Effect of Reversed Loading on Shear Behavior of
Reinforced Concrete

Thammanoon Denpongpan

A Dissertation submitted to
Kochi University of Technology
In partial fulfillment of the requirements forthe Degree of Master of Engineering

January 2001

ABSTRACT
During Hyogoken-Nanbu Earthquake in 1995, severe damages were encountered inmany RC structures including RC column of bridge piers, which support highway andrailway. Observations showed that shear failures with diagonal shear crack wereprominent among those damages. During earthquake occurring, earthquake wave willproduce force in any direction. Hence reversed loading is appropriate to assimilate thiscondition. Therefore shear behavior of RC short beam under reversed loading isnecessary to investigate. RC deep beam is particular RC structures, which are usuallyfound in transfer girders used in multistory buildings to provide column offsets, infoundation walls, and shear wall. In contrast to an ordinary beam, the depth of beam iscomparable to its span length. RC short beam with a/d 1.5 have been selected in thisstudy. To clarify shear mechanism in concrete solely, RC short beams without web
reinforcement were studied at first place.
The experimental frameworks were divided into two series according to percentage ofmain reinforcement, 1.15 or 1.805%. Nine RC beam without web reinforcement were
tested in this investigation. All beams were doubly reinforced with equaling tension andcompression steel in each case. The variables were reinforcement ratio, 1.15 or 1.805%,
and loading pattern, monotonic or reversed loading. Deform bars having yield strength
364 N/mm2 for diameter 13-mm. and 336 N/mm2 for diameter 16-mm. were used as
flexural reinforcement. Ordinary Portland cement with limestone 40% replacement, sea
sand, crush sand, aggregate and superplasticizer were used. Same mix proportion ofself-compacting concrete (SCC) with medium strength between 52-58 N/mm2 was usedin this experiment. In the area where you cannot easily reach, SCC with medium to highstrength is appropriate to use in real application. Twelve 150x200 mm. cylinders were
cast to determine the concrete compressive strength including checking the concrete
compressive strength whether reaches target strength and tensile strength. All beam andcylinder specimens were cast and cured in similar conditions. The beam and specimens
were kept covered under polyethylene sheets until it reaches target strength and takenout 24 hours.
The test beams were simply supported and were subjected to mid-span one-point load.
To obtain consistency of experimental results, two specimens were subject to the sameload pattern for each series. Electrical strain gauges were placed at mid-span to measurestrain in tension steel. Linear Variable Displacement Transducers (LVDT) was placed at
all supports and mid-span point both sides for measuring support settlement due tobearing paste settlement, and mid-span deflection. Hence relative mid-span deflection
can be calculated. The load was applied by 1000 KN universal testing machine. Test
program was divided into monotonic and reversed loading. For revered loadings, thetest beams were over turned upside down manually. From the test, it can be realized thatexperimental set-up was important to control the precision especially position of midspan load. The load-unload paths were applied according to following stages: flexuralicrack, diagonal shear crack, and first yield of tension steel. After this first yield, control
displacement was applied.
The experimental results showed that RC beams without web reinforcement with low
a/d could sustain the load greatly even forming of diagonal shear crack. This enhances
capacity resulted from arch action, which transfers shear force directly through diagonal
shear strut. The available strength from arch action is largely dependent on whether the
resulting diagonal compression stress can be accommodated. The horizontal
compressive force in concrete and the tension in the main reinforcement have toequilibrate the load. The behavior of diagonal shear crack can explain as; at once
diagonal crack formed and spread toward the compression zone, this crack will
penetrate and stop at the compression face, hence no sudden collapse occurs. Until theload is greatly higher than that the diagonal crack first form, failure by crushing of
diagonal compressive strut or bond slip of tension steel will become.
Reversed loading gives identical yield load as same as monotonic but significantly
lower ultimate deflection. To compare this ultimate deflection, ductility, which
expresses the element capacity to undergo inelastic behavior and absorb energy, isappropriate to use. Several forms of ductility are available. In this study, displacement
ductility was investigated. Displacement ductility is defined as the ratio of deflection at
ultimate load to the deflection at first yield of the tension steel. Ultimate load is the
maximum load applied for a beam during the test. For monotonic loading, higher
reinforcement ratio, 1.805%, is higher displacement ductility compared to that of lower
one, 1.15%. For reversed loading of reinforcement ratio 1.15%, displacement ductility
decrease approximately 40% while that of reinforcement ratio 1.805%, displacement
ductility decrease more than 50%. Hence higher reinforcement ratios will be higher lossof displacement ductility under reversed loading.
Finite element program namely WCOMD, which had been developed in the Universityof Tokyo, was used in this analysis. Effective RC zone, which is related to the bondcharacteristic of reinforcing bar, had been implemented. FE analysis show good
agreement of yield load but slightly lower ultimate load than experimental one.
In conclusion, RC short beam without web reinforcement can carry load even formingof diagonal shear crack due to arch action, which transfer load directly to support
through diagonal compressive strut. Effect of reversed loading reduces significantly
displacement ductility after yield of tension steel approximately 40% for reinforcement
ratio between 1.15-1.805% with shear span to depth ratio 1.5. Further study should be
extended to normal concrete with compressive strength 30-35 N/mm2. Since shear spanto effective depth ratio of 1.0-2.5 is widely used, further study should be covering thisrange. Finally to approach real application, RC with web reinforcement should be exist.
Low reinforcement ratio is selected to study at first place.

