Earthquake causes considerable damage to a large number of RCC highrise buildings and tremendous loss of life. Therefore, designers and structural engineers should ensure to offer adequate earthquake resistant provisions with regard to planning, design, and detailing in highrise buildings to withstand the effect of an earthquake and minimize disaster. As an earthquake resistant system, the use of coupled shear walls is one of the potential options in comparison with moment resistant frame (MRF) and shear wall frame combination systems in RCC highrise buildings. Furthermore, it is reasonably well established that it is uneconomical to design a structure considering its linear behavior during earthquake. Hence, an alternative design philosophy needs to be evolved in the Indian context to consider the postyield behavior wherein the damage state is evaluated through deformation considerations. In the present context, therefore, performancebased seismic design (PBSD) has been considered to offer significantly improved solutions as compared to the conventional design based on linear response spectrum analysis.
The growth of population density and shortage of land in urban areas are two major problems for all developing countries including India. In order to mitigate these two problems, the designers resort to highrise buildings, which are rapidly increasing in number, with various architectural configurations and ingenious use of structural materials. However, earthquakes are the most critical loading condition for all land based structures located in the seismically active regions. The Indian subcontinent is divided into different seismic zones as indicated by IS 1893 (Part 1) [
As an earthquake resistant system, the use of coupled shear walls is one of the potential options in comparison with moment resistant frame (MRF) and shear wall frame combination systems in RCC highrise buildings. MRF system and shear wall frame combination system are controlled by both shear behavior and flexural behavior; whereas, the behavior of coupled shear walls system is governed by flexural behavior. However, the behavior of the conventional beam both in MRF and shear wall frame combination systems is governed by flexural capacity, and the behavior of the coupling beam in coupled shear walls is governed by shear capacity. During earthquake, infilled brick masonry cracks in a brittle manner although earthquake energy dissipates through both inelastic yielding in beams and columns for MRF and shear wall frame combination systems; whereas, in coupled shear walls, earthquake energy dissipates through inelastic yielding in the coupling beams and at the base of the shear walls. Hence, amount of dissipation of earthquake energy and ductility obtained from both MRF and shear wall frame combination systems are less than those of coupled shear walls system in the highrise buildings [
Further, it is reasonably well established that it is uneconomical to design a structure considering its linear behavior during earthquake as is recognized by the Bureau of Indian Standards [
In the present context, therefore, performancebased seismic design (PBSD) can be considered to offer significantly improved solutions as compared to the conventional design based on linear response spectrum analysis. Performancebased seismic design (PBSD) implies design, evaluation, and construction of engineered facilities whose performance under common and extreme loads responds to the diverse needs and objectives of owners, tenants, and societies at large. The objective of PBSD is to produce structures with predictable seismic performance. In PBSD, multiple levels of earthquake and corresponding expected performance criteria are specified [
On the basis of the aforesaid discussion, an effort has been made in this paper to develop a comprehensive procedure for the design of coupled shear walls.
Coupled shear walls consist of two shear walls connected intermittently by beams along the height. The behavior of coupled shear walls is mainly governed by the coupling beams. The coupling beams are designed for ductile inelastic behavior in order to dissipate energy. The base of the shear walls may be designed for elastic or ductile inelastic behaviors. The amount of energy dissipation depends on the yield moment capacity and plastic rotation capacity of the coupling beams. If the yield moment capacity is too high, then the coupling beams will undergo only limited rotations and dissipate little energy. On the other hand, if the yield moment capacity is too low, then the coupling beams may undergo rotations much larger than their plastic rotation capacities. Therefore, the coupling beams should be provided with an optimum level of yield moment capacities. These moment capacities depend on the plastic rotation capacity available in beams. The geometry, rotations, and moment capacities of coupling beams have been reviewed based on previous experimental and analytical studies in this paper. An analytical model of coupling beam has also been developed to calculate the rotations of coupling beam with diagonal reinforcement and truss reinforcement.
The behavior of the reinforced concrete coupling beam may be dominated by (
There are various types of reinforcements in RCC coupling beams described as follows.
Conventional reinforcement consists of longitudinal flexural reinforcement and transverse reinforcement for shear. Longitudinal reinforcement consists of top and bottom steel parallel to the longitudinal axis of the beam. Transverse reinforcement consists of closed stirrups or ties. If the strength of these ties
According to IS 13920 [
Diagonal reinforcement consists of minimum four bars per diagonal. It gives a better plastic rotation capacity compared to conventional coupling beam during an earthquake when
Rotation capacities for coupling beams controlled by flexure as per FEMA 273 [
Type of coupling beam  Conditions  Plastic Rotation Capacity (Radians)  


