structures [Design](1) Thickness of steel deck(2) Eﬀective width【 Commentary 】(1) Thickness of steel slab
The thickness of a steel slab deck plate should be not less than the following values for roadbridges:
Roadway (under live load B)： t = 0.037 × b

where ，t≥ 12mm

(C14.6.2)

Roadway (under live load A)： t = 0.035 × b

where ，t≥ 12mm

(C14.6.3)

Sidewalk that acts as part of main girder ： t = 0.025 × b

where ，t≥ 10mm

(C14.6.4)

where b = spacing between vertical ribs (mm)The thickness of the deck plate for a sidewalk that does not act as part of the main girder canbe taken as 8 mm.
a) The minimum plate thickness of the vertical ribs should be 8 mm. If the corrosion environment is categorized as good or if adequate attention is paid to corrosion prevention, theminimum plate thickness of the ribs with a closed cross section can be taken as 6 mm.
b) Where a vertical rib intersects with a cross girder, the vertical rib should be as a generalrule penetrate the cross girder and be welded to it.
This requirement is described in the speciﬁcations for road bridges [Japan Road Association,
2002b]. In the case of railway bridges, a similar requirement is made in Design Standards forRailway Structures (Steel and Composite Structures) [Railway Technical Research Institute,2000]. For a steel slab with ballasted track, these standards include the following requirements:
1 the minimum thickness of the steel slab should be 12 mm and the spacing between vertical ribs
2 the height of rectangular cross section
should be not more than 30 times the slab thickness, vertical ribs should be not more than 12 times the slab thickness, and 
3 where a vertical rib
intersects with a cross girder (horizontal rib), the vertical rib should penetrate the cross girderand be welded to it.
(2) Eﬀective width of steel slab In Section 8.4.4 of the above speciﬁcations, the method of loading,the eﬀective width of steel slab, and the standard values of bending moment and shear force
used for the design in the ultimate limit state are speciﬁed [Japan Road Association, 200b].
Structural details, such as the layout and design of ribs, can be determined in accordance withthe speciﬁcations.
Other standards are described below.
1) Design Standards for Railway Structures (Steel and Composite Structures) [Railway Technical Research Institute, 2000]
In the Design Standards for Railway Structures, the requirements for steel slabs are
speciﬁed in Chapter 12 Floor Framing. The steel slab in these design standards is deﬁned
as a steel plate reinforced with vertical ribs and horizontal ribs (or cross girders) to support
the ballast. It is speciﬁed in Chapter 14 Plate Girders that in the case of deck plate girder
bridges of steel slab type, because the steel slab acts as not only a slab but also the main
girder ﬂange, the member forces of the slab as a main girder and the member forces speciﬁed
in Chapter 12.7 should be used for veriﬁcation of the slab.
The requirements set out in Chapter 12 are outlined below.

1 Structure of steel slaba) For ballasted track, the minimum thickness of the slab should be 12 mm and thespacing between the vertical ribs should, as a general rule, be not more than 30

Chapter 14 Slab Design

237

times the slab thickness.
b) The height of the rectangular cross section vertical ribs should be not more than
12 times the slab thickness.
c) Where a vertical rib and a cross girder intersect, the vertical rib should penetrate
the cross girder and be welded to it.
2 Design of vertical ribs for steel slabThe method of loading, the eﬀective width of the steel slab, and the standard valuesof bending moment and shear force used for design in the ultimate limit state are
speciﬁed.
3 Design of cross girders for steel slabThe method of loading, the eﬀective width of the steel slab, and the method of
calculating the bending moment are speciﬁed.
2) American Association of State Highway and Transportation Oﬃcials (AASHTO)
The AASHTO Speciﬁcations [AASHTO LRFD Bridge Design Speciﬁcations, AASHTO,
2003] describe general requirements for the analysis of steel slabs, the distribution angle ofwheel loads, the concept of the composite eﬀect of slab and pavement, reﬁned methods ofanalysis, methods of approximate analysis, and detailed requirements. These speciﬁcations
include cross-references to Chapter 2 General Design and Location Features, Chapter 4
Structural Analysis and Evaluation, and Chapter 6 Steel Structures.
3) The European Committee for Standardization (EUROCODE 3 (CEN, 2003))
In the EUROCODE, detailed speciﬁcations are described in Appendix C: Recommendations for Structural Details of Steel Slabs of EUROCODE 3/Part 2: Steel Bridges. Thisappendix comprises three chapters: C1 Road Bridges, C2 Railway Bridges, and C3 Halfﬁnished Products and Manufacturing Accuracy. In Appendix E Combination of Eﬀects ofWheel and Tire Loads and Traﬃc Loads of Road Bridges, combinations of the actions ofslab, ﬂoor framing, and main girder are speciﬁed.
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Decks of Steel Highway Bridges, pp.77-82.
Murai, Noise Control(1999) ：Road Business and Low-frequency Sound, Vol.23, No.5, pp.319-323.
Toshihiko Hase, Yasushi Kamihigashi, Toshio Yasumatsu(1999) ：Estimation of the Durability of Long-span
PC Slabs by Moving Wheel Load Fatigue Tests, Japan Highway Public Corporation Research Institute
Report, Vol.36, pp.25-34.
Moto Ikoma, Atsushi Honma, Koki Sugizaki, Tatsuhiko Kasai(1999) ：A Study on the Examination Methodon the Limit State of PC Slabs, 55th Annual Conference of the Japan Society of Civil Engineers, CS-285.
Railway Technical Research Institute(2000) ：Design Standards for Railway Structures and Commentary, Steeland Composite Structures ．
Sumio Sakamoto, Akihiro Nakasono, Yoshiyuki Yasukawa, Naofumi Inaba, Masatsugu Nagai(2002) ：A Simpliﬁed Method to Evaluate Bending Moment due to Dead Loads for PC slab decks consistingof two plate girdes, Journal of Structural Engineering, Vol.48A, pp.1409-1416.
Atsushi Honma, Toshihiko Hase, Kazushige Sakakibara, Kazumi Nakamura, Tadashi Uehara,
Tatsuhiko Kasai(2002) ：Design and Construction of Long-span Cast-in-situ PC Slabs, Bridge and Foundation
Engineering, Vol.36, No.10, pp.2-10.
Japan Road Association (2002a) ：Speciﬁcations for Highway Bridges and Commentary, I Common Speciﬁcations Volume.
Japan Road Association (2002b) ：Speciﬁcations for Highway Bridges and Commentary I Common Speciﬁcations, II Steel Highway Bridges Volume.
Japan Society of Civil Engineers (2002a) ：Standard Speciﬁcation for Concrete Structures, Construction Volume.
Japan Society of Civil Engineers (2002b) ：Standard Speciﬁcation for Concrete Structures, Structural Performance Veriﬁcation Volume.
Architectural Institute of Japan(2003) ：Japanese Architectural Standard Speciﬁcations, JASS5 Reinforced
Concrete Work 2003, pp.518-532.
Japan Concrete Institute(2003) ：Guidelines for Survey, Repair and Reinforcement of Cracks in Concrete 2003-.
Toshio Yasumatsu, Izumi Tanaka, Yasuhiro Sshimura, Tomonori Nakahara, Taro Tonegawa(2003) ：Study on Design of In Place PC Slab of continuous rigid frame 2- girder Bridge, Proceeding of 3rd
Symposium on Decks of Highway Bridges, pp.103-108.
Yasuo Kajikawa, Prestressed Concrete(2003) ：The Present Situation of Bridge Traﬃc Vibrations and Environmental Countermeasures, Vol.45, No.4, pp.37-42.
Atsunori Kawabata, Takuya Murakami(2004a) ：Dynamic Characteristics of Highway Bridges Deck Slabs, Proceeding of 4th Symposium on Decks of Highway Bridges, pp.79-84.