ii

ACKNOWLEDGEMENTS
I would like to express my profound gratitude and deepest indebtedness to my advisor
Professor Hiroshi SHIMA for his valuable advise, constructive suggestions, tireless
guidance, and enduring patience throughout this study. Without him, I do not have achance to continue study in Japan. I would like to express my deepest gratitude toProfessor Hajime OKAMURA for his sharp suggestion, valuable guidance and kindness
through out this research work.
Sincere word of gratitude must also go to the Professor Mikio KADOTA, co-advisor,
and Professor Eijin OTANI, member of committee, for their valuable suggestion andcomments.
I would like to express my profound gratitude to Assistant Professor Masahiro OUCHI
for his kindness and constant support.
I would like to express my deepest indebtedness to Mr. Masaru UENO for his keen
technical support, valuable advice, health look after, and enduring patient through out
experimental works. Without him, very special technical problems cannot restore.
Sincere words of thank also go to Mr. Supakit Swatekititham and Ms. Krittiya
Kaewmanee for their help in early stage of experimental work. My deepest and mostsincere thanks are due to Mr. Songkram Piyamahant and Mr. Krit Kangvanpanich fortheir constant help throughout the crucial experimental work.
I would like to express my deepest appreciate to Mr. JUNG Jong-Hyuck and Mr. KIM
Hee-Jin for permanent encouraging me to keep study in Japan and endless moral
support, which absolutely contributed me to complete this dissertation and my life inJapan.
I, also, wish to thank Mr. Shigehisa Komatsu for his certainly help in all Japanese
documents and kindness in any request.
I would like to express my deepest gratitude to Ms. Kubo MARIKO, Japanese teacher,for her truly kindness throughout the Japanese course and extra Japanese custom.
I would like to express my sincere words of thank to Mr. Chayanon Hansapinyo,
doctoral student at Sirindhorn International Institute of Technology, Thailand, for his
constant support in any request.
Finally, I would like to express my deepest appreciation to my parent and brother for
their endless love and moral support that made me can endure and passed over the all
obstacles.

iii

CONTENTS

ABSTRACTACKNOWLEDGEMENTSCONTENTS

i
iii
iv

CHAPTER 1 INTRODUCTION
1.1 General
1.2 Objective and scope of study

11
1

CHAPTER 2 LITERATURE REVIEW
2.1 Source of shear transfer
2.2 Beam action and arch action
2.3 Behavior of deep beam without web reinforcement

2
2
3
4

CHAPTER 3 EXPERIEMNTAL PROGRAM
3.1 Test specimens
3.2 Material properties
3.3 Mixing method
3.4 Fresh properties and mechanical properties
3.5 Test procedure

6
6
7
9
9
10

CHAPTER 4 NUMVERICAL PROCEDURE
4.1 Analytical procedure
4.2 In-plain constitute models of reinforced concrete
4.2.1Model of uncracked concrete
4.2.2Model of crack concrete
4.2.2.1 Crack concrete in tension
4.2.2.2 Crack concrete in compression
4.2.2.3 Crack concrete in shear

12
12
12
12
17
17
17
19

CHAPTER 5 EXPERIEMNTAL RESUTLS AND
FINITE ELEMENT ANALYSIS
5.1 Experimental results
5.2 Effective size of RC zone
5.3 Analytical results

21
21
32
34

CHAPTER 6 CONCLUSION REMARKS
6.1 Concluding remarks
6.2 Further study

39
39
39

REFERENCES

40

iv

CHAPTER 1
INTRODUCTION
1.1 General
During Hyogoken-Nanbu Earthquake in 1995, severe damages were experienced
in many RC structures including RC column of bridge piers, which support highway
and railway. Observation shown that shear failure with diagonal shear crack wereprominent among those of them.
RC deep beam is particular RC structures, which usually found in transfer
girders used in multistory building to provide column offsets (Fig. 1-1), in foundation
walls, and shear wall. In contrast to an ordinary beam, the depth of beam is comparable
to its span length. The beam with shear span-to-depth ratio, a/d, less than 1.0 isclassified as deep beam, and a beam with a/d exceeding 2.5 as ordinary beams. The
beam between these two ranges is classified as short beam. RC short beam with a/d 1.5
have been selected in this study.
During earthquake occurring, earthquake force will introduce force
unsystematically. Hence reversed loading is appropriate to assimilate this condition.
Therefore shear behavior of RC short beam under reversed loading is necessary toinvestigate.

