Proceedings of the Hokkaido University COE Workshop on
High Performance Fiber Reinforced Composites for
Sustainable Infrastructure System –material modeling, structural design and application
Sapporo, Japan, February 9, 2007

EVALUATION OF BENDING AND SHEAR CAPACITIES OFHPFRCC MEMBERS TOWARD THE STRUCTURAL APPLICATION
Toshiyuki Kanakubo, Katsuyuki Shimizu
Department of Engineering Mechanics and Energy, University of Tsukuba, Japan

Tetsushi Kanda, Satoru Nagai
Kajima Technical Research Institute, Japan

ABSTRACTThis paper describes the outline of the first building structure applied Reinforced
ECC (Engineered Cementitious Composite) coupling beams and the quality
assurance system by bending test for this actual application. To have knowledge
for evaluation of performance of ECC members, the loading test for beamspecimens is conducted with ECC tensile evaluation tests involving uniaxial
tension test and bending test. From the test results, the conversion factors fortensile strength and ultimate tensile strain of ECC between uniaxial tension test
and bending test are investigated. The evaluation methods for bending and shear
strength of R/ECC beams are proposed using these material test results.
Keywords: Engineered Cementitious Composite, Uniaxial tension test, Bending
test, Tensile strength, Ultimate tensile strain, Beam

1 INTRODUCTION
High Performance Fiber-Reinforced Cementitious Composites (HPFRCC), which show a strain
hardening branch and multiple cracking under
uniaxial tensile stress, have been focused by lots ofresearchers because of its unique mechanical performance. Engineered Cementitious Composites (ECC),
which are introduced by Li [1], exhibit a maximum
tensile strain of several percent owing to thesynergetic effect of high-performance fiber andspecifically designed mortar matrix. Unprecedented
high-performance structural members can be expected when ECC is applied to seismic components.
The large numbers of worldwide studies on ECC
presented so far have been limited to laboratory scale
without experiences in full-scale plants. In 2005,
however, reinforced ECC structural elements(R/ECC elements, hereafter) were first applied inbuilding structure [2]. This application utilized
R/ECC in a coupling beam connecting two structural
walls in a 27-story high-rise RC building. The
coupling beam is expected to have large deformation
capacity and energy absorption performance under
the seismic load. In addition to these mechanicalproperties, it is expected that high restoration
performance due to multiple cracking leads sustainable building systems after the huge earthquake.

To realize this building structure, it wasinvestigated in the project that quality assurance offresh and mechanical properties of ECC in the actual
plant is highly reliable, and its tensile properties canbe verified by some test methods. A statisticalevaluation of tensile properties and knowledge ofperformance standards are indispensable to thedesign of ECC structural members. In these flows ofutilizing ECC, however, tensile properties of ECC
are held as a mortgage to have an enoughperformance in the element level. The tensile
strength and tensile deformability of ECC has notbeen considered directly to the structural design of
R/ECC elements because of lacks of knowledge ofperformance standards necessary for designing ECC
members. There have been insufficient discussions
on how to refer to the design standard on tensile
properties or how to evaluate structural performanceof ECC members with keeping advantages to use
ECC. These problems have been the obstacle tospread the usage of ECC in practical applications
and needed to be quickly resolved.
This paper describes the outline of the firstbuilding structure applied R/ECC coupling beams
and the quality assurance system by bending test forthis actual application. To have knowledge for
evaluation of performance of ECC members, wehave conducted the loading test for beam specimens.

1ECC tensile evaluation tests involving both uniaxial
tension test and bending test, which was applied tothe actual application, were carried out together for
all beam test. These test results are also reported inthis paper. After that, evaluation methods forbending and shear strength of ECC members are
discussed based on the test results.
CONSTRUCTION
Fig.1

Application of ECC coupling beam

Fig.2

Omni mixer in actual plant

Table 1

Inspection outline for ECC

Testing
Judgement
Frequency
specification
for approval
Slump flow JIS A 1150
530±100mm
Air content JIS A 1128
9±4%
Fresh
Fresh
Over 5 lessOnce a day than 40 deg.
temperatureor once for Over 36MPa
Compressive
JIS A 1108 each 150m3
strengthat 56day age
placing
TensileOver 2MPa
Mechanicalstrength JCI-S-003at 56day age
2005
Ultimate
Over 0.5%
tensile strain
at 56day age
Property