Chapter 14 Slab Design

239

Atsunori Kawabata, Reiko Akimoto(2004b) ：Performance Based Design Method for Fatigue Strength of RC
Slab, Proceeding of 4th Symposium on Decks of Highway Bridges, pp.179-184.
Japan Society of Civil Engineers(2004a) ：Performance-Based Design of Decks of Highway Bridges, Rational
Design and Higher Durability of Decks of Highway Bridges, pp107-108.
Japan Society of Civil Engineers(2004b) ：Moving Wheel Load Test of Decks, Rational Design and Higher
Durability of Decks of Highway Bridges.
Highly-Functional Waterproof Committee(2004) ：Report on Evaluation of Durability of Highly-Functional
Waterproof System for Decks of Highway Bridges.
Japan Bridge Association, Expansive Additives Association(2004) ：Report on Evaluation and Study of Eﬀectiveness of Expansive Additives for Cast-in-situ PC Slabs.
Chitoshi Miki, Hisatada Suganuma, Masayuki Tomizawa, Fumitaka Machida(2005) ：Case Study on Fatigue
Damage in Orthotropic Steel Bridge Deck, Structural Eng./Earthquake Eng., JSCE, No.780/I, pp.57-70.
Chitoshi Miki, Yuji Goto ，Hitoshi Yoshida ，Takeshi Mori (1985) ：Computer simulation studies on the fatigue
load and fatigue design of highway bridges ，Journal of Structural Mechanics and Earthquake Engineeringof JSCE ，No.356 ，pp.37-46 ．
AASHTO(2003) ：AASHTO LRFD Bridge Design Speciﬁcations- S.I. Units 2003 Interim Revisions ．
CEN(2003) ：prEN 1993-2 : Eurocode 3 : Design of steel Structures, Part 2 : Steel Bridges, Stage 34 draft ．

240Standard Specifications for Steel and Composite Structures [Design]

Chapter 15 Design of Composite Girders
15.1 General
This chapter shall apply to a steel-concrete composite girder, in which a concrete deck or acomposite deck formed of steel and concrete is uniﬁed to the steel girders with shear connectors.
In the design of a composite girder, veriﬁcation shall be done to conﬁrm the required performance
regarding safety and serviceability of the girders as well as the connectors.
【 Commentary 】

In design of a composite girder which consists of RC deck, PC deck or steel-concrete composite
deck (see Chap.14) and the steel girders uniﬁed to it with share connectors, the required performanceat the serviceability limit state, safety limit state and so on shall be satisﬁed. Design consideration on
durability is also important. As for design of the steel girder section which resists own weight and thedeck weight, please refer to Chapter 5.
When the same grade steel is used for ﬂanges and web, the steel girder is called homogeneous type,and a girder is called hybrid type when the steel strength for the web, which usually receives smaller
stress, is lower than the steel for ﬂanges. Although the hybrid type seems to be eﬀective for cost
reduction, this chapter will cover only the homogeneous type because the hybrid girders have beenrarely constructed in Japan.
There are two types of the composite girder, each which has diﬀerent stress distribution inside thesteel girder and concrete deck. One is the shored construction in which whole dead load and live load
are resisted with the composite cross section. Another is unshored construction. In this structural
system, the weight of steel and concrete (the ﬁrst phase dead load) is resisted with the steel girder only,
and the second phase dead load such as curb, pavement and attachment as well as the live load aresupported with the composite cross section. At the intermediate supports where cracks are generated
into the concrete deck due to negative bending moment, the load is resisted with the structural systemcomposed of the steel girder and rebars in the deck.

+=(a) Shored construction(b) Unshored construction(composite section carrying all loads)(composite section carrying superimpose
dead load and live load)

Fig.C15.1.1 Stress in composite girders

At the serviceability limit state, the required performance of structure is such that; 1) excessivedeﬂection of the girder is not generated, 2) the steel member is free from permanent strain and keeps
the elastic behavior, 3) crack width in the concrete deck at intermediate supports is within allowable
range, and 4) no fatigue by repeating traﬃc load is introduced to welded portions of the web.
The above mentioned requirements are to be ascertained as the followings.
1) Deﬂection under the live load including impact shall be less than the value given in Highway

Chapter 15 Design of Composite Girders

241

Bridge Speciﬁcation [JRA, 2002]
2) Normal stress, shear stress and their equivalent stress shall be less than yield point of the steel.
3) Crack width in the deck shall be less than acceptable value deﬁned based on environmental
consideration. The calculation and veriﬁcation will be described in 15.6.
4) Web bleeding is a phenomenon that a thin web plate repeats out-of-plain deﬂection (elastic
buckling) because of the traﬃc load, and this deﬂection may cause fatigue damages to portions
such as the ﬁllet welding between the ﬂange and web, vertical stiﬀeners, corner of ﬂange andweb. In order to prevent such damages, limit value of the depth-to-thickness ratio of web as afunction by the span length is given in Eurocode [CEN, 2003].
At the safety limit state, safety of the structure under action of bending, share and their combination
shall be conﬁrmed. The composite girder is classiﬁed into three categories de-pending on the depththickness ratio of web plate: compact section, noncompact section and slender section. The compact
section can raise its ultimate bending strength up to the fully plastic moment without suﬀering any
local buckling, and the noncompact section raises the strength higher than the yield moment but lessthan the fully plastic moment. The slender section cannot reach the yield moment because of the web
buckling. In this chapter, the veriﬁcation methods of safety will be discussed with the above mentioned
deﬁnitions.
It shall be pointed out that veriﬁcation about the fatigue limit state is not mentioned here.

15.2 Strength of Composite Girder
15.2.1 Classification of cross sections(1) For calculation of the bending strength, cross sections of composite girders are classiﬁedby the same way for steel girders speciﬁed in Chapter 5: namely (a) compact section, (b)noncompact section, and (c) slender section.
(2) When a compression ﬂange of the steel girder is eﬀectively restrained from buckling with aconcrete deck by suﬃcient shear connectors, the section can be classiﬁed in accordance with
only the depth-thickness ratio of the web plate of steel girder.
(3) For a composite girder receiving negative bending moment or having a steel compression
ﬂange that is not suﬃciently uniﬁed to the concrete deck, the classiﬁcation of cross section
shall be done in accordance with the steel sections as being deﬁned in 5.3.3.1.
【 Commentary 】(1) Fig.C15.2.1 shows relationships between the bending moment and curvature for each section. In
this ﬁgure, Mpl and My denote the plastic and yields moments, respectively.
Bending momentcompact
Mpl
My

noncompact
slendercurvature

φ

Fig.C15.2.1 Bending moment-curvature relationship ofcomposite girder and section classi-ﬁcation

242Standard Specifications for Steel and Composite Structures [Design](2) Section classiﬁcations in AASHTO and Eurocode
Table C15.2.1 shows a summary of section classiﬁcations in AASHTO [AASHTO, 2005] andEurocode [CEN, 2003]. In this table, criteria for only web plate are listed, on condition that
there is no possibility of buckling in the compressive ﬂange plate of composite girders underpositive bending moment. In the table, tw and bw are the thickness and depth of the web plate
respectively, and the other symbols are deﬁned in Figs.C15.2.2 and C15.2.3.
Table C15.2.1 Section classiﬁcation in Eurocode and AASHTOAASHTOEurocodeClassDeﬁnition

Thickness/depth of web plate

Compact
Noncompact
Slender

Mmax ≥ Mpl
Mmax ≥ My
Mmax < My

2Dcp /tw ≤ 3.76 E/fy
2Dc /tw < 5.7 E/fy
other than those above

Class 1

Mmax ≥ Mpl

bw /tw ≤Class 2

Mmax ≥ Mpl

Class 3

Mmax ≥ My

Class 4

Mmax < My





36ε/α
for α ≤ 0.5
396ε/(13α − 1) for α > 0.5
41.5ε/α
for α ≤ 0.5
bw /tw ≤456ε/(13α − 1) for α > 0.542ε/(0.67 + 0.33ψ) for ψ > −1.0
bw /tw ≤√for ψ ≤ −1.062ε(1 − ψ) −ψother than those above

E: Young modulus of the steel
fy : Standard value of yield strength of the steel
ε = 235/fy [N/mm2 ](3) Section classiﬁcation by conﬁning eﬀect due to the concrete deck and initial bending moment
during erection
Since the section classiﬁcation criteria for composite girders in both AASHTO 2005 and Eurocode 2003 are based on those for steel girders, the conﬁning eﬀect due to the concrete deckon web buckling in composite girders is not taken into account. Furthermore, in the unshoredcomposite girder, only the steel girder has to support the whole dead load, which means that
initial bending moment in the erection stage is left. However, the inﬂuence of the initial bending
moment on the section classiﬁcation criteria is not considered in AASHTO nor Eurocode.
Reﬀerence[JSSC, 2006], [Gupta et al., 2006] and Draft for Limit State Design Methods for
Composite Girders [JSSC, 2006] have proposed the section classiﬁcation criteria in which theeﬀects of both concrete deck and initial bending moment are taken into consideration. The
composite section can be classiﬁed according to these references as shown below.
(a) Compact sections
When the depth-thickness ratio of the web plate satisﬁes the following criterion, the section
is classiﬁed as compact sections:

bw
2.0 E
≤
(here, α < 0.4)
(C15.2.1)twαfywhere α stands for the position of the plastic neutral axis (see, Fig.C15.2.2).
(b) Noncompact sections
Noncompact sections satisﬁes the followings:

E
bw
1.7Λ
≤
(ψ > −1.0)
tw0.67 + 0.33ψ fy
bw
E≤ 2.5Λ(1 − ψ) −ψ(ψ ≤ −1.0)
twfy(C15.2.2)(C15.2.3)

243

Chapter 15 Design of Composite Girders

0.85f’cd

tw

bw

Mpl

Dcp=αbw+
fy

Fig.C15.2.2 Stress distribution in a compact section under full plastic moment

σ1
t

-

b

+

+

+
M
(a)

Dc =α'b

=

+

M
(b)

=

ψσ1

M
(c)

Fig.C15.2.3 Superposition of stress in unshored composite girder

here :
Λ = 1 − 0.1



M1
Mys




+ 2.31

M1
Mys

2 
(where,M1≤ 0.4)
Mys(C15.2.4)

where, ψ is the parameter for stress gradient (see, Fig.C15.2.3) in the web; M1 denotes theinitial bending moment applied only steel section in unshored composite girders; Mys is the yield
moment of the bare steel section.
(c) Slender sections
Slender sections are deﬁned as other than above two.
(4) When the compressive ﬂange plate of a steel girder is connected to the concrete deck with enoughshear connectors, there is no possibility of buckling of the ﬂange. Accordingly, section may beclassiﬁed depending on the web plate only. Even in composite section receiving positive bending
moment, the compressive ﬂange has a potential for buckling when the pitch of shear connectors
is too large. If so, the current provision must not be applied.
(5) When the compressive ﬂange plate is not uniﬁed with the concrete deck or when a composite
girder receives negative bending moment, the section shall be classiﬁed in accordance with 5.2.

