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INFLUENCE OF CONCRETE TYPE AND STRENGTH
TO SHEAR BEHAVIOR OF RC PANEL

Masamichi ITOH*1, Yusuke KATOH*2 and Toshiyuki KANAKUBO*3

ABSTRACTCollins et al. reported a method to grasp the shear resistance of RC panels, considering the following three points;
compression characteristics of panels under tensile forces of concrete, softening field of panels in a relationship betweentensile stress and strain, and transmitting shear stresses across crack by aggregate interlock. Based on this report, anexperiment using more different cast materials and material strengths was performed and the evaluation method examined.
From the results, equations of tensile strain versus compressive strength were proposed when 50 MPa grade mortar wasutilized.
KEYWORDS: RC panels, bi-axial resistance, pure shear, stress versus strain, softening field

1. INTRODUCTION
In the past few decades, studies on shear resistance of reinforced concrete (RC) panels combining reinforcing
materials (rebars) and concrete have been reported. One of the most typical reports on these studies is the Modified
Compression-Field Theory (MCFT) by Collins et al.[1] Collins et al. proposed a method in which the shear resistance ofRC panels was understood, considering the following three points; compression characteristics of panels under tensile
forces of concrete, softening field of panels in a relationship between tensile stress and strain, and transmitting shear
stresses across cracks by aggregate interlock. In their study,
Bolt for LVDTHole to fix
however, only one kind of cast material and strength wasused. The effect of shear resistance of RC panels by varying
concrete strength and class was not clarified. In addition to acast material that Collins et al. used, higher strengths ofconcrete and mortar were prepared in this study. The sameexperiment was performed, and the results were analyzed in
the same way as Collins et al. did. The purpose of this study
is to examine the appropriateness of the evaluation method
proposed by Collins et al.

2. OUTLINE OF EXPERIMENT
2. 1 SPECIMENS

50Figure 1 shows a layout of a typical specimen. The
specimen size is 300×300×25mm. 24 holes were preparedfor a loading apparatus along the edges of the panel. Four40 40 40 40 40300
Fig. 150

Detail of specimen*1 Graduate student, University of Tsukuba*2 New Tokyo International Airport Authority*3 Assistant Professor, Institute of Engineering Mechanics and Systems, University of Tsukuba, Dr.E.

25unit : mm

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screw bolts for displacement transducers were located on each corner of the panel. The reinforcement bars were placed atintervals of 75mm parallel in both lateral and vertical directions. In addition, D4 deformed bars were prepared at 5mm and25mm from the edge of the panel in order to prevent loading locations from failure. As the parameters of the specimens,
two different kinds of concrete and one kind of mortar were used. Three different sizes of lateral and verticalreinforcements were utilized, which were D3, D4, and D6. Table 1 summarizes the details of the specimens.
Table 1 List of specimens
Reinforcements
IdentifiConcrete
cationtype
LateralVerticalρx (10-3)
C2-D33D3
2.83
D3
C2-D34D4
5.02
D320MPa
class
C2-D36
D611.3D3
concrete
C2-D44
D45.02
D4(C2)
C2-D46
D611.3D4
C2-D66
D611.3D6M5-D33
D32.83
D3
M5-D34
D45.02
D350MPaM5-D36
D611.3D3class
mortar
M5-D44
D45.02D4(M5)
M5-D46
D611.3
D4M5-D66
D611.3
D6C5-D33
D32.83D3
C5-D34
D45.02
D350MPaC5-D36
D611.3D3
class
concrete
C5-D44
D45.02
D4(C5)
C5-D46
D611.3
D4C5-D66
D611.3D6
ρ = (total sectional area of reinforcements) / (panel width×panel thickness)

ρy (10-3)
2.83
2.83
2.83
5.02
5.02
11.3
2.83
2.83
2.83
5.025.02
11.3
2.83
2.83
2.83
5.02
5.02
11.3