Inspection

60

100
R350

100

2.1 Outline of Application and Inspection of
ECC
R/ECC elements were first applied in building
structure as shown in Fig.1. This application utilized
R/ECC in a coupling beam connecting two structural
walls in a 27-story high-rise reinforced concretebuilding 93m high. The coupling beam was 500mm
wide by 900mm deep in cross section, and 1650mm
long. Structural features in this application arereferred to the literature [3].
These elements were produced one piece per day,for which ECC was mixed with an Omni-mixer inthe plant as shown in Fig.2. Production started in
November 2004 and was completed in June 2005.
Element products and specimens for inspection weresteam cured as for the full scale production
experiments, and then cured in a stock field for atleast 56 days.
The quality inspection process was determined asshown in Table 1, where lower bounds of tensile
properties were adopted at 2MPa for strength and
0.5% for ultimate strain. For compressive strength,
lower bound of 36 MPa, which is required fromnecessity in structural design, was adopted.
Tensile properties were inspected by bending test
specified by JCI-S-003-2005. In the project, both
uniaxial tension test shown in Fig.3 and bending testby 4 point loading shown in Fig.4 were executed toconfirm mechanical properties of ECC. The adopted
test method for uniaxial tension test has been
introduced by authors [4]. This tensile specimen isused to minimize the influence of fiber orientationand is expected to reproduce a more precise tensile
performance of ECC in a large size of members.
Sectional dimension in test region is 100 x 60mm
rectangle, which is 5 times larger than fiber length.
Support conditions are one of the important factors
for conducting uniaxial tension test for cementitious
materials. In actual loading, it is impossible toperform "pure tension" because of the nonuniformity of the material itself and variations in
specimen shapes and setup conditions. The "pin-fix"
ends condition is selected as the better way todecrease the effect of eccentricity moment of tensile
load and secondary moment after cracking [5].
Comparisons with uniaxial tension test results
performed by other test methods can be found on theliterature [5].

400

2 ACTUAL BUILDINGPROJECT USING ECC

R/ECC coupling beam

Steel
plate

Fig.3

Fig.4

Universal
joint

Uniaxial tension test

Bending test (JCI-S-003-2005)

2

The uniaxial tension test shown in Fig.3 requiresa larger specimen and hence longer preparation time
makes it difficult to adapt to a quality control routine
test in the production of ECC components. The
possible quality control method is the bending test,
which is more realistic than uniaxial tension test. For
the ultimate tensile strain and tensile strength,
bending test data analyzed by using JCI-S-003-2005
Appendix are compared with those of the uniaxial
tension test in Fig.5. It is shown that both ultimate
tensile strain and tensile strength of ECC can beevaluated on the safe side by multiplying by aconversion factor of 0.7 on the basis of bending test

Strength
Strain4

3 LOADING TEST ON BEAM SPECIMEN

3
2
1
Y = 0.7 X
0

1
2
3
4
5
6
Ultimate tensile strain (%)
or tensile strength (MPa) in flexural analysis

0

Fig.5 Tensile strength and ultimate tensile strain
correlation between tensile test and bending test

Slump flow (mm)700

Upper limit of approval

650

Fluctuation

600

Mean

550
500
Lower limit of approval

450

2.2 Results of Inspection of ECC
In the actual processing, all inspection items
were satisfied. The results of fresh property
inspection and mechanical property inspection are
depicted in Fig.6, where all fresh inspection data andall mechanical data satisfied the specification in
Table 1. In the 58 days of production, the lowest
magnitudes were: 36.3 MPa in compressive strength,2.37 MPa in tensile strength, and 0.59% in ultimate
tensile strain.

As described in Chapter 1, tensile properties of
ECC are held as a mortgage to have an enoughperformance in the element level in the previous
introduced application. The tensile strength andtensile deformability of ECC has not been
considered directly to the structural design of R/ECC
elements. In this chapter, bending shear test results
for beam specimens are reported in order tocomplement lacks of knowledge of performance

Air content(%)

Ultimate tensile strain (%)
or tensile strength (MPa) in test5

and associated analysis. Taking into account the easeof execution and simplicity of the apparatus, thebending test may be the most realistic solution for
quality control. Tensile properties of ECC were
inspected by bending test and the results in Fig.5 arereflected in the inspection process shown in Table 1.