15.2.2 Design bending resistanceThe design bending strength of a composite girder shall be determined by appropriate method(s)with consideration of the classiﬁcation depending on either the compact, noncompact or slendersection.
【 Commentary 】(1) Bending strength
In general, the design bending strength of composite girders shall be determined by Eq.(C15.2.5)∼ Eq.(C15.2.8).
Mrd = Mr /γb(C15.2.5)

244Standard Specifications for Steel and Composite Structures [Design]

・For compact sections

Mr = Mpl(C15.2.6)

・For noncompact sections

Mr = My(C15.2.7)

・For slender sections

Mr = Mef f(C15.2.8)

where, Mrd : design bending strength Mr : bending strength, Mpl : plastic bending moment,
My : yield bending moment, Mef f : bending moment with consideration of the eﬀective area ofthe steel member given in 5.3.3, γb : member factor.
Examples of the calculation of the bending strength by plastic theory or by elastic theory aredescribed below.
(2) Calculation of the bending strength by plastic theory
Mr can be determined by plastic theory. Examples of plastic stress distributions for a composite girder in positive and negative bending moment are shown in Fig.C15.2.4, where, bef f :
eﬀective width of the concrete deck, fcd: design compressive strength of concrete, fyd : design
yield strength of the steel member, fsd : design yield strength of the reinforcement, ，Nc,f :plastic axial force of the concrete deck, Ns1 , Ns2 : plastic axial force of the reinforcement, Npl(+) : plastic axial force of the steel member (tension side), Npl (-) : plastic axial force of thesteel member (compression side). The following assumptions are made in the calculation;(a) There is no slip between steel member, reinforcement and concrete.
(b) The eﬀective area of the steel member is decided by fyd (either tensile or compressive).
(c) The eﬀective area of the longitudinal reinforcement is decided by fsd (either tensile orcom-pressive). However, the reinforcement in a concrete deck under compression is to beneglected.
(d) The eﬀective area of concrete in compression is decided by the eﬀective width described in
15.7, and the concrete stress distribution between the upper surface of the concrete deck．
and the plastic neutral axis is assumed to be constant of 0.85fcd(a) When plastic neutral axis is within the concrete deck in positive bending(b) When plastic neutral axis is within the web receiving negative bending
Fig.C15.2.4 Examples of plastic stress distributions for a composite girderin positive or negative bending moment (positive: tension)

According to Eurocode 4 [CEN, 2002], when composite cross sections is composed of steel
grade S420 (fy =420 N/mm2 ) or S460 (fy =460 N/mm2 ) and when the distance xpl between theupper surface of the concrete deck and plastic neutral axis exceeds 15 % of the overall depth h

Chapter 15 Design of Composite Girders

245

as shown in Fig.C15.2.5, the bending strength Mr is to be βMpl , where β is the reduction factor.
In addition, when the values xpl /h are greater than 0.4, the bending strength is to be determinedby elastic theory or other appropriate methods.
Moreover, Eurocode 4 requires Mrb not to exceed 0.9Mpl , when elastic analysis is used for acomposite continuous girder with compact sections in positive bending moment area and when
the girder meets both of following (a) and (b) conditions. Otherwise, use of more accurate
inelastic global analysis is required.
(a) A cross section under negative bending moment or cross section neighboring a support iseither noncompact or slender.
(b) The length ratio between both spans neighboring an intermediate support is less than 0.6(shorter / longer).

Fig.C15.2.5 Reduction factor β (positive: tension)

On the other hand, AASHTO [AASHTO, 2005] speciﬁes the bending strength for the compact
sections under positive bending moment to be determined by either Eq.(C15.2.9) or Eq.(C15.2.10)
when the speciﬁed minimum yield strength of the steel ﬂanges does not exceed 485 N/mm2 .
Mr

=

Mr

=

Mpl



Dp
Mpl 1.07 − 0.7
Dt(Dp ≤ 0.1Dt )(C15.2.9)(0.1Dt < Dp ≤ 0.42Dt) (C15.2.10)

where, Dp : the distance between the upper surface of the concrete deck and plastic neutral axis(mm), Dt : total depth of the composite section.
However in a continuous span, Mr is required not to exceed the value decided by Eq.(C15.2.11),
when the following either condition meets;(a) The span under consideration and both sections neighboring an intermediate support do notsatisfy the prescribed requirement.
(b) Sections of both spans neighboring an intermediate support do not satisfy the required plastic
rotating capability.
Mr = 1.3Rh My(C15.2.11)

where ，Rh : hybrid factor ( = 1.0 for homogeneous sections) ．
(3) Calculation of the bending strength by elastic theory
The design bending strength of compact, noncompact or slender sections can be determinedby elastic theory. In use of the elastic theory, Bernoulli-Euler theory (a plane in the crosssection before deformation keeps plane after the deformation) is assumed, and the eﬀective width
speciﬁed in 15.7 is to be considered. As for the characteristic strength, the followings should bepremised:: Concrete in compression. Generally, the area of concrete in tension is to be neglected.
• fcd• fyd : Structural steel member in compression or tension.

246

Standard Specifications for Steel and Composite Structures [Design]• fsd : Reinforcement in compression or tension. Generally, reinforcement in a concrete deck
receiving compression may be ne-glected.
For the calculation of slender sections, the eﬀective area of the steel member speciﬁed in 5.3.3
should be used.

15.2.3 Verification of bending moment
The bending moment of a composite girder shall be veriﬁed using the following:
γiwhere ，

Mrd
Msd
γi

Msd
≤ 1.0
Mrd

(15.2.1)：Design bending moment：Design bending strength：Structural factor【 Commentary 】

The basic equation for veriﬁcation is Eq.(15.2.1). The followings are examples of the veriﬁcation
to steel sections and composite sections.
(1) Veriﬁcation of steel sections only
Steel girders of the unshored composite girders need to carry the dead loads such as own weight,
the weight of frame works, the weight of wet concrete, etc., until the concrete hardens. In
such case, safety of the steel girders should be veriﬁed by conﬁrming Eq.(15.2.1) to become notgreater than 1.0 while the following ﬁgures are used: Msd by the ﬁrst phase dead load, andMrd by the steel girder only. In addition, safety against the buckling of a ﬂange or a web, andlateral or lateral-torsional buckling of steel girders in the construction stage shall be ascertainedin accordance with Chapters 5 and 6.
(2) Veriﬁcation of composite sections
For the veriﬁcation to composite sections, such factors shall be appropriately considered as thedead load, the live load, the eﬀect of the construction sequence (history of given load), shrinkage
and creep of the concrete, and temperature diﬀerence between the concrete deck and the steel
girders, etc.
When the bending strength is calculated by plastic theory for compact sections, such points
can be neglected as the eﬀect of the construction sequence, shrinkage and creep of concrete, andtemperature diﬀerence between the concrete deck and the steel girders, because the veriﬁcation
is done against the plastic stress state. By contraries, these points shall be appropriately taken
into account when the bending strength is calculated by elastic theory for noncompact or slendersection, because the veriﬁcation is done against the elastic stress state.

15.2.4 Shear strength
The design shear strength of a composite girder is equal to that of the steel girder used in thecomposite girder.

【 Commentary 】

Although contribution by the ﬂoor deck on shear strength is expected, it is decided not to takeaccount for safety margin. Shear strength Vr of the steel girder can be calculated with Eq.(C15.2.12)

Chapter 15 Design of Composite Girders

247[Basler, 1961] ;√3 1 − τcr /τy
Vr
τcr
√
=
+
Vy
τy
2
1 + α2(C15.2.12)

where τcr is shear buckling stress, τy is yield shear stress, Vy = τy hw tw is yield shear strength, hw is
web depth, tw is web thickness, α is aspect ratio (≤ 3.0). Web shear buckling strength τcr (≤ τy ) is
calculated as follows;⎧⎨τ(τe ≤ 0.8τy )eτcr = (C15.2.13)⎩ 0.8τe τy(τe ≥ 0.8τy )π2 E
τe = ks
12(1 − ν 2 )where ks is to be calculated as follows
ks =



tw
hw

2

⎧
⎨5.34 + 4.00/α2(α ≥ 1)⎩4.00 + 5.34/α2(α ≤ 1)(C15.2.14)(C15.2.15)

In Eq.(C15.2.12), the ﬁrst term in the right hand side is shear buckling strength and the second
term is strength of the post-buckling due to diagonal tension ﬁeld. At the ends of girders, arranging
rigid vertical stiﬀeners is required by Speciﬁcations for Highway Bridges [JRA 2003], because the postbuckling strength cannot be always expected. When one horizontal stiﬀener is provided to the web,the sum of shear strength of each panel (upper and lower of the stiﬀener) calculated by Eq.(C15.2.12)
is to be shear strength of the stiﬀened web.