Fig. 1-1 Transfer girder [1].
1.2 Objectives and Scope of Study
The main objective of this research is to investigate effect of reversed loading on
shear failure behavior. To clarify shear mechanism in concrete solely, RC short beams
without web reinforcement were study at first place.

1

CHAPTER 2
LITERATURE REVIEW
2.1 Source of Shear Transfer
•
•

•
•
•

The transmission of shear force in concrete is mainly in the form of
Shear stress of concrete in compression zone, Vc. (Fig. 2-1)
Aggregate interlock across diagonal crack plan, Va. Aggregate interlock is
directly related to material properties of concrete i.e. maximum aggregate size,
shape of aggregate, and tensile strength of concrete. A shear force can transfer
via the bearing and overriding until crack width is large certainly.
Dowel action of longitudinal, Vd. Dowel action is mainly related to detailing of
reinforcement. In RC member, dowel action becomes active when cracking ismajor important; this stage is often reached in the ultimate load situation.
Shear reinforcement, Vs.
Arch action.

C
Va

VS

VC
T

Vd
VT

Fig. 2-1 Component of Shear force over crack plain.
From Fig. 2-1, the static equilibrium can express as follow
VT = VC + Vav + Vd + Vs
2.2 Beam Action and Arch Action
From Fig.2-2, the equilibrium of the section of beam between two crack can be
written as
M = T ⋅ jd
The relationship between shear and steel force can be written as2

Fig. 2-2 Shear stress between cracks [1]d(T ⋅ jd )dx
d (T )d ( jd )
V=
jd +
T
dx
dx
V=

3

If the lever arms, jd, remains constant as assume in elastic beam theory,d ( jd )= 0 thendxV=d (T )
jddx

where d(T)/dx is the shear flow across any horizontal plan between thereinforcement and the compression zone. This shear transfer mechanism is referred tobeam action, which represent by shear flow over cross section.
On the contrary, if shear flow equal zerod (T )
=0
dx

then

V =T

d ( jd )dx

This can occur if shear flow cannot be transmitted due to slip in main bar, or if
the transfer of show flow is prevent by an inclined crack extending from the applied
point load to support reaction. This shear transfer mechanism is referred to arch action(Fig. 2-3).

Fig.2-3 Arch action in a beam [1]2.3 Behavior of Deep Beam Without Web Reinforcement
The available strength from arch action is largely dependent on whether the
resulting diagonal compression stress can be accommodated. Short shear span, a/d from
1 to 2.5 develop inclined cracks, which able to carry the additional load by compressive
strut (Fig.2-4). A significant part of the load is transferred directly from the point ofapplied load to the support by this diagonal compressive strut. The horizontal
compression in concrete and the tension in the main reinforcement have to equilibrate
the load. The geometry of this mechanism, which contributes shear strength, is clearly
depending on placement of the loads and reactions. Failures usually due to crushing or
splitting in diagonal compressive strut, which is close relationship to a splitting test of
concrete cylinder.

4

Fig. 2-4 Strut and tile model [1]5CHAPTER 3
EXPERIMENTAL PROGRAM
3.1 Test Specimens
The experimental frameworks are divided into two series according topercentage of main reinforcement, 1.15 or 1.805%. Nine RC beam without web
reinforcement were test in this investigation. Fig.3-1 show beam dimensions,reinforcement details and loading arrangement for the beams. The test beams were
simply supported and were subjected to mid-span one-point load. To obtain consistencyof experimental results, two specimens were subject to the same load pattern for eachseries. Electrical strain gauges were instrumented at mid-span to measure strain in
tension steel. Linear Variable Displacement Transducers (LVDT) was instrumented at
all supports and mid-span point both side for measuring support settlement due tobearing paste settlement, and mid-span deflection. Hence relative mid-span deflection
can be calculated. The load was applied by 1000 KN universal testing machine. All
beams were doubly reinforced with equaling tension and compression steel in each case.
The variables were reinforcement ratio and loading pattern, monotonic or reversed
loading.