400
0

10

20 30
40
Inspection case50

20Lower limit of approval Mean

0
0

10

20 30
40
Inspection case5060

Tensile strength (MPa)Fresh temperature inspection results
5
Mean

4

Fluctuation

3
2
Lower limit of approval

1
0
0

10

20
30
40
Inspection case

50

60Comp. strength (MPa)

Fluctuation

Fluctuation

Lower limit of approval10

20 30 40
Inspection case

50

60

60
55
50
45
40
35
30
25
20

Fluctuation
Mean

Lower limit of approval
0

10

20 30
40
Inspection case

50

60

Compressive strength inspection results
Ultimate tensile strain (%)

Fresh temperature (deg.)

Upper limit of approval

10

Mean

Air content inspection results

40
30Upper limit of approval

060

Slump flow inspection results
50

14
12
10
8
6
4
2
0

4
Fluctuation
3.5
3
2.5
Mean
2
1.5
1
0.5
0 Lower limit of approval
0.0 10 20 3040
50 60
Inspection caseTensile strength inspection results
Ultimate tensile strain inspection results
Fig.6 Results of inspection of ECC properties3

standards necessary for designing ECC members.
The results of tensile property evaluation tests
involving uniaxial tension and bending test are also
discussed in this chapter.
3.1 Used Materials for ECC
PVA fiber shown in Table 2 was utilized in theexperimental program. These values are given by
manufacturer. Mix proportions are summarized inTable 3. Fiber volume fraction was set to 1.5 and 2%.
Compressive strength at the testing age ranges from35.7 to 50.3MPa by using 100φ-200mm cylinder test
piece. Hereafter, ECC with 1.5% and 2.0% PVA
fiber volume fraction is identified as PVA15 and
PVA20, respectively.
Table 2

Properties of PVA fiber

Fiberlength
(mm)
12

Fiber
type
PVA

Table 3
Water bybinder ratio
0.42

Diameter(mm)
0.04

Tensilestrength
(MPa)
1600

Elastic
modulus(GPa)
40

Mix proportion of PVA-ECC
Sand bybinder ratio
0.77

Air content(%)
10Fiber vol.
fraction (%)
1.5, 2.0

3.2 Tensile Property Evaluation
Uniaxial tension test shown in Fig.3 and bending
test shown in Fig.4 were executed. Examples oftensile stress – tensile strain curves and bending
moment – curvature curves are shown in Fig.7 andFig.8, respectively. Tensile strain in uniaxial tension
test is calculated that elongation measured by
LVDTs is divided by gauge length of 160mm.
Curvature in bending test is calculated as the slope ofstrains obtained by LVDTs set on the compression
and tension side.
Both PVA15 and PVA20 shows pseudo strain
hardening behavior in tension, and deflection
hardening behavior in bending. We had a total of 11
batches for PVA20 and 2 batches for PVA15
specimens combinations. All test results are
summarized in Table 4. From 3 to 6 specimens were
tested in each batch and the results are averagevalues. Tensile strength of PVA20 and PVA15
obtained by uniaxial tension test is 3.7MPa and3.3MPa as average values, respectively. Ultimate
tensile strain, which is defined that the point wherestress begins to decrease continuously with increase

PVA15

Bending moment (kNm)

Tensile stress (MPa)5At first crack
At maximum load

4
3
2
1
0

0

1

2
3
Tensile strain (%)

At first crack
At maximum load

1

0

4

PVA15

2

0

100
200
Curvature (µ/mm)

300

100
200
Curvature (µ/mm)

300

Bending moment (kNm)

Tensile stress (MPa)

5
PVA20
4
3
2
1
0

0

Fig.7

1

2
3
Tensile strain (%)