2. 2 MATERIALS
Table 2 shows the properties of concrete and mortar. The concrete strengths were designed as 20MPa and 50MPa.
Maximum diameter 8mm of coarse aggregates, maximum diameter 2.5 of fine aggregates, and standard Portland cement
were utilized for both kinds of concrete. The designed strength of the mortar was 50MPa. Pre-mixed mortar was used. The
properties of reinforcements are shown in Table 3. Three different deformed bars, D3, D4, and D6 were prepared asreinforcement bars.
Table 2 Concrete properties
Compressive
Elastic
Identifistrength
moduluscation(MPa)
(GPa)
C2
23.0
21.4
M5
48.5
20.5
C5
48.1
35.4

Table 3
Splittingstrength(MPa)
2.60
3.09
3.59

Identification
D3
D4
D6

Reinforcement properties
Yield
Elastic
Sectional
strengthmodulusarea(MPa)
(GPa)
(mm2)
7.07
222
225
12.6
290
200
32.0
412
186

2. 3 LOADING AND MEASUREMENT SYSTEM
Photo 1 shows the loading system. As shown in Photo 1, 24 oil jacks were used. The pure shear force was createdby loading tensile forces and compressive forces diagonal to the specimen. The 24 oil jacks were divided in two ways,
which were tensile and compressive. The loading jacks were controlled so as to create both tensile forces and compressive
forces uniformly. The measurement items were the load per an oil jack, deformations at each edge and a tensile diagonal,
and strains of rebars. Figure 2 and 3 illustrate the locations of displacement transducers and the placement of strain gauges,respectively. Arrows in both Figure 3 and 4 indicate loading directions of the oil jacks. The displacement transducers wereplaced at both sides of the panel. Four of the transducers were parallel to each edge (at 50mm from each edge) and one
was on a tensile diagonal. A gauge length of strain gauges was 1mm.

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D4

D1D5North
D3SouthD2

Photo 1 Loading system
3. TEST RESULTS

Down
3. 1 FAILURE PROCESS

Fig. 2 Set up of LVDTs

Shear stresses and shear strains were calculated using thefollowing equations with data of the experiment.

τ xy = 3 2 ⋅ P / (t ⋅ b )γ xy ={ 2 ⋅ δ − (δ + δ ) / 2 − (δ + δ ) / 2}/ l51324Up(1)0(2)

where,

τxy
γxy

G1G2NorthG4SouthG3

Casting
directionDownFig. 3

Position of strain gauges

3Shear stress τxy (MPa): shear stress of panel: shear strain of panelP: load per oil jackt
: panel thicknessb: panel width
δi: deformation by LVDTs (corresponding to Fig. 2): marked interval (=200mm)
l0Figure 4 illustrates a typical result of the shear stressversus shear strain curves. The three different lines in Figure 4
represent specimens that used deformed bars D3 for both lateraland vertical reinforcements. Some specimens were eventually
failed at the edge. However, shear stress versus shear strain
curves showed tri-linear type diagrams for most of thespecimens. The diagrams indicated that cracks of concrete,yield of rebars, and compressive failure of concrete occurred in
the failure process in this order. Table 4 summarizes the resultsof the experiment. The results include shear stress and strain
when the first crack occurred, shear stress at the ultimate
strength, the ultimate shear strain, and the final failure type. The
failure types were classified into three types as rebar rupture,edge failure, and concrete compressive failure. All strain gaugesof specimens D33, D34, and D44 indicated that thereinforcements of these specimens yielded before the specimens
failed.

2

1
C2-D33
C5-D33
M5-D33

3. 2 MAXIMUM SHEAR STRESS COMPARISONS

0Figure 5 illustrates the concrete compressive strength
versus the maximum shear stress for each specimen. Arrows inFigure 5 indicate that these specimens failed at the edge and themaximum stresses are possibly higher than the ones plotted.