Fig. 3-1 Detail of test beam and testing arrangements (all dimension in mm.)6

3.2 Material Properties
Ordinary Portland cement with limestone 40% replacement, sea sand, crush sand,aggregate and superplasticizer were used. Same mix proportion of self-compacting
concrete (SCC) with medium strength between 52-58 N/mm2 was used in thisexperiment. In hard-to- reach area, SCC couple with medium to high strength isappropriate to use in real application. Twelve 150x200 mm. cylinders were cast to
determine the concrete compressive strength including checking the concrete
compressive strength whether reaches target strength and splitting test. All beam andcylinder specimens were cast and cured similar conditions. The beam and specimens
were kept covered under polyethylene sheets until 24 hours before testing. All materials
properties are shown in Table 3-1.
Table 3-1Material Properties of concrete ingredientSpecific Gravity Absorption (%)
Ordinary Portland Cement
3.15
Lime Stone Powder
2.7
Small aggregate
2.69
Large aggregate
2.69
Sea Sand2.57
1.91
Crush Sand
2.55
1.70

A rational mix-design method for self-compacting concrete was proposed by
Okamura et. al in 1993 (Fig. 3-2) [8]. In this concept, concrete is assumed to be a twophase material between coarse aggregate and mortar. Coarse and fine aggregate contents
were proposed to limit at 50% of the solid volume in concrete and sand content were
proposed to limit at 40% of mortar volume. At the given aggregate content level,
optimum superplastizer to powder content ratio, Sp/P, and optimum water to cement
ratio by volume, Vw/Vp will evaluated by trial and error technique.
Limited Aggregate
Content

50% of Solid
VolumeAppropriate Mortar

Limited Sand
Concrete

40% of Mortar
VolumeProper Flow ability
Vary W/P and
Sp/P
Proper Viscosity

Fig. 3-2 Outline of a rational mix-design method for self-compacting concrete

7

The concrete mix proportion for all specimens are shown in Table 3-2.
Table 3-2 Concrete Mix Proportion
Ordnary portland cement with 40% limestone replacment
w/c
0.504
%
w/p (volume)
0.95
%
Water
184
kg/m3
Ordinary Portland Cement
Limestone Powder

365
201

kg/m3
kg/m3

Sea SandCrush Sand

386.48389.52

kg/m3
kg/m3

Small Gravel
Large Gravel

592.7
253.8

kg/m3
kg/m3

Superplasticizer
4.924
Air Content
1.6
Note:
Sea Sand : Crush Sand (by volume)
Small Aggregate : Large Aggregate (by weight)
Superplasticizer

kg/m3%
50 : 50
30 : 70
0.87% by weight of powder content

W1

70% by volume of powder content

Deform bar having yield strength 364 N/mm2 for diameter 13-mm. and 336
N/mm for diameter 16-mm. were used as flexural reinforcement as shown by tensile
test in Fig. 3-3 and Table 3-3.
2

Fig. 3-3 Tensile test of reinforcement

8

Table 3-3 Properties of reinforcement
No.
Grade
Diameter Cross Sectional Areammmm2
DB13 SD 295 A
12.7
126.7
DB16 SD 295 A
15.9
198.6

Yield Strength
N/mm2
364
336

Young Modulus
N/mm2
203800203800

3.3 Mixing Method
Mixing order of all specimens are shown in Fig.3-4
Cement +Sea sand+
Crush sand +Limestone powder

W1

30 Second

W2+SP

90 Second

Aggregate

30 Second60
30 SecondFig. 3-4 Mixing method of SCC
3.4 Fresh Properties and Mechanical Properties
To ensure deformability and flow ability of self-compacting concrete, threestandard self-compacting tests had been implement. First, flow ability of fresh concrete
can measure by slump flow test; the optimum value (from test) is 650mm x 650mm.
Second, filling ability can measure by U-type box test; minimum requirement is 300
mm. Last, concrete segregation can measure by V-funnel test; the minimum
requirement is 10 sec. All concrete fresh properties are shown in Table 3-4.
Table 3-4 Properteis of Fresh Concrete
Beam Number Slump flow Filling Height

Funnel TimeConcrete Temperature

mmxmm

mm

sec

Cο

S1-1M

613 x 619

300

8.80

29.6

S1-2M

317

S1-5R

681 x 687
600 x 611
688 x 689
662 x 632

313

11.86
13.75
12.09
10.72

15.6
14.1
15.9
15.0

S2-1M

631 x 614

317

9.55

25.0

S2-2M

530 x 539
581 x 567
625 x 638

302

13.60
13.56
13.42

14.4
15.8
14.1

S1-3M
S1-4R

S2-3R
S2-4R

314
296

301

313

For mechanical properties of concrete, six standard cylindrical specimens ofeach test beam were used in compressive test. The maximum and minimum
compressive strength of concrete were cut off, and the rest were used to determine
average value. Four standard cylindrical specimens of each test beam also were used todetermine tensile strength of concrete by splitting test. It can realize that precise set-up
for splitting test is very important to obtained reliable data.