Uniaxial tension test result
Table 4

PVA
15

PVA20

ID
Batch No.
No.1
No.2
No.3
No.4
No.5
No.6
No.7
No.8
No.9
No.10
No.11
No.1
No.2

1

0

4

PVA20

2

0

Fig.8

Bending test result

Test results and evaluation values by bending test

Uniaxial tension test
Ultimate tensile
Tensile strengthstrain
(MPa)
(%)
1.19
3.37
1.66
4.05
2.02
4.16
1.63
2.87
2.92
4.18
2.13
4.06
0.91
3.40
1.98
3.69
2.10
3.60
2.22
3.94
2.59
3.27
1.50
2.50
0.64
2.99

Curvature atmax. (1/m)
0.201
0.145
0.267
0.174
0.349
0.183
0.0839
0.297
0.344
0.370
0.382
0.124
0.0528

Bending test
Evaluation method
Maximum
momentUltimate tensile Tensile strength(kNm)
Strain (%)
(MPa)
2.07
1.72
4.58
2.03
1.21
4.57
1.66
2.36
3.59
1.33
1.49
3.01
1.53
3.10
3.33
2.11
1.53
4.75
1.86
0.67
4.33
2.16
2.56
4.83
2.30
2.99
5.07
2.00
3.22
4.41
2.25
3.32
4.97
1.66
1.02
3.83
1.55
0.41
3.66

4

in strain, of PVA20 and PVA15 is 1.9% and 1.1%,
respectively. The differences in strength and ultimate
strain due to fiber volume fraction are recognized.
Evaluation method for tensile strength andultimate tensile strain of fiber reinforced
cementitious composites has been introduced as theappendix of JCI-S-003-2005. The evaluation method
is introduced based on the following assumptions forstress distribution under the maximum bending
moment as shown in Fig. 9.
i) The stress distribution on the compression side istriangular.
ii) The stress distribution on the tension side isuniform (ft,b).
These assumptions represent a state in which thestrain on the tension edge has reached the ultimate
strain (εtu,b) but the stress on the compression edge
has not reached the compressive strength under the
maximum bending moment. It is considered thatthese assumptions generally agree with actual strain
and stress distributions of ECC.
xn

φu

and 0.7%, respectively. Fig.10 shows the comparisons of tensile strength and ultimate tensile strain
between obtained values by uniaxial tension test andevaluated value by bending test. From the regression
analysis, ultimate tensile strain and tensile strengthof uniaxial test is 0.85 and 0.82 of those of bending
test, respectively. Both values can be evaluated on
the safe side by multiplying by a conversion factor of
0.7 as same as Fig.5.
It is important to note that these conversion
factors may vary according to the material properties,
size of the bending test specimen and loading
conditions. This dependency originates from the factthat bending performance is a structural performancestrongly sensitive to specimen size and loading
conditions while tensile performance by nature canbe regarded as a material property. Thus, theprediction of tensile performance by means of abending test should be executed with special care of
the targeted materials, and the conversion factors
may vary depending on the bending test conditions.
At the present technical levels, the conversion
factors may not be derived theoretically and may bereasonably treated as experimental parameters.
A brief remark based on mechanics is presented
as follows. The difference on ultimate tensile strain
between tension test and bending test reflects easier
multiple crack formation under bending than under
tension. When the ultimate bending load exceeds theinitial cracking load during bending, an increase inflexural deflection is accompanied by multiple finecracking between the loads. This phenomenon is
known as deflection hardening, which isdemonstrated in Fig.8. Deflection hardening,although it looks similar to strain hardening under
tension as shown in Fig.7, occurs under milder
mechanical conditions than strain hardening. A
straightforward
exampleistheanalyticalconsequence by Naaman [6] that, when compressive
strength is high enough, the tensile strength of a

M max

f t,b

εtu,b

Fig.9 Stress distribution assumption (JCI-S-0032005)
Table 4 also includes the evaluation values fortensile strength and ultimate tensile strain by JCI-S003-2005 Appendix method. Tensile strength of
PVA20 and PVA15 evaluated by this method is
4.3MPa and 4.0MPa as average values, respectively.
Ultimate tensile strain of PVA20 and PVA15 is 2.2%