12345-3

Shear strain γxy (×10 )Fig. 4

Shear stress versus shear strain curves

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C2-D33
C2-D34
C2-D36
C2-D44
C2-D46
C2-D66
M5-D33
M5-D34
M5-D36
M5-D44
M5-D46
M5-D66
C5-D33
C5-D34
C5-D36
C5-D44
C5-D46
C5-D66

C*-33
C*-44
M*-33
M*-44
Maximum shear stress (MPa)

Identification

Table 4 List of Test results
Cracking Cracking Max. Ultimate
Failurestrainstrainstressstressmode-3-3(MPa) (×10 ) (MPa) (×10 )
1.81
0.03
2.16
24.9 Rupture
1.660.37
2.34
78.6
Comp
0.76
0.02
2.75
0.68
Edge
1.37
0.06
2.71
0.91
Comp
1.86
0.13
2.72
1.92
Edge
1.42
0.26
3.04
2.69 Rupture
1.83
0.04
2.08
6.56
Comp
1.03
0.30
2.58
9.54
Edge
1.07
0.04
2.68
10.8
Edge
1.26
0.05
2.73
50.6
Comp
1.39
0.14
3.21
2.67
Edge
1.12
0.11
4.91
3.17
Edge
1.67
0.12
2.56
4.02
Edge
2.03
1.33
2.57
37.8
Edge
1.89
0.07
2.83
2.14
Edge
1.57
0.36
2.93
46.1
Comp
1.41
0.16
2.93
15.6
Edge
1.66
0.16
4.03
1.53
Edge

C*-34
C*-46
M*-34
M*-46

C*-36
C*-66
M*-36
M*-66
(4.91)

43220304050

Concrete compressive strength (MPa)Fig. 5Comparison of maximum shear stressy4. VERIFICATION OF PRINCIPAL STRESS AND STRAIN
The concrete principal tensile/compressive stress versus
principal tensile/compressive strain and the principal tensile stressversus compressive concrete strength of cracked concrete were derived
using the Mohr’s strain circle principle. The data used in this principle
were obtained from the strain calculated from displacement transducers.
The results were compared and verified to the equation proposed byMCFT.

εyτxyε1θεxε24. 1 CALCULATION METHOD
The concrete principal stress versus principal strain was derived
as follows. Figure 6 and Figure 7 show stress and strain states of panels
and the Mohr’s strain circle, respectively. Strain of x direction(εx) and
one of y direction (εy) are calculated from the displacement transducers.
The average principal tensile strain (ε1) and the average principal
compressive strain (ε2) are obtained from the Mohr’s strain circle. It is
assumed that the average strains of concrete and reinforcements are thesame. Based on this assumption, the tensile and compressive stresses of
the reinforcements are calculated from the perfectly elastic – plasticstress versus strain relationship. Since the concrete stress is thedifference between the total stress of the specimen and the stress ofreinforcements, the principal tensile and compressive stresses of theconcrete are calculated.

xτxy
Fig. 6

Stress and strain on panel

εxγxy / 22θε2
γxy / 2Fig. 7ε1εyMohr’s strain circle

4.2 PRINCIPAL TENSILE STRESS VERSUS PRINCIPALTENSILE STRAIN
The MCFT proposed the following equations for the relationship between the principal tensile stress and theprincipal tensile strain.

 f c1 = Ec ⋅ ε1 (ε1 ≤ ε cr )f cr
f =(ε1 > ε cr )
 c1 1 + 200 ⋅ ε1


(3)

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(4)

wherefc: compressive strength of concrete (negative) (MPa)The calculated values from Equations (3) and (4), and experimentresults for specimens C2 are compared in Figure 8. Some
specimens using 50MPa of concrete compressive strength andusing mortar indicated that the experiment results were lower thanthe calculated results. However, the experiment results generally
correspond to the calculation analysis.
4.3 PRINCIPAL COMPRESSIVE STRESS AND PRINCIPALCOMPRESSIVE STRAIN
The MCFT proposed the following equations for therelationship between the principal compressive stress and theprincipal compressive strain of concrete.