15.2.5 Verification of shear
At the safety limit state, the section shall satisfy the following equation:
γiwhere ，

Vrd
Vsd
γi

Vsd
≤ 1.0
Vrd

(15.2.2)：Design shear strength ，Vr /γb：Design shear moment：Structural factor【 Commentary 】

The way of safety check against shear failure is given.

15.2.6 Verification of combined bending and shear
When bending moment and vertical shear force simultaneously act on a composite girder, thecombined action due to these forces shall be considered.
【 Commentary 】

When a composite girder is subjected to a combination of a large bending moment and a large
shear force, it is necessary to verify not only the action of each force individually but also the combined
eﬀect of the forces.
Design Standards for Railway Structures and Commentary [RTRI, 2000] gives the following quadratic

248Standard Specifications for Steel and Composite Structures [Design]
1
n=m=4

Mu/M

0

n=m=2

n=m=1

0
0

Fig.C15.2.6

Vu/V

0

1

Shear-moment interaction diagram

equation for plate girders and similar structures. This equation is based on Mises’ yield condition andalso takes into account post-buckling strength in the diagonal tension ﬁeld and the combined stresses
are taken. The strength ampliﬁcation factor is reduced according to past experience.
2  2 V
Mγa γb γi 2
<1+
(C15.2.16)
1.1
Mr
Vr
where,

M, V ： applied bending moment and applied shear force
Mr , Vr ： bending strength and shear strength
γa , γb , γi ： partial factors

Furthermore, the 4th-order Eq.(C15.2.17) is adopted for recently developed two-main-girders bridges(such as the Chidori-no-sawakawa Bridge).
4  4 
V
M
4
<1
(1.7)
+
(C15.2.17)
Mr
Vr
In the above two equations, Vr may be replaced by the sum of shear buckling strength and strength
due to the diagonal tension ﬁeld. However, this brings up the question of how the partial factors
and the strength in the diagonal tension ﬁeld can be evaluated. Further, attention is necessary forconsistency with the rules about vertical stiﬀener spacings given in Highway Bridge Speciﬁcations[JRA, 2002] when this 4th-order equation is used.
There are many studies covering the evaluation of bending strength, ultimate shear strength, andstrength against combined bending and shear force for web plates with vertical stiﬀeners only. In
particular, various correlative equations have been proposed by Basler et al. for combined ultimate
strength against bending and shear. Currently, the following power sum correlation is consideredeﬀective as a relatively simple design equation:n  m

Vu
Mu
+
= 1.0
(C15.2.18)0
Mu
Vu0
where,

Mu , Vu ： ultimate bending strength and ultimate shear strength
when both are simultaneously loaded
Mu0 , Vu0： ultimate bending strength and ultimate shear strength
when either one is loadedm, n： arbitrary constants

Figure C15.2.6 shows moment-shear interactions for m = n = 1, 2, and 4. As m and n are
increased, the interaction between bending and shear is drastically reduced.

249

Chapter 15 Design of Composite Girders

The natural properties of a girder are that bending moment is resisted mainly by the ﬂanges while
shear force is resisted by the web plate. In this respect, it is considered that the above interaction
curves at or around m = n = 4 well represent the behavior of a composite girder. If appropriate
factors were to be sought by colleting test data and/or by exact numerical calculation results, there isa high possibility that new interaction equations may become available as design tools, possibly using
diﬀerent values of n and m.

15.3 Structural Analysis and Resultant Force
Linear elastic analysis shall basically be used for structural design of composite girders. In
the case of continuous composite girders, tensile cracks may take place in the concrete deck nearintermediate supports, accordingly resultant forces shall be calculated with consideration of the
reduction of the stiﬀness caused by these cracks. When the full plastic bending moment is expected
as the bending strength, attention must be paid to the redistribution of the resultant forces
associated with the inelastic behavior.
【 Commentary 】

At the safety limit state of a composite girder, plastic region is widely spread into the girder,
and the stress resultant is accordingly redistributed. This phenomenon can be solved by nonlinear
analysis, though this is not necessarily preferable at practical design stage due to its complexity. In
this chapter, the maximum bending strength of girder is to be restricted up to Class 2 section deﬁned
in Eurocode, whose strength is equal to the plastic moment, and thus the elastic analysis can be usedwhile attentions are paid to the redistribution of stress resultant.
On the other hand, Class 1 section corresponds to rolled steel sections which have relatively large
plate thickness compared with the size of section, and its ultimate state usually becomes unstablemechanism in which plural hinges are formed inside the structure. Such case requires the plastic
analysis, but its design is often governed by the serviceability limit or the fatigue limit state insteadof the safety limit state.
Re-BarL1 > 0.6 L2

0.15L1 0.15L2

Concrete deck

L2

Fig.C15.3.1 Section to decide moment of inertia around intermediate support

At intermediate supports, the concrete cracks produce, and the ﬂexural rigidity depends on cracking
state which is inﬂuenced by load intensity and loading pattern. Exact evaluation of ﬂexural rigidity at
the section is thus diﬃcult. Though several propositions on deﬁning method for the ﬂexural rigidity
have been available [Johnson et.al., 1998], this speciﬁcation requires the moment of inertia for deciding
ﬂexural rigidity to be calculated from the cross section that is composed of the steel girder and re-bars
both which are located in 15% length of each span neighboring the intermediate support as being
shown in Fig.C15.3.1.

250Standard Specifications for Steel and Composite Structures [Design]

15.4 Shear Connectors
15.4.1 General(1) Shear connectors arranged at the interface of the concrete deck and steel girders shall be
veriﬁed to satisfy required performances.
(2) Shear connectors shall be properly designed for both safety limit state and fatigue limit statein order to ensure suﬃcient structural performance throughout the design working life.
(3) Shear connectors shall have suﬃcient deformation capacity enabling to redistribute the horizontal shear force between the concrete and the steel to wider area, because this redistribution can occur at the safety limit state(4) When two or more diﬀerent types of shear connector are used within the same span of acomposite girder, inﬂuence by the diﬀerence on shear force versus slip relationship shall beadequately considered.
【 Commentary 】(1) and (2) Shear connectors are important structural members indispensable for the composite
girder, and accordingly they shall be designed suﬃciently safe against each limit state. In particular, it is necessary to understand type, size and frequency of the acting force, and the transmission mechanism of the force by the shear connectors shall be clearly grasped. When thetransmitting force and the mechanism are not clear, suitable experiment or detailed analysis etc.
are needed to decide structure of the shear connectors and thus to conﬁrm their safety.
So far, the shear connectors of composite girders are designed only against the horizontal
shear force in the longitudinal direction. In the case of composite minimized-number of main
girders bridge, however, transverse load such as earthquake or wind has stronger inﬂuence thanthe longitudinal load in terms of the design load for shear connectors arranged near supports.
The load, accordingly, often governs design, because the transverse load is transmitted from theconcrete deck to cross beam at the support and then to the shoes.
Moreover such bridges usually have wide distance between the main girders, and the shear
connectors arranged around the internal cross beams may receive pullout force due to rotationof the concrete deck which is caused from the second phase dead load, the prestress and live
load [Sakai, et al. 1995, 1997]. The share connectors arranged this portion, therefore, must
be designed against not only the horizontal shear force in the longitudinal direction but also
the force in the transverse direction as well as the pullout force. As for evaluation of design
strength of the stud simultaneously receiving plural forces, a reference [Ohtani, et.al, 1994] isavailable. Eurocode[CEN, 2002] requires a special consideration when shear connectors are given
the pullout force being larger than 1/10 of their tensile strength.
(3) It is one method that some shear connectors are allowed to enter elastic state but safety andperformance of the structure are secured by whole group of connectors. However, it is necessary
to conﬁrm the safety when allowing the elasto-plastic behavior of the shear connectors over total
span of the main girder is intended.

15.4.2 Type of shear connectors(1) Shear connectors are devices provided at the interface between the steel element and theconcrete deck in order to resist internal shear.
(2) Shear connectors shall be mechanical devices that join the steel and the concrete. However,other types of shear connector can be used as long as their safety is veriﬁed in proper ways.