3

6
Ultimatetensilestrain(%)

Vf=2.0%Vf=1.5%

Obtained value by uniaxial tension test

Obtained value by uniaxial tension test

4

2

1
y=x
y=0.7xy=0.85x0

Fig.101
2
3
Evaluated value by bending test

4

5

Tensilestrength(MPa)

Vf=2.0%Vf=1.5%

4
3
2
1

0

y=x
y=0.7xy=0.82x1
2
3
45Evaluated value by bending test

6

Comparisons of tensile properties between uniaxial tension test and bending test evaluation

5

composite necessary to show deflection hardening is
one third of the strength of matrix cracking. Whenstrain hardening occurs under tensile loading, thetensile strength of the composite material should begreater than the matrix cracking strength. It is
important to note the difference between deflection
and strain hardening since multiple cracking occurs
more easily under bending than under tensile loading.
The difference on ultimate tensile strain between
tension test and bending test representing thedifference in conditions of multiple crack formation
in bending or in tension has a meaning that reduces
the ultimate strain predicted from a bending test.
The other difference on tensile strength between
tension test and bending test represents thedifference between tensile stress – strain relations
assuming perfect elasto-plasticity in Fig.9 and reality.
As can be seen from Fig.7, the stress-strain relationof ECC can in general be approximated as bi-linear
where stress increases gradually after initial cracking.
The predicted tensile strength is based on the perfectelasto-plastic model and is likely to be greater thanthat obtained in the uniaxial tension test (JCI-S-003-

2005 Appendix), and an error that may be involvedin the assumptions of the stress-strain relation forms.
3.3 Bending Shear Test on Beam Specimen(1) Specimen and loading method
The dimensions and reinforcing bar arrangements of the beam specimens are shown in Fig.11
and list of specimens are shown in Table 5.
Specimens have the 180 x 280mm size rectangularsection, and shear span ratio (M/QD) is 1.5 (Lspecimen) and 1.25 (S specimen). Arrangements ofmain bars and stirrups are D13 and D4 or D6 stirrup.
Parameters are PVA fiber volume fraction (Vf), shear
span ration, ratio of stirrup (pw) and yield strength ofmain bar (σy). Fiber volume fraction of PVA fiber
was set to 1.5 or 2.0%. Beam specimens named by
the last alphabet of F are designed to have flexural
yielding before failure. Other specimens aredesigned to show shear failure before flexural
yielding.
Loading was carried out by Ohno method underanti-symmentrical moment with monotoric manner.
LVDTs were set to measure relative displacement

Casting direction520

pw=0.60%

300

D6@59
480
8-D13 Strain gage
840
2480

820

Fig.11

Vf
Identification(%)
PVA15-00L
PVA15-15L
PVA15-30L
PVA15-60L
1.5
PVA15-89L
PVA15-89LF
PVA15-89S
PVA15-120S
PVA20-00L
PVA20-15L
PVA20-30L
PVA20-60L
2.0
PVA20-89L
PVA20-89LF
PVA20-89S
PVA20-120S

520

1040

30 35 35 30
150

280

180

Concrete

PVA-ECC

M/QD

1.50

1.25

1.50

820

Example of beam specimen arrangement (PVA20-60L)
Table 5 List of beam specimen
Main Bar
StirrupL
bxD(mm) (mm) Arrangement σy (MPa) Arrangement pw (%) σwy (MPa)
0.00
719
2-D4@93
0.15
295
2-D4@470.30
840
2-D6@59
0.60
711
334
2-D6@40
0.89
438
700

180
x
280

8-D13
pt=2.43%

691
719

840
711
438

1.25

700

691

4-D6@59
2-D4@93
2-D4@47
2-D6@59

1.20
0.00
0.15
0.30
0.60

2-D6@40

0.89

4-D6@59

1.20

427
295
334
427

6

(3) Test results
Beam specimens after loading are shown in
Fig.12, and shear force – translational angle curves
are shown in Fig.13. Bending and shear crack areobserved at 0.0025rad. The multiple cracks andrestrain effect of crack opening could be observed.
In beam specimens of shear failure type, when load
becomes around the maximum value, deformation
was concentrated on a certain one shear crack. The
width of other cracks decreased due to localized

between the stubs. Strain guages were set to measuremain bar and stirrup strain.
(2) Material test for PVA-ECC
Compression test using 100φ-200mm cylinder
test piece and bending test by JCI-S-003-2005 was
executed. The test results are shown in Table 6.
Tensile strength and ultimate tensile strain obtainedby JCI-S-003-2005 Appendix method is multipliedby 0.82 and 0.85, respectively, based on thediscussion in Section 3.2.