9

End

The empirical formula of tensile strength of concrete is used to compare withexperimental one.
2

f t = 0.23 f C `3

, fC `( N mm 2 )Testing program and mechanical properties of the tested beams are shown in
Table 3-5.
Table 3-5 Testing program and mechanical properties of the tested beams
Beam Number

Load Pattern

fc̀

fsp
2

S1-1M
S1-2M
S1-3M
S1-4R
S1-5R
S2-1M
S2-2M
S2-3R
S2-4R

N/mm
52.2
52.73
57.18
55.62
56.57
51.64
55.32
51.2
58.02

Monotonic
Monotonic
Monotonic
Reversed Cyclic
Reversed Cyclic
Monotonic
Monotonic
Reversed Cyclic
Reversed Cyclic

Diam.
2

N/mm
3.08
2.8
3.78
3.41
3.2
2.99
3.33

mm.
2φ13
2φ13
2φ13
2φ13
2φ13
2φ16
2φ16
2φ16
2φ16

ρ (%)

As
2

mm
253.4
253.4
253.4
253.4
253.4
397.2
397.2
397.2
397.2

3.5 Test Procedure
Test program is divided into monotonic and reversed loading. For revered
loadings, the test beams were over turn upside down manually as Fig.3-5. From the test,
it can be realizes that experimental set-up was important to control the precision of midspan deflection. The load-unload paths were according to following stage: flexural crack,
diagonal shear crack, and first yield of tension steel. After this first yield, control
displacement was applied.

10

1.15
1.15
1.15
1.15
1.15
1.805
1.805
1.805
1.805

Fig. 3-5 Over turn upside down manually for reversed loading11

CHAPTER 4
NUMERICAL PROCEDURE
4.1 Analytical Procedure
Finite element program, WCOMD-SJ, which had been developed at the
University of Tokyo, was used in this numerical analysis. The analytical program ismainly composed of programs WCOMRA and WCOMRC (Fig. 4.1). [5] The mainfunction and sub-program are explained as follow
WCOMRA: This part is deals with the input process. Input data are thedimensional shapes of the member composed of elements and the nodal data, andmaterial properties e.g. the elastic modulus and yield strength of reinforcement, and thecompressive strength.
WCOMRC: This is the main part, which reads nodal forces, nodal
displacement, incremental loads and indices for structuring the total matrix, andexecutes the analysis by using the element data.
INPUTG:
This sub-program reads the data of nodes, elements, and loads
from the input data file, arrange them and writes the indices for the data and overall
stiffness matrix on an external file.
MGN:
This sub-program reads the external data, calculates the B matrix
in the form of strain-node displacement matrix, and writes the calculated results on an
external file.
DISPI:
This sub-program initializes the data files for execution ofprogram WCOMRC.
MTRLRC:This sub-program describes the reinforced concrete plate element
model.
MTRLJO:This sub-program describes the reinforced joint element model.
MTRLRC and MTRLJO calculate stress from strains of each element, and give thevalue D matrix, which is necessary to construct the stiffness matrix for convergenceprocess to the main routine.
MTRLEL:
This sub-program describes the elastic material model.
PRINST:
This sub-program writes calculated stress and strain on an
external file.
WCOMRDM: This post-processing program process nodal displacements andexpress output in the form of load-displacement relationship.
WCOMRGP: This is another post-processing program, which process
deformation of shapes, stress distribution, strain distributions, crack pattern and failuremodes are graphically output.
4.2 In-Plain Constitutive Models of Reinforced Concrete
4.2.1 Model of Uncracked Concrete
The analytical model for concrete prior to cracking is constructed based onelasto-plastic and fracture model [5].

12Input Data

ProgramWCOMRA

ProgramWCOMRCDISPIMTRLRC

Post Processing Program

Load-Displacement Relations

MTRLJO
Node Data
INPUTGWCOMRDM

Load Data

MTRLEL
Deformation

Element
Data

SOLVENPRINST

MGN

Stress, Strain

Deformational shape,
Stress distribution,
Crack and failure mode

B Matrix

Note

WCOMRGP

External File

Fig. 4-1 Structure of WCOMR

13

Fig. 4-2 gives the schematic outline of elasto-plastic and continuum fracturingsystem [10]. Concrete elasticity is modeled as spring while concrete plasticity ismodeled as sliders. The damage in concrete is modeled as broken springs, which isirreversible process. Total stress is assembled from the internal stress, which develop
over the non-damaged elasto-plastic components. Then elastic strain is proportional
directly to internal stress intensity, which applies over these non-damage elatio-plastic
components.