Chapter 15 Design of Composite Girders

251【 Commentary 】(1) This chapter describes a composite girder bridge where the concrete deck is united with theshear connectors to the upper surface of the ﬂange of steel girder. The shear connectors in acomposite structure are jointing devices to integrate both steel and concrete, and in this sense,steel members or a part of them both buried into the concrete like steel framed concrete structures
belong to the shear connectors. However, it is necessary for designing the share connectors of
the composite structure to distinguish the diﬀerences in dynamic behavior, fatigue characteristic,
etc. of them from those of the burial type.
(2) The shear connectors are classiﬁed into (a) mechanical joint, (b) friction bonding, (c) adhesion,and (d) adhesives, each which contains the following methods.
(a) (a)Mechanical joints: Stud (High strength stud [Eguchi,et.al.1999]), Cupler-joint stud [Ishikawa,et.al.2001], High-rigidity stud [Hiragi,et.al.2001], Delayed-composite stud [Kitagawa,et.
al.2001], Shape steel, Block dowels, Perforated-plate dowels and Angle-connector.
(b) Friction type joint: High tensile bolt.
(c) Adhesion type joint: Protrudent rolled steels (checkered steel plate, rugged-surface H-shapesteel).
(d) Bonding type joint: Epoxy resin.
Among these, mechanical joins have been overwhelmingly used because high composite eﬀect
can be expected even with small contacting area. In this speciﬁcation, mechanical joints are
regarded as the prime shear connectors for composite girder bridges based on domestic andforeign researches and the construction experiences.
In road bridges, the headed stud connectors have been very widely applyed, because they areexcellent in construction easiness and high economy. For railway bridges, shear connectors calledblock dowels are generally used. This type of connector consists of a steel block or a horseshoeshape plate to which a semicircle re-bar is welded. This re-bar prevents the deck from lifting up.
Other than the headed studs and block dowels, there are perforated-plate dowels [Leonhalt,1987]
and angle-connector which uniﬁes the ﬂange plate and concrete deck in corrugated steel-web
bridges [Igase,et.al.2002].
On the other hand, connection methods other than mechanical joints, such as high tension
bolts, are used for precast concrete deck panels. The adhesion type joint and the bonding
type joint have no record of being solely used, though the adhesion type joint and the friction
connector with high tensile bolts are recently studied for practical use[Uenaka,et.al.1998; Tokumitsu,et.al.1998]. However, the adhesion type joint keeps the connection only at the interface
between the steel and concrete, this type thus has an anxiety of durability that peeling from theinterface of the concrete may precede when only this type connectors are used.
In the case of a composite minimized-number of main girders bridge, arrangement of connectors
might face diﬃculty because too many connectors are needed per one main girder when only
mechanical joints are used. This tendency will be remarkable for the case of precast deck panels,
because the location for the shear connectors to be arranged is restricted. If a mechanical joint isgoing to be used, one method of easy arrangement is use of the group studs for instance. As forother methods, using mechanical joints or friction joints together with the adhesion type joints
or the bonding type joints can be eﬀective, though such idea needs a lot of studies in the future.

15.4.3 Ultimate limit state for shear connectors
Safety and durability of the shear connectors shall be veriﬁed against the safety limit state andthe fatigue limit state, respectively. The ultimate load shall be applied to the former, while theservice load shall be used to the latter.

252

Standard Specifications for Steel and Composite Structures [Design]【 Commentary 】

Safety and durability are considered as required performances associated with shear connectors.
The safety limit state and fatigue limit states are selected to represent these required performances.

15.4.4 Verification at safety limit state
At the safety limit state, shear connectors shall satisfy both of the following equations:


1
qsd
≤ 1.0
(15.4.1)
γi
1.1
qrd
Qsd
γi
≤ 1.0
(15.4.2)
Qrd
where ，

qsd
qrd
Qsd

：Horizontal design shear force per unit length

Qrd
γi：Total horizontal design shear strength over the same length：Horizontal design shear strength per unit length：Total horizontal design shear force over a longitudinal length where the size,

type, and spacing of shear connectors are kept same
：Structural factor. For a standard structure, taken to be γi = 1.0.

【 Commentary 】

In this speciﬁcation, plastic deformation of shear connectors is allowed at the safety limit state,so similar to Eurocode, qsd can exceed qrd by 10% as shown in Fig.C15.4.1. In this case, local slip
deformation between the steel girder and the concrete deck occurs. However, when Qsd does not exceed
Qrd for each longitudinal length (Lab ) where the type and conﬁguration of shear connectors are kept
unchanged as shown in Fig.C15.4.1, the section is judged to possess adequate ﬂexural capacity as acomposite section. Hence, Eq.(15.4.1) and Eq.(15.4.2) are employed to check the safety limit state forshear connectors. To exert the full ﬂexural capacity as a composite section in such cases, it is necessarythat the shear connectors have suﬃcient deformation capacity as pointed out at 15.4.1(3).
The boundary of Lab can be taken at such points that the type and pitch of the shear connector arechanged, inﬂection points where the bending moment becomes zero and points where the maximum
or minimum bending moment is generated.
Qsd can be calculated as the diﬀerence between the axial forces Na and Nb in concrete deck (a and

CL
Na
xa
qsd

Nb

xb

qsd
Nb

Na
qrd

Msa

Msb

Qrd

Lab
xa

xb

Fig.C15.4.1 Horizontal design shear force and design strength

253

Chapter 15 Design of Composite Girders

b are arbitrary two sections in the deck).
Qsd = Nb − Na =

 xb

qsd dx(C15.4.1)

xa

On the other hand, Qrd can be calculated from
Qrd = nab Vud(C15.4.2)

where Qrd is the number of the shear connectors installed within Lab , and Vud stands for the design
shear strength of one connector.

15.4.5 Verification at fatigue limit state
At the fatigue limit state, shear connectors shall satisfy the following equation:
γiwhere ，

Vsd
≤ 1.0
Vrd

(15.4.3)

Vsd：Fluctuation of design shear force acting on an individual shear connector

Vrd
γi：Allowable ﬂuctuation of the design shear strength against fatigue.

or one group of the connectors.
：Structural factor【 Commentary 】

Vrd of a stud is written as Vsd in Eq.(C15.4.5) and Eq.(C15.4.6) in the commentary of 15.4.6.
15.4.6 Design strength of shear connectors
This clause covers rules regarding the design shear strength of (1) headed stud connectors, (2)perforated-plate dowels (perfobond ribs), and (3) block dowels. Use of the other types of shear
connector is of course allowed, but the design strength shall be properly determined throughexperiment or other methods.
15.4.6.1 Design shear strength of headed studs(1) The design strength of headed studs shall be determined by using appropriate methods withconsideration of the casting direction of the concrete for the deck.
(2) When headed studs are subject to tensile force as well as shear force and when the inﬂuenceof the tensile force is not negligible, a more accurate method enabling to consider the tensile
force shall be used.
(3) When headed studs are arranged in groups, inﬂuence of the grouped arrangement shall betaken into consideration by appropriate method(s).
【 Commentary 】(1) It is well known that casting direction of concrete aﬀects the shear strength of connector. As being
shown in Fig.C15.4.2, casting direction of the concrete associated with the structural system isclassiﬁed into 4 types, namely, type A: composite bridges, type B: lower ﬂange of corrugatedsteel-web bridges, type C and D : steel-RC mixed girder bridges or composite piers.
The design shear strength of a headed stud shall preferably be calculated by the following
equations given in Manual for Veriﬁcation of Performance of Hybrid Structures [JSCE, 2002].
・Safety limit state (Type A, B, C, D)254Standard Specifications for Steel and Composite Structures [Design]

The following two equations whichever generates a smaller value.
 + 10000)/γ
Vsud = (31Ass (hss /dss )fcdb
Vsud

= Ass fsud /γb(C15.4.3)(C15.4.4)

However, hss /dss > 4 ．
where, Vsrd : design shear strength of the stud (N) ，Ass : area of the shank of the stud (mm2 ),: design comdss : diameter of the shank of the stud (mm), hss : height of the stud (mm), fcd2
pressive strength of concrete (N/mm ) (=fck /γc ), fck : the characateristic compressive strengthof concrete (N/mm2 ), fsud : design tensile strength of the stud (N/mm2 ) (= fsuk /γs ), fsuk :characateristic tensile strength of the stud (N/mm2 ), γc : material factor of concrete (=1.3), γs: material factor of the stud (=1.0), γb : member factor (=1.3).
・Fatigue limit state(Type A, C, D)

Vsrd /Vsu0 = 0.99N −0.105(Type B)