Table 6 Material test results of PVA-ECC
Compression test
Bending test*1
Elastic
Compressive
Strain at
TensileUltimate
Type
Specimen formodulusstrength
strength
strengthtensile strain
(GPa)
(MPa)
(%)
(MPa)
(%)
19.5
39.1
0.36
3.90
1.30
pw=0.00 - 0.30% L
PVA20
19.5
45.8
0.39
3.55
0.57
pw=0.60 - 0.89% L
19.9
44.3
0.48
3.93
0.91
pw=0.89 - 1.20% S
16.3
35.7
0.35
3.14
0.87
pw=0.00 - 0.30% L
PVA15
19.4
50.3
0.39
3.00
0.35
pw=0.60 - 0.89% L
17.4
42.0
0.42
1.98
0.36
pw=0.89 - 1.20% S*1 Obtained by JCI-S-003-2005 Appendix method multiplied by 0.82 for tensile strength and 0.85 forultimate tensile strain

PVA15-00L

PVA20-00L
Fig.12
pw=0.00%

PVA15-89S

PVA20-60L
Failure pattern after loading

PVA20-89S

400

PVA20-00L
PVA15-00L

Shear force (kN)Shear force (kN)

400

PVA15-60L

300
200
100
0

10

20

30

40

50

200
100

400

PVA20-89L
PVA15-89L

300
200
100
0

10

20

30

40

50
-3

Translationa angle (x10 rad)

20

30

40

50

60

Translational angle (x10 rad)Shear force (kN)Shear force (kN)

pw=0.89%10-3Translational angle (x10 -3rad)

400

PVA20-60L
PVA15-60L

300

0

60

pw=0.60%

60

pw=0.89% M/QD=1.25

PVA20-89S
PVA15-89S

300
200
100
0

10

20

30

40

50

60

-3

Translational angle (x10 rad)Fig.13 Shear force – translational angle curves7

Table 7 Test results of beam specimen
At maximum load
Ultimate
Translational angle (x10-3rad) at
FailureIdentification
angle*1
Main bar
Shear force
Trans. angle*2
Mode
Stirrup yielding(x10-3rad)yielding(kN)(x10-3rad)
PVA15-00L
143
8.7
10.4
S
PVA15-15L
2.60
170
15.0
17.9
S
PVA15-30L
3.27
183
12.0
14.3
S
PVA15-60L
8.34
296
16.9
31.1
S
PVA15-89L
11.8
22.7
344
23.3
>50
F -> S
PVA15-89LF
13.1
10.8
270*3
>50*3
>50
F
PVA15-89S
8.36
296
17.5
46.0
S
PVA15-120S
7.34
344
22.0
56.1
S
PVA20-00L
183
10.6
12.6
S
PVA20-15L
206
12.8
15.2
S
PVA20-30L
5.50
209
19.0
22.6
S
PVA20-60L
11.1
310
18.8
23.9
S
PVA20-89L
11.5
19.2
341
19.2
43.1
F -> S
PVA20-89LF
11.6
10.8
272*3
>50*3
>50
F
PVA20-89S
9.43
337
16.6
38.6
S
PVA20-120S
9.23
19.7
409
23.9
44.9
F -> S*1 : Translational angle when load decreases to 80% of Maximum *2 : S=Shear failure, F=Flexural yielding*3 : At the last point for deloading (1/20rad.)plasticity model. The ultimate tensile strain (εu) of
the model is given by 0.85εtu,b and tensile strength(σt) of the model is given by 0.82ft,b. Compressive
stress – strain relation is modeled by parabolic
curves referring to the compression test results.
These models are shown in Fig.14. Elastic modulus
for tension side is regarded as same as the elastic
modulus obtained by compression test (cE).
Compressive stressdeformation. The large difference between PVA15
and PVA20 specimen could not be recognized. In
PVA15-89LF and PVA20-89LF specimens, load isin process of increasing when translational angle
becomes 0.05rad.
Test results are summarized in Table 7.
Maximum load and translational angle at maximum
load increase as fiber volume fraction and stirrup
ratio also increases.
4 EVALUATION OF BENDING AND SHEAR
STRENGTH OF BEAM SPECIMEN
To complement the lacks of knowledge ofperformance standards necessary for designing ECC
members, we would like to propose evaluation
methods for bending and shear strength of R/ECC
members based on the test results. Material
properties are most important in evaluating member
structural performance. In this paper, material
properties for tension of ECC have been cleared byboth uniaxial test and bending test. In this chapter,evaluated value by JCI-S-003-2005 Appendix
method is adopted as tensile strength and ultimate
tensile strain of ECC. The conversion factors of 0.82
for tensile strength and 0.85 for ultimate tensile
strain is multiplied to these evaluated values.
4.1 Bending Strength
Bending strength is calculated by fiber analysis
under the assumption that plane section remains
plain. This basis is as same as the case of ordinary
reinforced concrete. The tensile stress of ECC isconsidered by representing model of tensile stress –tensile strain relations of ECC as perfect elasto-