IO  LS  CP  
Conventional longitudinal reinforcement with conforming transverse reinforcement 

0.006  0.015  0.025 

0.005  0.010  0.015  
Conventional longitudinal reinforcement with nonconforming transverse reinforcement 

0.006  0.012  0.020 

0.005  0.008  0.010  
Diagonal Reinforcement  NA  0.006  0.018  0.030 
Flexure dominant steel coupling beam 








Truss reinforcement represents a significant and promising departure from traditional coupling beam reinforcements. The primary load transfer mechanism of the system is represented by the truss taken to its yield capacity. A secondary load path is created by the global strut and tie. The load transfer limit state will coincide with the yielding of all of the tension diagonals, provided the soproduced compression loads do not exceed the capacity of the concrete compression strut. The yield strength of the primary truss is governed by the tensile strength of its diagonal; whereas, the primary truss transfer mechanism must include the shear travelling along the compression diagonal. According to Penelis and Kappos [
When the postyield rotational level is much higher compared to rotational level for truss reinforcement, then steel beam can be provided as a coupling beam. There are two types of steel beams which are provided as coupling beams based on the following factors as per Englekirk [
The bending moment capacity of coupling beam depends on the geometry and material property of coupling beam. Bending moment capacity and shear force capacity of the coupling beam are related with each other. Englekirk [
Shear capacity of coupling beam with conventional reinforcement can be calculated as
For Isection type of steel coupling beam, shear capacity (permissible shear resisted by web only) for shear dominant steel coupling beam is denoted as
The transferable shear force (
The rotation capacity in coupling beams depends upon the type of coupling beam. When the rotational demand is greater than rotational capacity of RCC coupling beam with conventional flexural and shear reinforcement then diagonal or truss reinforcement type of coupling beam could be provided depending on the
Rotation capacities for coupling beams controlled by shear as per FEMA 273 [
Type of coupling beam  Conditions  Plastic Rotation Capacity (Radians)  


IO  LS  CP  
Conventional longitudinal reinforcement with conforming transverse reinforcement 

0.006  0.012  0.015 

0.004  0.008  0.010  
Conventional longitudinal reinforcement with nonconforming transverse reinforcement 

0.006  0.008  0.010 

0.004  0.006  0.007  
Shear dominant steel coupling beam  0.005  0.11  0.14 
Rotation capacities for coupling beams controlled by flexure as per ATC 40 [
Type of coupling beam  Conditions  Plastic Rotation Capacity (Radians)  


IO  LS  CP  
Conventional longitudinal reinforcement with conforming transverse reinforcement 

0.006  0.015  0.025 

0.005  0.010  0.015  
Conventional longitudinal reinforcement with nonconforming transverse reinforcement 

0.006  0.012  0.020 

0.005  0.008  0.010  
Diagonal reinforcement  NA  0.006  0.018  0.030 
Rotation capacities for coupling beams controlled by shear as per ATC 40 [
Type of coupling beam  Conditions  Plastic Rotation Capacity (Radians)  


IO  LS  CP  
Conventional longitudinal reinforcement with conforming transverse reinforcement 

0.006  0.012  0.015 

0.004  0.008  0.010  
Conventional longitudinal reinforcement with nonconforming transverse reinforcement 

0.006  0.008  0.010 

0.004  0.006  0.007 
Rotation capacities for coupling beams as per Galano and Vignoli [
Type of coupling beam  Aspect ratio  Rotation Capacity (Radians) 