Vsrd /Vsu0 = 0.93N−0.105(C15.4.5)(C15.4.6)

where,
Vsu0 = (31Ass + 10000)/γ(hss /dss )fckb

where, Vsrd : design shear strength of the stud for fatigue (range of ﬂuctuation) (N), N : fatigue
life or equivalent number of repeating cycles of load, γb : member factor (=1.0).
Most design of the headed stud connectors in Japan is done in accordance with the Highway
Bridge Speciﬁcation [JRA 2002]. However, the design shear strength of the headed studs described here is only for the serviceability limit state because this speciﬁcation is based on theallowable stress design method. In addition, application of the minimized-number main girders
bridge is not necessarily intended in this speciﬁcation.
The equations of Eq.(C15.4.3) - Eq.(C15.4.6) are obtained through multivariable linear regression analyses on the typical push-out test data [Hiragi,et al, 1989]. The correlation coeﬃcients forthe static strength and the fatigue strength are relatively high as 0.894 and 0.795, respectively.
The applicable range of the equations Eq.(C15.4.3) and Eq.(C15.4.4), which are valid for all thetypes of A to D for; the diameter of the shank of stud is 13–32 mm; the height of the stud is 50 210 mm; the tensile strength of stud is 402–549 N/mm2 , and the design compressive strength of
concrete is 14–63 N/mm2 . The applicable range of the equations Eq.(C15.4.5) and Eq.(C15.4.6)
for; the diameter of shank of stud is 13–22 mm; the height of stud is 60–150 mm; the tensile
strength of stud is 402–549 N/mm2 ; and the design compressive strength of concrete is 20–55
N/mm2 .
Neighboring sections of an intermediate support of composite continuous girders are subjected
to repeated negative bending moment due to the traﬃc load, accordingly the fatigue strengthof the steel ﬂange having welded studs was found to decrease in proportion to the shear force
acting on the studs [Kajikawa et al., 1985]. It is therefore desirable to reduce suitably the fatigue
strength of the headed studs which are calculated by Eq.(C15.4.5) or Eq.(C15.4.6), dependingon the magnitude of tensile stress acting in the ﬂange.
For fsuk , the lowest value given in speciﬁcations (for example, JIS B 1198 Headed studs:
fsuk = 400 N/mm2 ) shall be used. And, the member factor for the safety limit state γb shall be
1.3 with consideration of complex stress distribution around studs and the structural importanceof them.
(2) Headed studs shall be mainly used to resist the longitudinal and transversal shear force. Whenthe headed studs receive not only the shear force but also the tensile force and when this inﬂuenceChapter 15 Design of Composite Girders

255

can not be neglected, additional investigations are needed to decide the design strength of stud,to which references [e.g. Otani et. al, 1994] are available.
(3) Grouped arrangement of headed studs is useful when, for example, precast concrete deck panels
are used in a composite bridge. However, if the studs are arranged so closely, reduction of theshear strength per one stud may be induced due to overlapping of the concrete stress near thestuds. In this case, a suitable reduction factor to be used in Eq.(C15.4.3) - Eq.(C15.4.6) must
be determined while taking this inﬂuence into account. References [e.g. Okada et. al, 2006] canbe used for this evaluation.
The following points should be considered for application of the grouped arrangement of headed
studs.
• Non-uniform distribution of the longitudinal shear force.
• Possibility of slip or separation between the concrete deck and the steel girder.
• Buckling of the steel ﬂange.
• Local failure of the concrete deck due to high concentrated forces acting on the grouped
studs.
• In the case of precast concrete deck panels, shape of holes for installing the grouped studs,
the distance between the side face of a hole and the shank of studs, etc. [Kurita et al, 2005].

15.4.6.2 Design shear strength of perforated-plate dowels(1) The design shear strength of the perforated-plate dowels shall be separately evaluated forthe two cases by suitable way(s); one is that transverse re-bars run through a perforations
and the other is that transverse re-bars do not run through.
(2) The shear strength of a perforated steel plate itself shall be greater than the whole strength
as a shear connector.
【 Commentary 】(1) In perforated-plate dowels, the shear force is resisted with the portion of concrete ﬁlled into holesof the perforated steel plate as if the portion acts like shear connectors. The horizontal shear
force acting to the interface of the steel and the concrete deck is supported as the bearing stressof the concrete, and the steel plate which receives the reaction from concrete transmits the force
to entire steel girder through the ﬁllet welding between the plate and girder.
The design shear strength of perforated-plate dowels for the ultimate state may be calculated

Type

Direction of concrete
casting

A

B

C

D

Fig.C15.4.2 Classiﬁcation of headed studs depending on concreting irection

256Standard Specifications for Steel and Composite Structures [Design]

by the following equations:(a) For perforated-plate dowels without transverse re-bars: 1/2t2
3
Vaud = 3.38d
fcd − 121 × 10 /γbd(C15.4.7)

with the application limit as the followings based on experimental parameters:
35.8 × 103 < d2

 1/2t
fcd< 194.0 × 103
d(C15.4.8)

where d is the diameter of a perforation (mm), t is the thickness of the perforated steel plate(mm), fcd
is the deign strength of concrete (N/mm2 ).
(b) For perforated-plate dowels with transverse re-bars:





Vaud = 1.45 (d2 − φ2st )fcd
+ φ2st fst − 106.1 × 103 /γb(C15.4.9)

with the application limit as the followings based on experimental parameters:+ φ2st fst < 488.0 × 103
73.2 × 103 < (d2 − φ2st )fcd

(C15.4.10)

where φst and fst are the diameter (mm) and the tensile strength (N/mm2 ) of the re-bar. The
member factor γb can be 1.3.
Two equations Eq.(C15.4.7) and Eq.(C15.4.9) present design shear strength at the safety
limit state for the two kinds of perforated-plate dowels [Hosaka, et.al. 2000]. These equations
are obtained by a regression analysis of the logarithm type that puts experimental data of thestudies into the Leonhardt’s equation [Leonhardt, 1987]. Eq.(C15.4.7) is with considerationof thickness-diameter ratio (t/d), and Eq.(C15.4.9) takes the diameter as well as the tensile
strength of re-bars into consideration besides t/d. The correlation coeﬃcients calculated instatistical processing have high accuracy of 0.971 (without re-bars) and 0.979 (with re-bars), andthe curves derived from the equations lowered by two times of standard deviation so that theymight cover the scatter of experimental data. However, the applicable range of two equations
shall be properly set so as to produce positive value for the design shear strength.
Leonhardt[1987] proposed the equation for such case that no transverse re-bars were arranged,
because he considered that this type of share connectors was purely made of concrete, however, experimental studies [Hosaka, et.al. 1998] showed that the maximum shear strength of
perforated-plate dowels was improved by arranging the transverse re-bars. The ﬁrst term in
Eq.(C15.4.9) shows the shear strength given as concrete-connectors, and the second term shows
the shear strength added by presence of the transverse re-bars. Moreover, the transverse rebars can increase slipping capability at the contact area between the steel girder and concrete
deck, which in turn reduces drop of the post-peak bearing performance and raises the deﬂection
capability.
Although any problems about fatigue of this type connectors used in composite girders havenot been reported yet, suitable veriﬁcations shall be conducted when necessity of checking fatigue
safety of perforated-plate dowels or the welded portions arises.
(2) Shear strength of the perforated steel plate between one hole to another can be calculated inaccordance with [Leonhardt, 1987]:
Vr =100 σy√ As
60 3(C15.4.11)

where, Vr : Shear strength of the perforated steel plate (N), As : Cross-sectional area of the plate
between two holes (mm2 ), σy : Yield strength of the steel plate (N/mm2 ).

257

Chapter 15 Design of Composite Girders

The design shear strength of the steel plate calculated from Eq.(C15.4.11) shall exceed thedesign shear strength Vsd of perforated-plate dowels calculated in (1), and shall be veriﬁed withthe following equation.
γi

Vsd
≤ 1.0
Vrd

(Vrd =

Vr)γb(C15.4.12)

When the perforated-plate dowels are used in restrained concrete like inside a steel cell, etc.
where rise of the shear strength can be expected, proper examination to calculate real strengthis needed.

15.4.6.3 Design shear strength of block dowels
The design shear strength of block dowels shall be evaluated in proper way(s).
【 Commentary 】

Design strength of block dowels for the safety limit state can be calculated with the equation
Eq.(C15.4.13) or Eq.(C15.4.14) whichever yields smaller value when consideration of the fatigue is notneeded, and can be determined with Eq.(C15.4.15) when consideration of the fatigue is needed.
a) When considerations of the fatigue is not needed:

where,Vbud= (fbud A1 + 0.7fu A2 /γs )/γb(C15.4.13)

Vbud= (fbud A1 + 30φB/γc )/γb(C15.4.14)

Vbud： Design shear strength of block dowel without considerationof the fatigue (N).
fbud = ηfck /γc： Design bearing strength of the concrete in front of the block
dowel (N/mm2 ),here ，⎧⎨1.1
η=
⎩0.55 A/A1

(A ≥ 4A1 )(A < 4A1 )A1： Eﬀective bearing area of a block dowel (mm2 ).
A2： Cross sectional area of semicircle re-bar which is diagonally ﬁxed
to block (mm2 ).

A=

⎧
⎨2h2

(for deck without haunch)⎩b 0 hc(for deck with haunch)0h0： Thickness of the deck (mm).
hc： Distance between the upper surface of steel ﬂange and the uppersurface of deck (mm).
b0： Width at the lower end of haunch where the steel ﬂange and concrete deck meet (mm).
fu： Characteristics tensile strength of the steel (N/mm2 ).
φ： Diameter of semicircle re-bar which is diagonally ﬁxed to block(mm).
B： Width of the block (mm).
γc： Material factor for concrete, and can be generally set to 1.3.
γs ： Material factor for steel, and can be generally set to 1.0.
γb ： Member factor, and can be generally set to 1.3.