σB

εB

0
Tensile stressCompressive strain

σt

cE

0

εu
Tensile strain

Fig.14Stress – strain models for fiber analysis.

84.2 Shear Strength
It is assumed that principal tensile stress of ECC
keeps tensile strength (σt) at shear failure. The
average of tensile stress on beam is expressed by σtwith a reduction factor (νt). We considered that beamspecimen exhibits the maximum load whencompressive strut is failed by principal compressive
stress as shown in Fig.15. As a matter of fact,compressive failure at crack zone of beam specimen
was recognized as shown in Fig.16. Because thecompressive strut has some angles with main shear
crack, local compressive failure takes place at thecrack surface. This approach has same way toordinary RC beam. In case of RC, shear transmitting
force at the crack surface is carried by mainly
bearing of coarse aggregate. In case of R/ECC, theforce is carried by bridging of fiber.

νt σt

jt

Co
mp
re s

Fig.15

siv

es

t ru
t

φ

In above formulas, effective coefficient ofcompressive strength of ECC (ν) is treated as sameas case of ordinary concrete proposed by fib.
Reduction factor for tensile strength of ECC (νt)
is unknown. We decided the value of νt by reverse
calculation using test results of beam specimens. The
result of reverse calculation is indicated in Table 8.
The value ranges from 0.27 to 0.56. The tendency by
any structural factor such as shear span ratio, stirrup
ratio and fiber volume fraction can not be observed.
The average for all specimens is 0.41.
Though the precise meaning of this reduction
factor is unknown, the followings may be pointed

Model for shear strength

加力終了後
After
loading

At最大荷重直後
max. load

Fig.16

Local compression failure on beam

If we use AIJ A-Method [7] as a basic formula toexpress shear strength, shear strength of R/ECC
beam is calculated as follows;
V = Vt + Va + VECC
Vt = b ⋅ jt ⋅ pw ⋅ σ wy ⋅ cot φ

Va = tan θ ⋅ (1 − β ) ⋅ν ⋅ σ B ⋅ b ⋅ D 2

tan θ =(

(L D ) + 1 − (L D )
2

(1)
(2)
(3)
(4)

β = 1 + cot φ ⋅ pw ⋅ σ wy ν ⋅ σ B)(5)

ν = 1.70σ B −0.333

(6)

2

⎧2.0
⎪
cot φ = min ⎨ jt ( D ⋅ tan θ )(7)⎪ ν ⋅σ ( p ⋅σ ) −1
Bw
wy⎩
VECC = b ⋅ jt ⋅ν t ⋅ σ t ⋅ cot φ(8)where,
V : shear strength
Vt : shear strength by truss mechanism
Va : shear strength by arch mechanismb : width of member
jt : distance between compression andtension bars
pw : stirrup ratio
σwy : yield strength of stirrup
σB : compressive strength of ECC
φ : angle of compressive strutθ : angle of arch mechanismν : effective coefficient of compressive
strength of ECC
D : depth of member
L : clear span lengthνt : reduction factor for tensile strength ofECC
σt : tensile strength of ECC