Fig. 4-2 Schematic outline of elasto-plastic and continuum fracturing system
Therefore elastic strain is selected to represent the internal stress intensity thatgoverns the plasticity and fracturing in the concrete continuum. The index namely
fracture parameter, K, is introduced to represent the ratio of non-damage components,
which can carry the stress in concrete. The relationship between equivalent stress S andequivalent strain E is formulated with initial elastic modulus E0 =2, fracture parameter K,
and equivalent plastic stain EP as shown in Fig. 4-3. The equivalent plastic strain EP and
fracture parameter have been formulated solely with the maxi mum equivalent totalstrain as defined in Fig.4-4.
The advantage of this model is the capability to cover any loading history,
including unloading and reloading in biaxial stress states, which use one uniquemathematical expression.

14

Fig. 4-3 Uncracked concrete modeling, which express in the term of equivalentstress S, equivalent strain E and initial elastic modulus E0
The definition of equivalent stress and equivalent strain are express as follow

15

Fig. 4-4 Mathematical definition of equivalent plastic strain E P and fracture
parameter K

16

4.2.2 Model of Crack Concrete
4.2.2.1 Crack Concrete in Tension
Tension failure of concrete is accompany with growth crack. After forming of
crack, concrete in the crack plain cannot carry tensile force. In between crack concrete,concrete still continue carry tensile force by transmitting to reinforcing bar throughbond action. This phenomena is known as tension stiffening. The model of concrete
under tensile stress is independent of the spacing of cracks, the direction of reinforcing
bar and reinforcement ratio. Therefore the model is formulated in the term of average
stress and average strain as shown in Fig. 4-5.

Fig. 4-5 Stress transfers through bond action.
In the reversed loading, the former crack will close. Hence concrete stress cantransmitted both to main reinforcing bar and these close crack. The unload process will-6
bring surface of crack contact each other. A tensile strain of 150x10 had been given forthis mechanism. (Fig. 4-6)
4.2.2.2 Crack Concrete in Compression
The main factor that reduces compressive strength of concrete in two
dimensions is transverse strain. This concrete softening effect can account in the modelby reducing fracture parameter K of uncracked concrete as a function of the tensile
strain, which perpendicular to crack. (Fig. 4-7)

17

Fig. 4-6 Stress transfer by closing of crack

Fig. 4-7 Reduction in fracture parameter due to concrete softening as function oftensile strain perpendicular to crack18

4.2.2.3 Crack Concrete in Shear
The modeling of concrete under shear stress is based on contact density function(Li, et. al, 1989). The model is formulated based on two parameters; shear displacement,
δ, and crack width, ω, and applicable to any loading history. In reinforced concrete, theshear stiffness is depending mainly on the stiffness of crack plain.
In reversed loading, closing of the crack will increase shear stiffness of crack
plain. Uncracked concrete portion should be contributed to increase shear stiffness.
Parametric numerical analysis for any loading condition had been conducted to obtainthear model as shown in Fig. 4-8.

Fig. 4-8 Simplified shear transfer model.
The formulation of shear stress and shear strain are defined as follow:

19

20

CHAPTER 5
EXPERIMENTAL RESUTLS AND NUMERICAL ANALYSIS
5.1 Experimental Results and Discussion
To confirm the consistency of the test, three RC beam in series 1 and two RC
beam in series 2 subjected to monotonic loading were executed and the experimental
results with crack pattern are shown as follow
MONOTONIC LOADING
Px 1.15%160
Mid-span Point Load (KN)

140
120
100

S1-1M

80
60
40
20
0
0

1

2
3
4
Mid-span Deflection (mm)56Fig. 5-1 Mid-span deflection of specimen S1-1M under monotonic loading

Fig. 5-2 Crack pattern of specimen S1-1M under monotonic loading

21

Fig. 5-3 Mid-span deflection of specimen S1-2M under monotonic loading

Fig. 5-4 Crack pattern of specimen S1-2M under monotonic loading22

Fig. 5-5 Mid-span deflection of specimen S1-3M under monotonic loading

Fig. 5-6 Crack pattern of specimen S1-3M under monotonic loading23

Fig. 5-7 Mid-span deflection of specimen S2-1M under monotonic loading

Fig. 5-8 Crack pattern of specimen S2-1M under monotonic loading24

Fig. 5-9 Mid-span deflection of specimen S2-2M under monotonic loading

Fig. 5-10 Crack pattern of specimen S2-2M under monotonic loading25For reversed loading, two beam specimens in series 1 and two beam specimens
in series 2 were shown as follow

Fig. 5-11 Mid-span deflection of beam specimen S1-4R under reversed loading

Fig. 5-12 Crack Pattern of specimen S1-4R under reversed loading26

Fig. 5-13 Mid-span deflection of beam specimen S1-5R under reversed loading

Fig. 5-14 Crack Pattern of specimen S1-5R under reversed loading27

Fig. 5-15 Mid-span deflection of beam specimen S2-3R under reversed loading

Fig. 5-16 Crack Pattern of specimen S2-3R under reversed loading28

Fig. 5-17 Mid-span deflection of beam specimen S2-4R under reversed loading

Fig. 5-18 Crack Pattern of specimen S2-4R under reversed loading29Under monotonic loading, three beam specimens in series 1 and two beamspecimens in series 2 were combined in Fig. 5-19 and 5-20 respectively.

