SHEAR BEHAVIOR OF MULTI-STORY REINFORCED
CONCRETE WALLS WITH OPENINGS
Rafik Taleb∗
MEE09187

Supervisor: Susumu KONO∗∗

ABSTRACT
Static loading test was conducted on five 40%-scale specimens in order to evaluate the shear transfer
mechanisms of structural walls with and without openings. The experimental variables were the sizeand location of openings. Failure modes for each specimen and in each direction of loading wereidentified, and connection between failure modes and the prediction accuracy of the maximum
strength by the design equations was made.
From experimental results, shear strength of specimens were estimated using the existing design
equations with AIJ and Ono reduction factors. It was shown that the shear strengths of specimens were
well estimated combining the shear strength of structural walls without openings estimated by truss
and arch mechanism equation and Ono’s reduction factor, and it was proved that this method may beapplied to structural walls with the opening ratio up to 0.46.
The two-dimensional finite element model constructed well simulates lateral load-drift angle relationand damage distribution for specimens with no or small openings. Both monotonic and cyclic analysis

was conducted.
Keywords: Multi-story structural wall, wall with openings, shear strength, strength reduction

factor.
1. INTRODUCTION
Multi-story structural walls, which are one of the most important lateral load carrying components inbuilding structures, often have openings for architectural reasons. The number, location and size of theopenings affect the stiffness and the strength structural walls with openings; however, it’s difficult toevaluate their shear strength and stiffness since the shear resisting mechanism has not been clarified.
The Japanese building design standard and guidelines employ strength and stiffness reduction factors
computed from the size of openings. This method is simple
and convenient but do not reflect the location of openings.
The strength reduction factor is given function the opening
ratio, η, which expresses the size of the opening. The

opening ratio, η, is expressed as:­ h0 ⋅ l0 l0 h0 ½
, , ¾
¯ h⋅l l h ¿η = max ®

(1)

Where h and l is the story height and length, h0 and l0 isthe opening height and length as shown in Figure 1.
∗Figure 1. Graphical representation ofopening in wall

National Center of Applied Research on Earthquake Engineering (CGS), Algeria.
Assoc. Professor, Department of Architecture and Architectural Engineering, Kyoto University, Japan.

∗∗− 55 −2. EXPERIMENT
2.1 Specimens
Five specimens were a 40% scale model of a lower three-story structural wall system taken from thetransverse direction of a typical six-story residential building in Japan. The third story was provided
for releasing the confinement caused by the stiff loading beam at the top as shown in Figure 2. Testvariables were the size and location of openings. N1 had no openings (η=0.0), S1 had small openings(η=0.3), M1 had medium openings (η=0.34), and L1 and L3 had large openings (η=0.46). The
opening location of L1 is eccentric; while for L3 is central. As one of the aims of this study was toclarify the effect of openings on the shear behavior of a structural wall, specimens were designed to
fail in shear prior to flexure. Table 1 shows the section size and reinforcement arrangement common tofive specimens. Experimental variables are listed in Table 1.
The AIJ shear strength reduction factor due to openings is expressed as follows:r = 1 −η(2)

AIJ standards (AIJ 1999, AIJ 2010) require that the ultimate shear strength of structural wall with
opening shall be computed by multiplying the reduction factor to the shear strength of structural wallwithout openings. This reduction concept can be applied as long as the opening ratio is less than 0.4 in
AIJ standard. This means that the ultimate shear capacity of N1, S1, and M1 can be obtained in thismanner but that of L1 and L3 are required to be computed as a frame composed of columns with astanding wall.
Loading Beam

Loading Beam

Loading Beam

Opening
200x400

Beam B2

Wing wallD6@100Wing wallD6@100Opening
400x800

Foundation Beam

Opening
500x800

Isolated Column

Wing wallD6@100Opening
400x800

Beam B2

Opening
500x800(b) S1(c) M1

Loading Beam

Loading Beam

Opening
750x200

Beam B3

Beam B2

Opening
750x1000

Wing wallD6@100Foundation BeamWing wallD6@100Opening
750x1000

Beam B2

Wing wallD6@100Boundary Column

Wing wallD6@100Isolated Column

Opening
750x1000

Beam B3

Boundary Column

Beam withhanging wall

Opening
750x1000

Foundation Beam(d) L1(e) L3

Figure 2. Specimen configurations and reinforcing bar arrangement− 56 −

Wing wallD6@100Foundation Beam

Foundation Beam(a) N1

Wing wallD6@100Boundary Column

Beam B3

Boundary Column

Beam withhanging wall

Isolated Column

Beam B2

Boundary Column

Wing wallD6@100Beam B3

Isolated Column

Boundary Column

Beam B3

Table 1. Reinforcement arrangement around the openings

MemberSection Longitudinal bar Shear reinforcement
size
SteelSteel
TypeType(mm)
ratio
ratio