Table 8 Reverse calculation result for νt
Identification
νt
PVA15-00L
0.32
PVA15-15L
0.35
PVA15-30L
0.32
PVA15-60L
0.54
PVA15-89L
0.56
PVA15-89S
0.27
PVA15-120S
0.42
Average
0.40
PVA20-00L
0.40
PVA20-15L
0.41
PVA20-30L
0.34
PVA20-60L
0.54
PVA20-89L
0.49
PVA20-89S
0.28
PVA20-120S
0.44
Average
0.41

9

out.
・ ECC may not carry constant tensile strength
along the shear crack under complex bi-axial
stress field.
・ Superposition of each term for truss, arch and
ECC mechanism is based on the plasticity
theory. This may need some reductions forcertain term.

Max. shear force / bending strength

4.3 Verification
The experimental value of maximum shear force
in beam test is plotted with calculated shear strengthin Fig.17. Both maximum shear force and calculated
shear strength is standardized by calculated bending
strength in shear force. The calculated values are
estimated by former sections’ methods. In spite of
the constant value of νt, experimental values show
good agreement with calculated values.

1

0.5
PVA20
PVA15
Void：Shear failure
Solid：Flexural yielding

0

0.5

1

1.5

Shear strength / Bending strength

Fig.17Comparison of calculated strength

5 SUMMARIESThis paper described the outline of the firstbuilding structure applied R/ECC coupling beams
and the quality assurance system by bending test forthis actual application. To have knowledge for
evaluation of performance of ECC members, theloading test for beam specimens was conducted with
ECC tensile evaluation tests involving both uniaxial
tension test and bending test.
From the test results, the conversion factors fortensile strength and ultimate tensile strain of ECC
between uniaxial tension test and bending test as thematerial properties were found out. The evaluation
methods for bending and shear strength of R/ECC
beams were proposed using these material test

results.
It is most important that structural performanceof R/ECC members is evaluated and inspected bycertain material properties. In the case of ordinary
RC structure system, the compression test is the only
one method considering structural design of RC
members. In case of ECC and HPFRCC, it isindispensable to evaluate and inspect tensile
characteristics of material such as tensile strength,
tensile deformation capacity, and so on. The one
example using bending test by JCI-S-003-2005 wasintroduced in this paper for evaluation of themember strength.
REFERENCES[1] V.C. Li : From Micromechanics to StructuralEngineering -the Design of Cementitious
Composites for Civil Engineering Applications,
JSCE J. of Struc. mechanics and Earthquake
Engineering, 10(2), pp.37-48, 1993
[2] T. Kanda, S. Tomoe, S. Nagai, M. Maruta, T.
Kanakubo and K. Shimizu : Full Scale
Processing Investigation for ECC Pre-Cast
Structural
Element,
Journalof
Asian
Architecture and Building Engineering, Vol.5,
No.2, pp.333-340, 2006.11[3] M. Maruta, et al. : New High-Rise RC Structure
Using Pre-Cast ECC Coupling Beam, Concrete
Journal, Vol.43, No.11, pp.18-26, 2005 (inJapanese)[4] K. Shimizu, T. Kanakubo, T. Kanda and S.
Nagai : Shear Behavior of Steel Reinforced
PVA-ECC Beams, 13th World Conference on
Earthquake Engineering, Conference Proceedings DVD, Paper No. 704, 2004
[5] T. Kanakubo : Tensile Characteristics Evaluation
Method for Ductile Fiber-Reinforced Cementitious Composites, Journal of Advanced Concrete
Technology, Vol.4, No.1, pp.3-17, 2006
[6] A.E. Naaman : Toughness, Ductitlity, Surface
EnergyandDeflection-Hardening
FRC
Composites, Proceedings JCI International
Workshop on Ductile Fiber Reinforced
Cementitious Composites (DFRCC), pp.33-57,
2002[7] Architectural Institute of Japan : Design
Guidelines for Earthquake Resistant Reinforced
Concrete Buildings Based on Ultimate Strength
Concept, pp.106-116, 1990

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