258Standard Specifications for Steel and Composite Structures [Design]

In both equations of Eq.(C15.4.13) and Eq.(C15.4.14), the ﬁrst term of the right hand side shows
the strength by the block itself, and the second term shows the strength by the semicircle re-bar.
Regarding this second term, Eq.(C15.4.13) is for the case when the semicircle re-bar governs thestrength, and Eq.(C15.4.14) is derived on condition that the upper limit of bearing strength of re-bars
suﬃciently embedded into concrete with appropriate cover is considered 30 N/mm2 .
b) When considerations of the fatigue is needed:= (fbud A1 )/γbVbud

(C15.4.15)


where, Vbud
： Fluctuation of design shear strength when considerationsof the fatigue is needed (N)γb： Member factor, and can be generally set to 1.3 ．

Portions where fatigue may occur are: (a) welded part between shear connectors and the steel
girder, (b) the semicircle re-bar, and (c) the concrete facing shear connectors, among which the part(c) is in mind here. However, contribution by the semicircle re-bar is omitted from Eq.(C15.4.15)
because the welded point of the re-bar seems to be vulnerable against cyclic loading.
The clauses and explanations given here follow [JSCE, 2002], but its original is written in [RTRI,
2000]. The block dowel is combination of a steel block or horseshoe-shaped steel plate and a semicircle
re-bar, and this type of shear connectors has been widely used in railway structures.
The slip of block dowel between the steel girder and concrete is small under ordinary service
condition, so veriﬁcation for the service limit state is not generally required. However, the performanceof this type of shear connectors diﬀers depending on direction, which heterogeneous eﬀect is notobserved in the headed stud connectors. The veriﬁcation equations shown here are for the longitudinal(along the bridge axis) horizontal shear force, and thus they are not directly applicable to the transverse(perpendicular to the bridge axis) horizontal shear.

15.4.7 Influence of steel girder plasticity on horizontal shear force
If the steel girder shows plastic behavior at the safety limit state, the horizontal design shear
force acting the connectors within this plastic zone shall be properly determined with considerationof this inﬂuence.
【 Commentary 】

When design is made on so-called compact section in which some portion inside the steel girder
enters the plastic range, it should be noted that the distribution of horizontal shear diﬀers from one
obtained with the linear elastic analysis because of this inﬂuence. The total horizontal shear force
from xa to xb section can be a diﬀerence of the axial force Na and Nb of the concrete deck as shownin Fig.C15.4.3. In this example, the axial force Na is calculated from conventional elastic beam theory
since the section at xa is assumed to be elastic. When the section at xb is full plastic, then the axial
force of the concrete deck can be obtained easily, but calculating the axial force is not easy when
the section at xb is partially plastic. In this case, N can be decided as the corresponding point toan arbitrary M on the line shown in Fig.C15.4.3 which linearly connects the initial yielding state(Ny , My ) and the full plastic state (Np , Mp ).

259

Chapter 15 Design of Composite Girders
CL

xa
Na

Nb
qsd

M
M

xb

Mp
My

Nb

Na
Msa

Msb
xa

xb

Np

Ny
N

Fig.C15.4.3 Relationship between bending moment and axial force of concrete deck

15.5 Detailing of Shear Connectors
15.5.1 Headed stud connectors(1) The standard shank diameter shall be 19mm or 22mm. For determination of material properties, types, shapes and proportions, it is desirable to obey JIS B 1198 Headed stud connectors.
(2) The maximum spacing of headed stud connectors shall be determined so that the required
performance as the shear connectors may be satisﬁed while preventing occurrence of bucklingof the ﬂanges of the girders and other undesirable behaviors.
(3) The minimum spacing of headed stud connectors shall be determined so that the required
performance as the shear connectors may be satisﬁed while allowing easy work execution
and preventing generation of harmful cracks in the concrete deck.
(4) The distance between the shank surface of a headed stud connector and the edge of thegirder ﬂange shall preferably be greater than 25mm.
(5) In a composite minimized-number main girders bridge, headed stud connectors shall bearranged with consideration of not only longitudinal shear force but also transverse shear
force as well as tensile force.
(6) Cross section of the concrete deck near headed stud connectors shall have suﬃcient safety
against the shear force acting from the connectors.
(7) Holes provided in precast concrete deck panels for installing the shear connectors shall haveappropriate details to enable doing easy work as well as avoiding local failure.

【 Commentary 】(1) Based on actual experiences in design and construction, a standard diameter of the shank is
decided 19mm or 22mm. Experimental study [JH, 1998] and analytical study [Okada et. al, 2005]
on the shear strength of 25mm diameter stud, however, were conducted, and real applications of
25mm diameter studs have been increased. Studs having other diameter than the standard values
can be thus used, if the required performance of the stud is properly evaluated by experiments
or analyses.
(2) As for the maximum spacing of the stud, Highway Bridge Speciﬁcation [JRA, 2002] gives theregulation that the required performance as shear connectors for composite girders can be re-260Standard Specifications for Steel and Composite Structures [Design]garded satisfactory when the maximum spacing of the studs is not greater than 3 times of thetotal thickness of the concrete deck nor 600mm. AASHTO[AASHTO, 2005] sets the maximum
spac-ing to be not greater than 800mm. Eurocode[CEN, 2003] decided the maximum spacing to
be not greater than 4 times of the total thickness of the concrete deck nor 800mm and also gave
additional restrictions for the class 1 or class 2 section depending on the thickness and the yieldstrength of the compressive ﬂange in order to prevent buckling.
(3) As for the minimum spacing of the studs, Highway Bridge Speciﬁcation [JRA, 2002] gives the regulation that the required performance as shear connectors for composite girders can be regarded
satisfactory when the longitudinal minimum spacing is 5d (d : diameter of the shank) or 100mm
whichever is larger and when the transverse minimum spacing is d+30mm. AASHTO[AASHTO,
2005] sets the minimum longitudinal and transverse spacing to be 6d and 4d, respectively. Eurocode 4[CEN, 2003] decided the minimum longitudinal spacing to be 5d and the minimumtransversal spacing to be 4d for rigid deck and 2.5d for other decks. Appropriate design is needed
based on these rules.
(4) This is in accordance with Highway Bridge Speciﬁcation [JRA, 2002], AASHTO[AASHTO, 2005]
and Eurocode 4[CEN, 2003].
(5) In a composite minimized-number main girders bridge or other similar types of bridges where thewidth of deck is large; elimination of the lateral bracings and simpliﬁcation of the cross girders
are often done, studs should be suitably arranged with consideration of the transverse force andthe tensile force which are induced by wind, earthquake, prestress, traﬃc load and so on.
(6) A cross section of the deck near the studs where local shear failure may happen, it is necessary
to check if adequate safety against the shear force acting on the headed studs is secured or not.
If needed, supplementary reinforcement should be arranged there. The head of a stud should be
generally embedded in main part of the concrete deck (instead of the haunch) deeper than 50mm
in order to exert enough anchoring eﬀect.
(7) The share holes provided in a precast deck panel shall have appropriate detail to allow easy
concreting work, and attention is also needed about the concrete property to be cast in-situ. For
example, the size of shear holes shall be large enough to accommodate the grouped studs andto compact concrete properly. Moreover, adequate reinforcement should be arranged to preventfrom local faire of the concrete at or near the shear holes.

15.5.2 Perforated-plate dowels(1) The thickness of a perforated steel plate and the diameter of the re-bars running throughthe perforations shall be properly determined.
(2) The diameter of the perforations shall be properly determined with consideration of compaction work and bleeding of the concrete.
(3) The maximum longitudinal spacing of two adjacent perforations shall be determined so as
to satisfy the required performance as the shear connectors.
(4) The concrete cover over the perforated-plate dowels shall be suﬃcient value.
(5) When two or more perforated steel plates are installed in parallel, suﬃcient transverse spacing shall be secured.
(6) Details of the perforated-plate dowels shall be determined with suﬃcient consideration of
fatigue.