 
Conventional reinforcement  1.5  0.051 
Diagonal reinforcement  1.5  0.062 
Truss reinforcement  1.5  0.084 
Rotation capacities for coupling beams as per Englekirk [
Type of coupling beam  Aspect ratio  Rotation Capacity (Radians) 


 
Conventional reinforcement  1.5  0.02 
Diagonal reinforcement  1.5  0.04 
Truss reinforcement  1.5  0.06 
Specifications in Tables
As per Tables
When shear span to depth ratio
Conventional longitudinal reinforcement with nonconforming transverse reinforcement is not accepted for new construction.
If the behavior of coupling beam is controlled by flexure [aspect ratio
Similarly, specifications in Tables
For aspect ratio
The above study shows the inconsistent modeling parameters and inconsistent evaluative parameters. However, the behavior of coupled shear walls is controlled by the characteristics of various coupling beams. These characteristics depend on the following parameters:
Beam span to depth ratio.
Reinforcement details.
For this reason, more study is required to investigate into the limitations on behavior of coupling beams. Since computer programme ATENA2D [
Material, element, and reinforcement can be modeled individually, and
Geometric and material nonlinearity can be provided.
Only static loading in one direction can be applied.
There were eighteen RCC coupling beams and three different reinforcement layouts considered in the analytical program using ATENA2D [
The concrete (M20 grade) and steel (Fe 415 grade) were considered as two materials to model the coupled shear walls. The Poisson’s ratio was considered as 0.2. The unitweight of concrete was considered as 23 kN/m^{3} and the unitweight of steel was considered as 78.5 kN/m^{3}. Both coupling beam and shear wall elements were assigned as 4noded quadrilateral elements; material in coupling beam was assigned as SBeta (inelastic), whereas, material in shear wall was assigned as plane stress elastic isotropic.
Figure
(a) investigative model of coupling beam in ATENA2D [
Coupling beam  

Type 



Reinforced steel  
Longitudinal  Transverse  
Conventional beam with longitudinal and transverse conforming reinforcement  0.6 

585.4  8–10 
2legged 16 

1171  8–20 
2legged 25 

0.9 

623.5  8–10 
2legged 16 


1247  8–20 
2legged 25 

1.2 

661.7  8–10 
2legged 16 


1323  8–20 
2legged 25 
Coupling beam  

Type 



Reinforced steel  
Longitudinal  Transverse  
Beam with diagonal reinforcement  0.6 

585.4  8– 
2legged 16 

1171  8– 
2legged 25 

0.9 

623.5  8– 
2legged 16 


1247  8– 
2legged 25 

1.2 

661.7  8– 
2legged 16 


1323  8– 
2legged 25 
Beam  

Type 



Reinforced steel  
Longitudinal  Transverse  
Beam with truss reinforcement  0.6 

585.4  8– 
2legged 16 

1171  8–20 
2legged 25 

0.9 

623.5  8–10 
2legged 16 


1247  8–20 
2legged 25 

1.2 

661.7  8–10 
2legged 16 


1323  8–20 
2legged 25 
Initial sketch of the analytical model.
The depth of the wall is considered as
Here, Young’s modulus for concrete in beam
The results using ATENA2D [
Compare the Modeling Parameters and Numerical Acceptance Criteria with FEMA 273 [
Longitudinal reinforcement and transverse reinforcement 

Rotational limit at collapse prevention level (CP) in radians 
Crack width in coupling beam at CP level in meters by ATENA2D [  

Member controlled by flexure  Member controlled by shear  ATENA2D [ 

FEMA 273 [ 
FEMA 
FEMA 273 [ 
FEMA 356 [ 





 
Conventional longitudinal reinforcement with conforming transverse reinforcement 

0.025  0.025  0.015  0.020  0.000881  0.00104  0.002325  0.000263  0.000306  0.000559 

0.015  0.02  0.010  0.016  0.00348  0.00528  0.00886  0.0007125  0.001726  0.003124  
Diagonal 

0.03  0.03  —  —  0.00235  0.011  0.0111  0.000494  0.004315  0.00372 

0.03  0.03  —  —  0.00292  0.00833  0.00978  0.0005724  0.002961  0.003228  
Truss 