Boundary300×300 8-D19column
Beam 200×300 2-D13
Wallt=80

2.55% 2-ĳ10@75 0.63%
0.47% 2-D6@100 0.32%

D6@100(Staggered) 0.4%
in both vertical and horizontal shear reinforcement

Table 2. Section size and reinforcing
bars in common
Opening Reinforcement around the openingratio
Vertical Horizontal Diagonal
N10
S1 0.30
1-D13
2-D10
1-D13
M1 0.34
3-D13
3-D10
L1 0.46
1-D16
2-D13
1-D16
L3 0.46
4-D13
4-D10

2.2 Loading system

Figure 3 shows the loading system. The cyclic reversal lateral load, Q, was applied statically at themidspan of the loading beam through two 2000kN hydraulic jacks. Loading was controlled bydisplacement at the mid-height of beam B3. The loading protocol was two cycles each at drift angles,
R, of ±0.05%, ±0.1%, ±0.25%, ±0.5%, ±0.75% and±1.0%. During the cyclic horizontal loading, verticalaxial loads were also applied by two 1000-kN
hydraulic jacks assuming that the specimens arerepresenting a part of the lower three stories of atypical reinforced concrete building with six stories.
Hence, the vertical axial load was determined inaccordance with the assumed long-term axial loads
for a six-storied wall with one span. Thus, 488 kN
B3(244 kN for each jack) was determined as the basic
axial load. Moreover, controlling two hydraulicjacks, two vertical axial loads were adjusted to eachB2other so as to keep the apparent shear span ratio(M/(Qd)) always 1.0, where M is the flexural
moment applied to the base of the wall, Q presents
the horizontal load applied to the loading beam, andd is the distance between the center to center
spacing between two side columns. (Warashina etal., 2008).
Figure 3. Loading system

2.3. Experimental Results
Figure 4 shows the damage observed in the specimens at R= 0.75%. The shear cracks in the wall
panels and the flexural cracks in the tensile column were observed at R=0.05%, and the number ofcracks increased until R=0.5%. The load reached the peak between R=0.5% and 0.75% and damage
progressed further after the peak load. At this stage, some longitudinal bars of the beams and thereinforcement of the wall were exposed due to the spalling of cover concrete. The buckling of the wall
reinforcement in the first story was also observed. At the final loading stage, the shear sliding of thewall occurred and the strength dropped suddenly. Three types of failure mode were observed at themaximum strength, namely, failure due to wide opening of shear cracks developed in wall panels andfloor beams, failure due to sliding between shear cracks in wall panels and floor beams and failure due
to shear of short span floor beam. Failure modes in all specimens were due to opening or sliding ofshear cracks in wall panels and floor beams except for S1 specimen which fail due to shear failure ofshort span floor beams.

− 57 −

(a) N1(b) S1(c) M1(d) L1(e) L3Figure 4. Observed damage at R=0.75%

3. PREDICTION OF SHEAR STRENGTH
The shear strengths are calculated from the design Eq. (3) in AIJ guidelines (2004) based on arch andtruss mechanism and the Arakawa design Eq.(4) in JBDPA (2001):
Vu = t wlwb psσ sy cot φ + tan θ (1 − β )twlwaνσ B 2(3)ª 0.053 pte0.23 (18 + Fc )º+ 0.85 pse .σ wy + 0.1σ 0e ».be . je
Qsu = «+MQ.
l0.
12()
¬¼

(4)