  ε   ε  2 f c 2 = f c 2 max ⋅ 2 ⋅  2  −  2    ε c   ε c  f c 2 max
1=≤ 1.0
0.8 − 0.34 ⋅ ε1 / ε cfc(5)(6)

where,
fc2
fc2max: principal compressive stress of concrete (negative): compressive strength of cracked concrete (negative)
εc: strain at compressive strength (negative)
Equation (5) represents the principal compressive stress of concrete
versus principal compressive strain of concrete at the purecompressive state, fc2max = fc. Equation (6) represents the decline ofconcrete compressive strength because of cracked concrete where
the tensile force works. Figure 9 compares the calculated resultsfrom Equations (5) and (6) to the experiment data for specimen
C2-D33. The experiment results generally correspond to thecalculation analysis.

Principal tensile stress / fcr

f cr = 0.33 − f c1
Test(C2)
Eq. (3)

0.8
0.6
0.4
0.2

0Fig. 8Principal compressive stress / fc

: principal tensile stress of concrete: elastic modulus of concrete
εcr: concrete strain at cracking
The equations above mean that the tensile stress of the concrete is
proportional to the tensile strain of the one until before concrete
cracks and that after concrete cracks, the tensile stress of theconcrete gradually decreases corresponding to the increase oftensile strain. The fcr represents cracking strength of concrete. The
equation, fcr, is as follows.

51015-3
Principal tensile strain ( ×10 )Principal tensile stress – strain curves

1Eq. (5), (6)Test (C2-D33)
Eq. (6)( fc2max =fc)

0.5

00.5
1
1.5
Principal compressive strain / εcFig. 9

Principal compressive stress – strain curves

1.5
Compressive strength / fc

where,fcl
EcC2C5M5Eq. (6)
Eq. (7)

10.54.4 PRINCIPAL TENSILE STRAIN VERSUS COMPRESSIVE
STRENGTH

051015Principal tensile strain / εcFig. 10

Compressive strength of cracked concrete

Figure 10 illustrates fc2 /fc versus ε1 /εc using the experimentdata. Equation (6) is represented as a dot line. In Figure 10,specimens that the fc2max could not be calculated because the Mohr’s strain circle did not cross to the y-axis in Figure 7
were excluded. Specimens C2 and C5 showed the experiment data were generally close to the calculation analysis byMCFT, regardless of the concrete strength. However, in terms of specimens using mortar, the experiment data tended to belower than the calculated values from the proposed equations. This is because the fc2max of specimens using mortar
decreased faster than the one of specimens using concrete. It is assumed that there was no aggregate in mortar which
supposed to make compressive stress stronger.

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f c 2 max
1=−
≤ 1.0
0.95 ⋅ ε1 / ε cfc(7)Figure 11 shows the difference of the calculation analysis
from Equation (6) and (7). The data of specimen M5-D44 wereadopted as a typical example of the shear stress versus shear strain.
The diagrams of Equations (6) and (7) were the same. However, it
indicated that the fc2max of Equation (7) declined as the shear strain
increased. In other words, it represented that a compression
failure tends to occur in the early phase.

5. CONCLUSIONS

5Shear stress τxy (MPa)

Equation (7) was obtained from the regression analysis by
the least square method (square deviation 0.28). The range ofx-axis value from this experiment was from 0.926 to 7.033.

43210Fig. 11Test (M5-D44)
using Eq. (6)using Eq. (7)02040
6080-3Shear strain γxy (×10 )Comparison of shear stress – strain curves

The calculation analysis by MCFT was compared to theexperiment results in terms of the concrete principal tensile/compressive stress versus principal tensile/compressive strain.
The principal tensile strain versus compressive strength of specimens using mortar represented that the calculation
analysis slightly differentiated from the experiment results. In order to improve this difference between the calculation
analysis and the experiment results, new equations were proposed for this relationship for specimens using mortar. Since
the calculation results corresponded to the experiment data for specimens using compressive strength grade 20MPa and50MPa of concrete, the proposed equations by MCFT were generally appropriate for both concrete.

REFERENCE[1] Vecchio, F.J. and Collins, M.P. : “The Modified Compression-Field Theory for Reinforced Concrete Elements
Subjected to Shear”, ACI Journal, pp.219-231, March-April 1986.