NA  NA  NA  NA  0.001176  0.000422  0.00093  0.0003144  0.0001066  0.000204 

NA  NA  NA  NA  0.001413  0.00297  0.0029  0.000344  0.0007514  0.00066 
Compare the Modeling Parameters and Numerical Acceptance Criteria with ATC 40 [
Longitudinal reinforcement and transverse reinforcement 

Rotational limit at collapse prevention level (CP) in radians 
Crack width in coupling beam at CP level in meters by ATENA2D [  

Member controlled by flexure  Member controlled by shear  ATENA2D [ 

ATC 40 [ 
ATC 40 [ 





 
Conventional longitudinal reinforcement with conforming transverse reinforcement 

0.025  0.018  0.0001023  0.000784  0.00198  0.0000001308  0.0005  0.001613 

0.015  0.012  0.0002423  0.001944  0.00344  0.00163  0.00136  0.00297  
Diagonal 

0.03  —  0.00012  0.000416  0.00055  0.0000194  0.0002184  0.00021 

0.03  —  0.000415  0.000422  0.001533  0.0001795  0.0001483  0.00093 
Hence, the results obtained from the above study using ATENA2D [
Schematic diagram of coupling beam.
The effect of gravity loads on the coupling beams has been neglected.
Deflection of the coupling beam occurs due to lateral loading.
Contra flexure occurs at the midspan of the coupling beam.
The confined concrete, due to the confining action is provided by closely spaced transverse reinforcement in concrete, is assumed to govern the strength.
Total elongation in the horizontal direction (Figure
Maximum rotations in radians.
Type of eeinforcement 

Value as per ( 
Galano and Vignoli [ 
Englekirk [ 
ATC40 [ 

Diagonal 


0.062  0.04  0.03 
Truss  1.5 to 4.0  0.03 to 0.08  0.084  0.06  — 
It can be observed from Table
Based on the above study, Table
Modified Parameters governing the coupling beam characteristics controlled by shear.
Type of coupling beam  Shear Span to Depth Ratio 

Type of detailing  Plastic Rotation Capacity (Radians)  


CP  
Reinforced concrete coupling beam 

No limit  Conventional longitudinal reinforcement with conforming transverse reinforcement 

0.015 

0.010  

Diagonal Reinforcement (strength is an overriding consideration and thickness of wall should be greater than 406.4 mm)  — 


1.5 to 4.0  Truss Reinforcement (additional experimentation is required)  —  0.03–0.08  
Steel coupling beam 