Where tw is the thickness of the wall panel, hw is the height of the wall,
lwb and lwa are the equivalent lengths of the wall panel in the truss
mechanism and the arch mechanism respectively, σB is the compressive
strength of concrete, σsy is the strength of shear reinforcement in thewall panel, ps is the shear reinforcement ratio in the wall panel, φ is theangle of the compressive strut in truss mechanism. And pte is theequivalent tensile reinforcement ratio, Fc is the concrete compressive
strength, be is the equivalent wall thickness, pse is the transversal
equivalence ratio, σwy is the yield strength of the transversal
reinforcement, σ0e is the axial stress, je is the stress center distance.
The maximum strengths observed in the test, Qexp, are compared withFigure 5. Area of diagonal
the calculated ultimate strengths, Qs, as shown in Figure 6 and Figure 7.
compression field
Both axes are normalized by the flexural strength, Qf, computed fromthe approximate design equation based on the flexural theory.
In this study, the AIJ’s reduction factors (AIJ 1999, AIJ 2010) based on opening size; while, the Ono’sreduction factors, ru, given by Eq (5) (Ono et al., 1995) is based on the compression field of theconcrete panel as shown in Figure 5 were used. For multi-story wall, Ono’s reduction factor can becalculated as the minimum of each story (approach 1) or as a one story wall (approach 2).
ru =¦ A / hle− 58 −(5)A good prediction is given by truss & arch mechanism equation while Arakawa’s equation gives
conservative prediction. The best prediction is guaranteed by truss & arch mechanism equation with
Ono’s reduction factor (approach 1).
1.2

1.2

Ono’s reduction factor(approach 1)

1.0

0.8

0.4

0.6

Negative direction

Positive direction
Negative direction

0.2

0.0

0.6
0.4

0.4

Positive direction

0.2

0.8
Qexp/Qf

0.6

0.5

1.0

1.5

00.0

Qs/Qf

Positive direction
Negative direction

0.20.00.0

Ono’s reduction factor(approach 2)

10.8
Qexp/Qf

Qexp/Qf

1.2

AIJ’s 1999 reduction
factor

1.00.5

1.0

Qs/Qf

0

1.5

0.5

1Qs/Qf

1.5

Figure 6. Experimental evaluation of truss and arch design equation
1.2

1.2

Ono’s reduction factor(approach 1)

1.0

0.8

0.4

0.8
Qexp/Qf

0.6

0.6
0.4

Positive direction
Negative direction

0.2

0.5

1.0
Qs/Qf

1.5

Positive direction
Negative direction

0.2

0.0

0.0

0.6
0.4

Positive direction
Negative direction

0.2

0.0

Ono’s reduction factor(approach 2)

10.8
Qexp/QfQexp/Qf

1.2

AIJ’s 2010 reduction
factor

1.00

0.0

0.5

Qs/Qf

1.0

1.5

00.5

Qs/Qf

1

1.5

Figure 7. Experimental evaluation of Arakawa design equation

4. FEM ANALYSIS
4.1. Analytical model
In order to simulate the restoring force characteristics and damage, apushover analysis was carried out using a two-dimensional FEM
analysis program. Figure 8 shows the finite element mesh for N1
specimen which employed four-node quadrilateral isoperimetricelements. The element size in the wall panels was 200x200mm.
Horizontal and vertical reinforcement was smeared assuming a perfectbond but diagonal reinforcement was neglected. The loading beam andthe foundation beam were assumed to be elastic. The concrete
constitutive law adopted for cracked concrete is based on the tension
stiffening model, the compression model and the shear transfer model(Naganuma et al., 2004). Stress-stain relationship of reinforcement
was based on Ciampi model (Naganuma et al., 2004).
Figure 8. Finite element
mesh for N1

4.2. Analysis results

Analytical lateral load-drift angle relations are compared with test results in Figure 9. The analyticalresults agreed well with the envelops of experimental results for all specimens. The Results illustrate avery good agreement for the maximum strength for all specimens. For the initial stiffness, the analysis
was smaller than the experimental value of both positive and negative loading direction for specimens
N1, S1 and M1. For specimens L1 and L3, the model slightly overestimates the initial stiffness. For
drift angle at the maximum strength, a good agreement is observed for specimens N1 and S1, while forthe other specimens, the model tends to underestimate it. This can be explained by the fact that forspecimens with large openings, there is certain contribution of flexural behavior.