【 Commentary 】(1) Perforated-plate dowels shall have enough strength against the bearing stress from concrete and,be preferably thicker than 12mm which is considered necessary by previous experiences in order to261

Chapter 15 Design of Composite Girders

induce shear failure of the concrete. In addition, the standard diameter of transverse re-bars is tobe 13mm, because the re-bars must resist not only the horizontal shear force but also lifting up of
the concrete deck. The steel portion of perforated-plate dowels placed in even compressive stresszone is basically free from occurrence of buckling due to conﬁnement given from the concrete.
(2) The diameter of the hole should preferably be more than the value equivalent to the diameter oftransverse re-bars plus the maximum aggregate size.
(3) The center-to-center spacing of perforations is desirably small as much as possible to transmit
the shear force smoothly, but 500mm or less that corresponds to 2.5 times of the minimum deck
thickness is regarded as a standard. In the case of larger spacing more than 500mm, enoughreinforcement around the perforated-plate dowels is needed.
(4) The cover from the top surface of concrete to the upper edge of perforated steel plate is preferably
more than 100mm. When the cover is thin, concrete bearing strength in front of the dowels andwhole strength as share connector will be reduced.
(5) When two or more perforated steel plates are arranged in parallel, their spacing is preferably wider
than the value of about three times of the height of plate, as the experimental result [Hosaka,
et.al, 2002] concluded that two shear connectors arranged in this manner did not inﬂuence eachother and the concrete in-between worked eﬀectively.
(6) Basically, perforated-plate dowels have high fatigue resistance [Taira, et.al, 1997]. It is necessary
to secure suitable distance from the bottom of perforations to the bottom of concrete deck forsake of keeping welding quality of the perforated-steel plates and the upper ﬂange of girder andavoiding generation of the fatigue cracks from the perforations. Especially when the perforations
are provided in very large tensile stress zone, veriﬁcation about fatigue of the main body as wellas the welded portion of the perforated-plate dowels is to be done.
It has been recently known that arrangement of two or more perforated-plate dowels in parallel,
instead of only one just above the web of girder, is eﬀective to raise the fatigue resistance when
the horizontal shear and uplifting force simultaneously act [Hosaka, et.al, 2002].

15.5.3 Block connectors(1) In block dowels having a semicircle re-bar, the angle between the re-bar and the uppersurface of steel ﬂange shall generally be 45 degrees.
(2) The standard thickness of steel plate and the diameter of a re-bar used in block dowels shallbe at least 16mm.
(3) Any shear connectors that may induce a wedge action to the concrete deck are not allowed.

【 Commentary 】

These clauses are quoted from [RTRI, 2000].

15.6 Veriﬁcation of Crack Width in Composite Girders
Crack width in the concrete deck due to composite action with a steel girder and crack width
due to local bending caused by the wheel load shall satisfy the following equations:
wmd
wa
wbd
γi
wa

γi

≤

1.0

(15.6.1)≤

1.0(15.6.2)

262

Standard Specifications for Steel and Composite Structures [Design]where ，

wa
γi

：Design critical value of crack width：Structural factor; for standard structures γi = 1.0【 Commentary 】(1) Design critical value of crack width
The design critical value of crack width for concrete decks shall be determined with consideration of environmental condition as well as a type and presence or absence of waterproof layer
in the concrete deck. If no special investigation about the critical crack width is carried out, thevalue given in Concrete Standard Speciﬁcation [JSCE, 2002] may be used. The critical crack
width is given there as a function of environmental conditions and cover C.
(2) Crack width due to main girder eﬀect
There are several methods to calculate the crack width of a concrete deck as shown in [JSCE,2002], [CEB/FIP-90,1993], [Hanswille, 1996, 1997] and [Nagai et.al, 2002]. The calculation
method proposed by Nagai et al. [2004] taking the initial crack state into account will be
explained below.
The design crack width wmd is given in term of the negative design bending moment for crack
width calculation Md :⎧wER −wCR⎨w
CR + MER −MCR (Md − MCR ) (MCR ≤ Md ≤ MER )(C15.6.1)
wmd =
⎩wER
(MER ≤ Md )where MCR is the negative bending moment at initial cracking, and MER is the negative bending
moment at the boundary from the initial crack state to the stabilized crack state. The initial
crack width wCR and stabilized crack width wER are obtained as follows.
a) Initial crack widthNCRβm NCRwCR = L−
− csd
(C15.6.2)(βm = 0.60)
Es As
Es As
where NCR = σm (1 + nρs )Ac is the axial force of a concrete deck at initial cracking; σm stands
for the stress at the middle section of the concrete deck; Es denotes the Young’s modulus of steel;As and Ac are the cross sectional area of re-bars and the concrete deck, respectively; n = Es /Ecis the modular ratio; ρs is the reinforcement ratio. csd denotes shrinkage, and may assign to
csd = −150μ under normal conditions. The crack spacing in the initial cracking sate is givenby:L=

σsr2 φ2.7fct (1 + nρs )(C15.6.3)

where σsr2 = NCR /As and fct is the tensile strength of concrete, and φ is the re-bar diameter.
b) Stabilized crack width


Md
βfct
βfct
wER = L
ysr +
−
− csd
(β = 0.2) (C15.6.4)
Es IstEs αst ρs
Es ρs
where αst = Ast Ist /Ag Ig ; Ast and Ist are the area and inertia moment of the steel girder withre-bars respectively; Ag and Ig are the area and inertia moment of the steel girder; ysr denotes
the distance between the centroid decided by re-bars as well as the steel girder and the upper
re-bars. The mean crack spacing in the stabilized state is:
L = 4C + 0.7(Cs − φ)where C is the pure cover of re-bars, and Cs is the pitch of re-bars.

(C15.6.5)

263

Chapter 15 Design of Composite Girders(3) Crack width due to deck eﬀect

wbd = L

σB
βfct
−
− csd
Es
Es ρs


(β = 0.2)(C15.6.6)

Reinforcement ratio(4) Minimum reinforcement required from initial cracking stage
The relationship between the crack width and the reinforcement ratio in the initial cracking
stage is obtained from Eq.(C15.6.2). The reinforcement ratio is thus led as a function of thecrack width as shown in Fig.C15.6.1 on condition that stress gradient within a concrete deckis neglected for simplicity and cracks generation occurs when the stress at the middle sectionof the concrete deck σm becomes the tensile strength of concrete, The approximate minimum
reinforcement ratio can be estimated from this ﬁgure.

0.024

φ=19mm
φ=22mmφ=25mm

0.022
0.02
0.018
0.016
0.14

0.16

0.18 0.2 0.22
Crack width [mm]

0.24

0.26

Fig.C15.6.1 Relationship between reinforcement ratio and crack width
in initial crack state (concrete tensile strength= 2.5N/mm2 , csd = −150μ )15.7 Eﬀective Width of Concrete Deck for Composite Girders
Eﬀective width of the concrete deck of composite girders shall be properly determined dependingon which limit state is under consideration.
【 Commentary 】

The eﬀective width given in Speciﬁcations for HIghway Bridges [JRA, 2002] is based on the linear
elastic theory, and the eﬀective width accordingly dose not change depending on the magnitude ofload. In the limit state design method, however, the eﬀective width may change depending on thecorresponding limit states. In the followings, the eﬀective widths for individual limit states will be
explained.
(1) Eﬀective width for ultimate limit states
In the ultimate state when the concrete deck for the compact section becomes inelastic, thewider eﬀective width can be expected than that in the elastic stress state owing to inelastic
redistribution of stress in the concrete deck. It is possible to estimate the eﬀective width directly
by means of FE analyses with consideration of shear-lag eﬀect. Unless a precise analysis suchas FEM or experiment is used, the eﬀective width at the ultimate state may be estimate inaccordance with Eurocode [CEN, 1997] or AASHTO [AASHTO, 2005].
(2) Eﬀective width for fatigue limit state
The eﬀective described in Highway Bridge Speciﬁcation [JRA, 2002] may be applied, because
the stress condition is nearly assumed to be elastic.

264

Standard Specifications for Steel and Composite Structures [Design](3) Eﬀective width for crack width calculation
Strain in re-bars in the concrete deck is needed for calculation of crack width in a concrete
deck. The eﬀective width Be is thus deﬁned as the width of the concrete deck for estimation of
the maximum strain εmax in the re-bars, and is obtained by integrating the re-bar strain εse over
the transverse width B1
εse ds(C15.7.1)
Be =εmax 0where the deﬁnitions of Be and B are shown in Fig.C15.7.1.
CL

B
Be

λ1

B*

λ2

Fig.C15.7.1 Deﬁnitions of eﬀective width Be and total width B

An eﬀective width equation Eq.(C15.7.2) [Okui et al., 2005] have been proposed for a standard
two I-girders composite bridge under the dead load as well as live load but without considerationof shrinkage of the concrete.
 
 2
B
B
Be0
= 1 − 1.09
(C15.7.2)+ 1.57
B
Le
Le
for 0.2 < B/Le < 0.35, where Le is the equivalent span length. In this equation, Be0 stands forthe eﬀective width, in which subscript e0 is used to clarify neglecting shrinkage.
Since the eﬀective width varies depending on the strain, a correction equation is also proposed:



2
εmax
Be
εmax
= 1.17 − 0.228(C15.7.3)+ 0.068
Be0
εcr
εcr
for 1 ≤ εmax /εcr ≤ 3.5, where εcr = fct /Ec is the concrete crack strain calculated form thetensile strength fct and Young’s modulus Ec of concrete.
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265

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Standard Specifications for Steel and Composite Structures – 2007
I. General provision, II. Structural Planning, III. DesignFirst edition 2007

Published byCommittee on Steel structure
Subcommittee of Standard Specifications for Steel and Composite Structures
Japan Society of Civil Engineers
Yotsuya 1-chome Shinjuku-ku Tokyo, 160-0004 JapanFax +81-3-5379-2769
http://www.jsce.or.jp
ISBN 978-4-8106-0565-5

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