Shear dominant  — 

In this paper an attempt has been made to develop a technique to design coupled shear walls considering its ideal seismic behavior (stable hysteresis with high earthquake energy dissipation). For preparing this design technique, symmetrical coupled shear walls have been considered. Design/capacity curve of coupled shear walls is obtained at the collapse mechanism of the structure based on this technique. This technique is applied to both fixed base and pinned base coupled shear walls. To start with, this technique is useful in selecting the preliminary dimensions of symmetrical coupled shear walls and subsequently arrives at a final design stage. Further, this technique is particularly useful for designer, consultant and practicing engineer who have no access to sophisticated software packages. A case study has been done implementing the technique with the help of Microsoft Excel Spreadsheet and the results have also been validated.
In Figure
(a) Coupled shear walls. (b) Free body diagram of coupled shear walls.
The following assumptions are adopted for the design technique to obtain the ideal seismic behavior of coupled shear walls.
The analytical model of coupled shear walls is taken as twodimensional entity.
Coupled shear walls exhibit flexural behavior.
Coupling beams carry axial forces, shear forces, and moments.
The axial deformation of the coupling beam is neglected.
The effect of gravity loads on the coupling beams is neglected.
The horizontal displacement at each point of wall 1 is equal to the horizontal displacement at each corresponding point of wall 2 due to the presence of coupling beam.
The curvatures of the two walls are same at any level.
The point of contra flexure occurs at midpoint of clear span of the beam.
The seismic design philosophy requires formation of plastic hinges at the ends of the coupling beams. All coupling beams are typically designed identically with identical plastic moment capacities. Being lightly loaded under gravity loads they will carry equal shear forces before a collapse mechanism is formed. All coupling beams are, therefore, assumed to carry equal shear forces.
In the collapse mechanism for coupled shear walls, plastic hinges are assumed to form at the base of the wall and at the two ends of each coupling beam. In the wall the elastic displacements shall be small in comparison to the displacements due to rotation at the base of the wall. If the elastic displacements in the wall are considered negligible then a triangular displaced shape occurs. This is assumed to be the distribution displacement/velocity/acceleration along the height. The acceleration times the mass/weight at any floor level gives the lateral load. Hence, the distribution of the lateral loading is assumed as a triangular variation, which conforms to the first mode shape pattern.
The following iterative steps are developed in this thesis for the design of coupled shear walls.
Selection of a particular type of coupling beam and determining its shear capacity.
Determining the fractions of total lateral loading subjected on wall 1 and wall 2.
Determining shear forces developed in coupling beams for different base conditions.
Determining wall rotations in each storey.
Checking for occurrence of plastic hinges at the base of the walls when base is fixed. For walls pinned at the base this check is not required.
Calculating coupling beam rotation in each storey.
Checking whether coupling beam rotation lies at collapse prevention level.
Calculating base shear and roof displacement.
Modifying the value of
The steps which are described above have been illustrated in this section as follows.
The type of coupling beam can be determined as per Table
In Figure
In this step, it is explained how to calculate the shear force developed in the coupling beams for different types of boundary conditions. CSA [
So based upon the above criteria and considering (
For fixed base condition following equation can be written as
Therefore, based on the Assumption (
Values of constant






6  2.976  0.706  0.615  0.698 
10  2.342  0.512  0.462  0.509 
15  1.697  0.352  0.345  0.279 
20  1.463  0.265  0.281  0.190 
30  1.293  0.193  0.223  0.106 
40  1.190  0.145  0.155  0.059 
DC is 1 for pinned base condition from (
After obtaining
Overturning moment at a distance “
Resisting moment in wall due to shear force in the coupling beam at a distance “
Consider (i) Tensile forces at the base of wall 1 (
(ii) Compressive loads at the bases of wall 1 and wall 2 are calculated due to gravity loading.
(iii) Net axial forces at the bases of wall 1 and wall 2 are calculated, that is, Net axial force
(iv) Then, according to these net axial forces for the particular values of
(v) Therefore, if calculated bending moment value at any base of the two walls is greater than yield moment value, plastic hinge at that base would be formed, otherwise no plastic hinge would be formed.
The rotation of coupling beam in each storey is determined in Figure
Rotation of coupling beam at
For plastic hinge rotation at the fixed base of wall or real hinge rotation at the pinned base of wall, (
Deformed shape of a
The rotational limit for collapse prevention level of different types of RCC coupling beams and steel beams are given in Table
The roof displacement can be calculated as per the following equations
The
To obtain the collapse mechanism of the structure, it is required to increase
The following numerical example has been considered to validate the propose design technique. In this study, plan and elevation with dimensions and material properties of the coupled shear walls have been adopted as given in Chaallal et al. [
The coupled shear walls considered here are part of a 20storey office building (Figure
Dimensions and material properties of coupled shear walls for validation of proposed design technique.
Depth of the wall ( 
4 m 
Length of coupling beam ( 
1.8 m 
Depth of coupling beam ( 
600 mm 
Number of storeys ( 
20 
Wall thickness ( 
300 mm 
Width of coupling beam ( 
300 mm 
Storey height ( 
3.0 m 
Modulus of concrete ( 
27.0 GPa 
Modulus of steel ( 
200.0 GPa 
Steel yield strength ( 
415 Mpa 
(a) Plan view of building. (b) Coupled shear walls at section “aa”.
Figures
Dead loads (DL) of 6.7 kN/m^{2} and live loads (LL) of 2.4 kN/m^{2} have been considered as suggested in Chaallal et al. [
The modeling of coupled shear walls involving Figure
Modeling in SAP V 10.0.5 [
Bilinear representation for Capacity Curve.
The obtained design/capacity curve from the proposed design technique, SAP V 10.0.5 [
It can be seen from Figure
Coupled shear walls at section “aa” as shown in Figure
RCC coupling beam with Conventional longitudinal reinforcement and conforming transverse reinforcement in each storey has been selected as per Step
Ductility of coupled shear walls considering different approaches.
Method  Ductility  