− 59 −

N1

S1

400

0-400

㻠㻜㻜㻜
㻙㻠㻜㻜
㻙㻤㻜㻜

-800
Experiment
Analysis-2-10Drift Angle (%)

12

㻙㻞

㻙㻝

㻜
㻰㼞㼕㼒㼠㻌㻭㼚㼓㼘㼑㻌㻔㻑㻕㻙㻠㻜㻜㻱㼤㼜㼑㼞㼕㼙㼑㼚㼠㻭㼚㼍㼘㼥㼟㼕㼟

㻝

㻞

㻙㻞

㻙㻝

㻜
㻰㼞㼕㼒㼠㻌㼍㼚㼓㼘㼑㻌㻔㻑㻕

㻝

㻞

㻝㻞㻜㻜

L1

L3

㻤㻜㻜

㻠㻜㻜

㻸 㼍㼠㼑 㼞㼍㼘㻌㼘㼛㼍㼐 㻌㻔㼗 㻺 㻕㻸 㼍㼠㼑 㼞㼍㼘㻌㼘㼛㼍㼐 㻌㻔㼗㻺 㻕㻜㻙㻝㻞㻜㻜㻝㻞㻜㻜㻤㻜㻜㻠㻜㻜㻙㻤㻜㻜㻱㼤㼜㼑㼞㼕㼙㼑㼚㼠㻭㼚㼍㼘㼥㼟㼕㼟

㻙㻝㻞㻜㻜

-1200

M1㻤㻜㻜㻸㼍㼠㼑㼞㼍㼘㻌㼘㼛㼍㼐㻌㻔㼗㻺 㻕㻤㻜㻜㻸 㼍 㼠 㼑 㼞㼍 㼘㻌㻸 㼛 㼍 㼐 㻌㻔㼗 㻺 㻕

800

L a te ra l lo a d (k N )㻝㻞㻜㻜㻝㻞㻜㻜1200㻜㻙㻠㻜㻜㻙㻤㻜㻜㻠㻜㻜㻜㻙㻠㻜㻜㻙㻤㻜㻜㻱㼤㼜㼑㼞㼕㼙㼑㼚㼠㻭㼚㼍㼘㼥㼟㼕㼟㻙㻝㻞㻜㻜㻱㼤㼜㼑㼞㼕㼙㼑㼚㼠㻭㼚㼍㼘㼥㼟㼕㼟㻙㻝㻞㻜㻜㻙㻞㻙㻝㻜㻰㼞㼕㼒㼠㻌㼍㼚㼓㼘㼑㻌㻔㻑㻕㻝㻞㻙㻞㻙㻝㻜㻰㼞㼕㼒㼠㻌㼍㼚㼓㼘㼑㻌㻔㻑㻕㻝㻞

Figure 9. Lateral load–drift angle relationships

5. CONCLUSIONSThe observed damages and failure modes are affected by the openings size and location. Care should
be taken to short span beams to avoid their shear failure prior to the wall panels.
It was predicted that shear capacity decreases as the openings stay closer to the center of the wall panel
since diagonal compressive strut is difficult to form, especially for large openings. Damage aroundopenings affects also the formation of compressive struts.
The constructed FEM model was verified using experimental results. It was predicted that shear
capacity decreases as the openings stay closer to the center of the wall panel since diagonalcompressive strut is difficult to form, especially for large openings. Damage around openings affects
also the formation of compressive struts. The FEM results show that the shear resisting mechanisms
vary depending on the location or size of openings.
6. RECOMMENDATION
It is recommend, using the established FEM model, to perform a parametric study by varying theopening size and location in order to appreciate the accuracy of Ono’s shear strength reduction factor
more in depth. The main objective of such parametric study is to understand how the opening location
affects strength reduction factor.
AKNOWLEDGEMENT
I would like to express my sincere gratitude to my supervisor Pr. S. Kono and to Dr M. Sakashita from
Kyoto University for their continuous support, valuable help and guidance during my study.
REFERENCES
Architectural Institute of Japan (AIJ) Standard for RC structures, 1999, Tokyo.
Architectural Institute of Japan (AIJ) Guidelines for RC structures, 2004, Tokyo.
Architectural Institute of Japan (AIJ) Standard for RC structures, 2010, Tokyo. (in Japanese)
Japan Building Disaster Prevention Association, 2001, Tokyo.
Warashina M., Kono S., Sakashita M. and Tanaka H., (2008), 14th WCEE, China.
Naganuma K., Yoneza K., Kurimoto O. and Eto H., (2004), 13th WCEE, Canada.

− 60 −