Fig. 5-19 Mid-span deflection under monotonic loading of beam in series 1

Fig. 5-20 Mid-span deflection under monotonic loading of beam in series 230

In series 1, for monotonic loading, three beam specimens show well agreementof first yield at 135 KN. After yielding of main reinforcing bar, load capacity gradually
increase until reach ultimate load due to strain hardening effect. These three beams
specimens have different compressive strength of concrete as follow 52.2, 52.7, and57.18 for specimen S1-1M, S1-2M and S1-3M, respectively. Shear capacity of RC
beam without web reinforcement should be depend greatly on web concrete
compressive strength. Therefore the difference on ultimate load should come from thedifference in concrete compressive strength. However to quantitative how much forthese effect, normal concrete and high strength should be conducted to compare withthese existing data. Another possible effect is environmental temperature, which affectcreep and plastic strain. Specimen S1-1 and S2-1 was tested in summer season (averagetemperature is 25o), while the rest were tested in winter season (average temperature is5o). The temperature difference is approximately 20o.
In series 2, for monotonic loading, two beam specimens show well agreement of
first yield at 188 KN. The ultimate load is slightly different as similar as in series 1.
However, in safe side, specimen S2-1M, which has lower ultimate load, should beselected.
From experimental in series 1 and 2 show that higher reinforcement ratio will
increase ultimate load and deflection under monotonic loading. In this case, increasingof reinforcement ratio from 1.15% in series 1 to 1.805% in series 2 by 57% will
increase ultimate deflection by 76%.
For reverse loading, the experimental results show that first yield load of RC
beam subjected to reversed loading is identical to that one subjected to monotonic. The
cross diagonal cracks in web concrete is not affect the first yield load because the crack,
which occur from load in opposite direction, will close as shown in Fig. 5-21.

Opening Crack

Closing Crack

Fig. 5-21 Closing crack in reversed loading.
The opening and closing of cracks will cause a deterioration of the concrete
resulting in stiffness degradation.
For reversed loading, the ultimate load is almost the same yield load as same as
monotonic but significant lower ultimate deflection. To compare this ultimate deflection,
ductility, which expresses the element capacity to undergo inelastic behavior and absorb
energy, is appropriate to use. Several forms of ductility are available. In this study,
displacement ductility was investigated.

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Displacement ductility factor, µ, is defined as the ratio of deflection at theultimate load to the deflection at first yield of the tension steel. [4]According to above definition, displacement ductility factor of all specimens areshown in Table 5-1.
Table 5-1 Displacement ductility factor of all specimens
Specimen No. Load Pattern
S1-1M
S1-2M
S1-3M
S1-4R
S1-5R
S2-1M
S2-2M
S2-3R
S2-4R

Monotonic
Monotonic
Monotonic
ReversedReversed
Monotonic
Monotonic
ReversedReversedρ (%)

Yield Deflection

FailureDeflection

Ductility Factor

1.15
1.15
1.15
1.15
1.15
1.805
1.805
1.805
1.805

mm
1.3
1.3
1.3
1.4
1.4
1.5
1.6
1.9
1.6

mm
5.1
5.3
10.1
3.3
3.0
9.0
16.3
4.1
3.1

δUltimate/δYield
3.9
4.1
7.8
2.4
2.1
6.0
10.2
2.2
1.9

For reinforcement ratio 1.15%, the effect of reversed loading will decrease
displacement ductility factor by 38% while that one for reinforcement ratio 1.805% will
decrease by 63%.
5.2 Effective Size of RC Zone
The size of RC zone in the finite analysis has an effect directly on stiffness ofmember. The past research by An X. proposed that size of RC effective zone is related
to the bond characteristic of reinforcing bar as Fig. 5-22. [2,3]After the forming of crack, stress in concrete will transfer to steel bar. Hencelarger concrete covering is earlier yield of steel bar. If the area of concrete is too large,
the stress increase should be limit to yield strength of steel bar. Hence the maximum
size of concrete zone for one certain bar can express as32

where AS :AC,max :fy:

area of steel bar,maximum area of bond effect zone in concreteyielding strength of steel bar.