Fixed base  Pinned base  
Proposed Design Technique  7  7.5 
DRAIN3DX [ 
6.75  7.45 
SAP V 10.0.5 [ 
6.92  7.47 
(a) Capacity curve for fixed base condition. (b) Capacity curve for pinned base condition.
Figure
The results obtained from the proposed design technique are satisfactory. However, it is necessary to find the limitations of the proposed design technique. Therefore, in the following section, parametric study is elaborately discussed to detect the limitations of the proposed design technique.
It has been observed from the CSA [
Therefore, this study has been restricted on length of the coupling beam and number of stories as basic variables and other parameters are considered as constant. These parameters have been considered in proposed method to make out effect on the behavior of coupled shear walls. Further, modifications to achieve ideal seismic behavior according to the proposed method have been included in this study.
A typical building with symmetrical coupled shear walls is shown in Figures
(a) Plan view of building with symmetrical coupled shear walls. (b) Coupled shear walls at section “aa”.
Dead loads (DL) of 6.7 kN/m^{2} and live loads (LL) of 2.4 kN/m^{2} have been considered as per the suggestions made by in Chaallal et al. [
Table
Dimensions and material properties of coupled shear walls for parametric study.
Depth of the wall ( 
4 m 
Length of beam ( 
1 m, 1.5 m and 2 m 
Depth of beam ( 
800 mm 
Number of stories ( 
10, 15 and 20 
Wall thickness ( 
300 mm 
Width of coupling beam ( 
300 mm 
Storey height ( 
3.6 m 
Modulus of concrete ( 
22.4 GPa 
Yield strength of steel ( 
415 MPa 
The above mentioned building has been studied by the design technique. The results for different parameters have been described in this section.
To study the influence of length of the coupling beam (
For more details, see Figures
(a) Storey displacement for fixed base condition at CP level. (b) Storey displacement for pinned base condition at CP level.
(a) Wall rotation for fixed base condition at CP level. (b) Wall rotation for pinned base condition at CP level.
(a) Beam rotation for fixed base condition at CP level. (b) Beam rotation for pinned base condition at CP level.
(a) Capacity curve for fixed base condition. (b) Capacity curve for pinned base condition.
The deflection for the case of pinned base condition is much higher than the case of fixed base (Figure
The rotation of the cantilever wall is maximum at the free end of the wall. This rotation decreases towards the base of the wall and is zero at the base for fixity.
Fixed base coupled shear walls with short span coupling beam is behaving as a cantilever wall (
Beam rotation is proportional to the wall rotation.
Therefore, it can be said from the above observations that coupled shear walls with short span coupling beam (
With the help of Section
Ductility of coupled shear walls for
Base condition  Length of the coupling beam ( 
Values 

Fixed  1 m  3.33 
1.5 m  4.8  
2 m  6.3  
 
Pinned  1 m  5.11 
1.5 m  6.35  
2 m  7.1 
It has been observed from Table
For more details, see Figures
(a) Storey displacement for fixed base condition at CP level. (b) Storey displacement for pinned base condition at CP level.
(a) Wall rotation for fixed base condition at CP level. (b) Wall rotation for pinned base condition at CP level.
(a) Beam rotation for fixed base condition at CP level. (b) Beam rotation for pinned base condition at CP level.
(a) Capacity curve for fixed base condition. (b) Capacity curve for pinned base condition.
With the help of Section
Ductility of coupled shear walls for
Base condition  Length of the coupling beam ( 
Values 

Fixed  1 m  2.93 
1.5 m  4.0  
2 m  5.9  
 
Pinned  1 m  4.5 
1.5 m  5.85  
2 m  6.87 
It has been observed from Figures
For more details, see Figures
(a) Storey displacement for fixed base condition at CP level. (b) Storey displacement for pinned base condition at CP level.
(a) Wall rotation for fixed base condition at CP level. (b) Wall rotation for pinned base condition at CP level.
(a) Beam rotation for fixed base condition at CP level. (b) Beam rotation for pinned base condition at CP level.
(a) Capacity curve for fixed base condition. (b) Capacity curve for pinned base condition.
Figures
The remedy for the cases of
(a) Storey displacement for fixed base condition at CP level. (b) Storey displacement for pinned base condition at CP level.
(a) Wall rotation for fixed base condition at CP level. (b) Wall rotation for pinned base condition at CP level.
(a) Beam rotation for fixed base condition at CP level. (b) Beam rotation for pinned base condition at CP level.
(a) Capacity curve for fixed base condition. (b) Capacity curve for pinned base condition.
Figures
Hence, it can be said from the above results that proposed design technique is useful to design the coupled shear walls during earthquake motion. To confirm it more, nonlinear static analysis is considered in the following manner to assess the proposed design technique.
In this paper, nonlinear static analysis is carried out to determine the response reduction factors of coupled shear walls at different earthquake levels.
The following design example is presented for carrying out the nonlinear static analysis of coupled shear walls. These walls are subjected to triangular variation of lateral loading. The base of the walls is assumed as fixed. Table
Dimensions and material properties of coupled shear walls for nonlinear static analysis.
Depth of the wall ( 
4 m 
Length of beam ( 
1 m 
Depth of beam ( 
800 mm 
Number of stories ( 
20 and 15 
Wall thickness ( 
300 mm 
Width of coupling beam ( 
300 mm 
Storey height ( 
3.6 m 
Modulus of concrete ( 
22.4 GPa 
Modulus of steel ( 
200.0 GPa 
Steel yield strength ( 
415 MPa 
(a) Plan view of building with coupled shear walls. (b) Coupled shear walls at section “aa”.
Dead loads (DL) of 6.7 kN/m^{2} and live loads (LL) of 2.4 kN/m^{2} have been considered as given in Chaallal et al. [
The results and discussions are described in Figure
(a) Capacity curve for
Place considered here is Roorkee which belongs to the seismic zone IV and Z is 0.24 as per IS 1893 (part 1) [
Performance point at the MCE level for
In this case, modal mass coefficient
In this case, modal mass coefficient
Performance point at the DBE level for
In this case, modal mass coefficient
Performance point at the MCE level for
In this case, modal mass coefficient
Performance point at the DBE level for
Table
Response Reduction Factors for DBE and MCE levels.
Parameters 









DBE  1.04  1.004  1.02  1.04  1.004  1.5 or 2 for coupled shear walls with conventional reinforced coupling beam 
MCE  2.05  1.2  1.58  2.05  1.34  