Fig.5-22 Crack control capability and concrete area.
In the two dimensional finite element computations, equivalent maximum areaof bond effect zone, AC, max from circular shape to RC zone height as Fig. 4-7 is suitable
to implement as follow

Hence the height of RC zone used in computation isFig. 5-23 The height of RC zone in computation

33

5.3 Analytical Results
Finite element program namely WCOMD, which had been developed in the
University of Tokyo, was used in this analysis. Effective size of RC zone according to
An X., 1996, had been implement. RC element and plain concrete element in FE
modeling of specimen S1-2M are shown in Fig. 5-24

RC MeshPlain Concrete Mesh

Fig. 5-24 RC zone and PL zone of FE modeling of specimen S1-2M
The analytical result of specimen S1-2M is compare to experimental result asshown in Fig. 5-25.

Fig. 5-25 Comparison of analytical and experimental results.

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The crack pattern of analytical and experimental is shown in Fig. 5-26 and 5-27.

Fig. 5-26 Crack pattern of analytical result of specimen S1-2M

Fig. 5-27 Crack pattern of experimental result.

35

For series 2, specimen S2-1M, which has lower ultimate load, was selected forsafe side to model. RC element and plain concrete element in FE modeling are shown in
Fig. 5-28

RC MeshPlain Concrete Mesh

Fig. 5-28 RC zone and PL zone of FE modeling of specimen S2-1M
The analytical result of specimen S1-2M is compare to experimental result asshown in Fig. 5-29.

Fig. 5-29 Comparison of analytical and experimental results.

36

The crack pattern of analytical and experimental is shown in Fig. 5-30 and 5-31.

Fig. 5-30 Crack pattern of analytical result of specimen S2-1M

Fig. 5-31 Crack pattern of experimental result

37

The analytical result shows good agreement of yielding load with experimental
one. After flexural crack is presented, deflection of experimental specimen will increase
rapidly compare with analytical one. Strain hardening effect on experimental specimen
is gradually increasing the load, while analytical model cannot govern this part.
However for safe side, only accuracy of first yield load can cover design in realapplication in lower bound. Hence, the capability of present finite element program cancover the application of short beam with implementation of zoning method proposed by
An. X. 1997.

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CHAPTER 6
CONCLUDING REMARKS
6.1 Concluding Remarks
1. RC short beam without web reinforcement can sustain the shear force after
forming of diagonal crack because of arch action, which transfers the load
directly to support via diagonal compressive strut. Concrete strength in the
web of RC beam is the main parameter to control crushing-shear failuremode.
2. Reversed loading will decrease ultimate deflection because of material
deterioration, which results from crack opening and closing. Displacement
ductility factor of the beam under reversed loading will reduce
approximately by 40% of that one under monotonic loading.
6.2 Further Study
1. Shear strength of RC beam without web reinforcement is strongly related tocompressive strength of concrete. Normal concrete with fc`30-35N/mm2 isappropriate to compare with self-compacting concrete.
2. Application of deep beam with shear span to effective depth ratio 1.0-2.5 iswidely used. Experimental extend should be cover this range.
3. To enhance the precision of experimental results, reversed loading couple
with frame system should be implement.
4. To approach real application, RC with web reinforcement should be exist.
Low reinforcement ratio is selected to study at first place.

39

REFERENCES[1] James G. Macgregor, Reinforced concrete-Mechanics and Design, 3rd Ed., Prentice
Hall,1997.
[2] Koichi Maekawa, Xuehui An, Shear Failure and Ductility of RC Columns after
Yielding of Main Reinforcement, Journal of Engineering Fracture Mechanics 65 (2000)
335-368.
[3] An Xuehui, Failure Aalysis and Evaluation of Seismic Performance for Reinforced
Concrete in Shear, Doctoral Doisertation, The University of Tokyo,1996, pp.25-28.
[4] R. Park and T. Paulay, Reinforced Concrete Structures, John Wiley & Sons, 1975
pp.549[5] Hajime Okamura and Koichi Maekawa, Nonlinear Analysis and Constitutive Modelof Reinforced Concrete, Tokyo, Japan, 1991
[6] Standard Specification For Design and Construction of Concrete Structures-1986,
Part1 (Design), 1st Ed., JSCE
[7] Proceeding of The International Workshop on Self-Compacting Concrete, ConcreteEngineering Series 30, JSCE, 1998[8] Ouchi M., and Edamatsu Y., A Rational Mix-Design for Mortar in Self-Compacting
Concrete, Proceeding of the Six East-Asia-Pacific Conference on StructuralEngineering & Construction, Taipei, Taiwan, 1998
[9] Thomas T. C. Hsu, Unified Approach to Shear Analysis and Design, Journal of
Cement and Concrete Composite 20 (1998) 419-435[10] Paulus Irawan, Three-Dimensional Analysis of Reinforced Concrete Structures,Doctoral Dissertation, The University of Tokyo, 1995, pp.7-8, 130-139.

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