DBE  1.01  1.00  1.002  1.01  1.00  
MCE  1.87  1.13  1.39  1.87  1.22 
From Table
From the above studies, the following recommendations have been made for the design of coupled shear walls under earthquake motion.
Design technique should be adopted for fixing the dimensions of coupled shear walls.
Coupled shear walls with
Pinned base condition can be provided at the base of the shear wall as this type of base condition offers better nonlinear behavior in compare to the fixed base condition.
The behavior of coupling beam should be governed by shear.
Area of symmetrical coupled shear walls
Area of concrete section of an Individual pier, horizontal wall segment, or coupling beam resisting shear in in^{2} as per ACI 318 [
Gross area of concrete section in in^{2} For a hollow section,
Reinforcing steel in one diagonal as per Englekirk [
Area of nonprestressed tension reinforcement as per Englekirk [
Reinforcement along each Diagonal of Coupling beam as per IS 13920 [
Total area of reinforcement in each group of diagonal bars in a diagonally reinforced coupling beam in in^{2} as per ACI 318 [
Width of coupling beam
Flange width of Ibeam as per FEMA 273 [
Web width of the coupling beam as per FEMA 273 [
Compressive axial force at the base of wall 2
Collapse prevention level
Overall depth of the steel Icoupling beam section
Degree of coupling
Dead loads
Design basis earthquake
Effective depth of the beam
Depth of the coupling beam
Distance from extreme compression fiber to centroid of compression reinforcement as per Englekirk [
Displacement at
Elastic displacement (
Displacement at limiting response
Roof displacement
Roof displacement at CP level
Roof displacement at yield level
Displacement at ultimate strength capacity
Displacement at yield strength capacity
Actual displacement at
Modulus of elasticity of concrete
Young’s modulus for concrete in beam
Young’s modulus for concrete in wall
Elasticperfectlyplastic
Earthquake resistant design
Modulus of elasticity of steel as per FEMA 273 [
Young’s modulus for steel in beam
Young’s modulus for steel in wall
Clear span of the coupling beam + 2
Strain in concrete
Force
Maximum amplitude of triangular variation of loading
Federal emergency management agency
Ultimate force
Yield stress of structural steel
Specified compressive strength of concrete cylinder
Characteristic compressive strength of concrete cube
Specified yield strength of reinforcement
Overall height of the coupled shear walls
Distance from inside of compression flange to inside of tension flange of Ibeam as per FEMA 273 [
Storey height
Moment of inertia of symmetrical coupled shear walls
Moment of inertia of coupling beam
Immediate occupancy level
Storey number
Unloading stiffness
Postyield stiffness
Elastic stiffness
Initial stiffness
Secant stiffness
Length of the coupling beam
Diagonal length of the member
live loads
Life safety level
Depth of coupled shear walls
Distance between neutral axis of the two walls
Member over strength factor as per Englekirk [
Moment of symmetrical coupled shear walls
Moment at the base of the wall 1
Moment at the base of the wall 2
Maximum considered earthquake
Multidegree of freedom
Nominal flexural strength at section in lbin as per ACI 318 [
Moment capacity of coupling beam as per Englekirk [
Total overturning moment due to the lateral loading
Moment resistant frame
Displacement ductility capacity relied on in the design as per NZS 3101 [
Ductility
Energy based proposal for ductility under monotonic loading and unloading
Energy based proposal for ductility under cyclic loading
Total number of storeys
Not applicable
National earthquake hazard reduction program
Nonlinear static procedure
Axial force as per IS 456 [
Performance based seismic design
Percentage of minimum reinforcement
Shear span to depth ratio
Performance point
Response reduction factor
Reinforced cement concrete
Ductility related force modification factor
Ductility factor
Redundancy factor
Overstrength factor
Spectral acceleration
Spectral displacement
Singledegree of freedom
Tensile axial force at the base of wall 1
Tensile strength of One diagonal of a diagonal reinforced coupling beam
Tensile strength of truss reinforced coupling beam’s diagonal as per Englekirk [
The residual chord strength as per Englekirk [
Flange thickness of steel Icoupling beam as per Englekirk [
Inclination of diagonal reinforcement in coupling beam
Coupling beam rotation
Rotational value at ultimate point
Maximum rotational value
Wall rotation
Yield rotation as per FEMA 273 [
Wall thickness
Web thickness of steel Icoupling beam
Shear force in the coupling beam
The shear or vertical component of one diagonal in a primary truss travelled along the compression diagonal as per Englekirk [
The shear in a secondary truss produced by the residual tension reinforcement activated the load transfer mechanism as per Englekirk [
Base shear
Nonfactored design base shear
Factored design base shear may be less than or greater than
Base shear for elastic response
Base shear at limiting response
Nominal shear strength in lb as per ACI 318 [
The transferable shear force for flexure dominant steel coupling beam as per Englekirk [
Shear capacity of coupling beam as per Englekirk [
Shear strength of closed stirrups as per ATC 40 [
Capacity corresponding to
Factored shear force as per IS 13920 [
Factored shear force at section in lb as per ACI 318 [
Shear force at the base of the shear wall
Shear force at the base of wall 1
Shear force at the base of wall 2
Base shear at idealized yield level
Actual first yield level
Total nominal shear stress in MPa as per NZS 3101 [
Total gravity loading for symmetrical coupled shear walls
Compressive strut width as per Englekirk [
Zone factor
Plastic section modulus of steel coupling beam.