# .4.4 location of shear wall is assured.

.4.4 Modeling of shear wall
A. Equivalent frame method (EFM)
ln equivalent frame method, which is also known as wide column analogy, each shear wall is replaced by an idealized frame structure consisting of a column and rigid beams located at floor levels. The column is placed at the wall’s centroidal axis and assigned to have the wall’s inertia and axial area. The rigid beams that join the column to the connecting beams are located at each framing level. A sample model is shown in Fig.4.l3. In this method, the axial area and inertia values of rigid arms are assigned very large values compared to other frame elements. Due to its simplicity, the equivalent frame method is especially popular in design offices for the analysis of multistory shear wall- frame structures.

Fig.4.13 modeling of shear wall by equivalent frame method
B. Modeling steps
In this section modeling procedure for modeling of shear wall by wide column analogy is discussed. Modeling is carried out as per assumption made in the wide column frame analogy. Following are major steps involved in the modeling of shear wall.
a. Defining the co-ordinate
Shear walls are represented as two line elements one is center line of shear wall and other is center line of rigid beam. By de?ning a correct co-ordinate system proper location of shear wall is assured. Columns, to which the shear wall elements are attached, are not modeled separately; rather, they have been considered to be inside the shear wall cross section. Then, the shear wall and the columns on both ends are modeled as a single frame element. For all building models, the foundations are not included in the structural model and bottom ends of the columns and the shear walls are assumed as ?xed based as shown in Fig.4.14

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Fig. 4.14 modeling of shear wall by wide column analogy
b. Defining material
The M-25 grade of concrete is assigned for construction of shear wall and elastic modulus of concrete is Ec =25000000 kN/m2. Grade of steel is Fe 415. The elastic modulus of the rigid beam material is taken as 1.999E + 11 kN/m2, which are 1000 times more than elastic modulus of shear wall material.
c. Plastic hinge property for shear wall
As mentioned in previous point in case of equivalent frame model shear wall is modeled as combination of mid-pier and rigid beams. The material nonlinearity of the shear wall is modeled considering a plastic hinge on column or mid-pier element. The nonlinear model of mid-pier frame is based on plastic hinge concept and a bilinear m0m¢nt-curvature relationship. Taking into account for the analysis purpose, the plastic (P-M-M Interaction) hinges are assumed on the plastic zones at the end of the structural elements. Due to the capability of defining default plastic hinges, in the SAP2000 one can use previous defined hinges for their studies in compliance with relative modern codes.
4.4.5 Location of shear walls in soft storey building
Fig 4.15 shows the arrangement of Shear walls at soft storey level of building as retrofitting scheme. Shear walls are provided at the corners of building in both X and Y direction.

a) G+12/ GL+ 4th floor retrofitted with shear wall b) GL+ 8th floor retrofitted with shear wall

c) GL + 12th floor retrofitted with shear wall
Fig. 4.15 retrofitting with shear wall at outer periphery of soft storey
4.4.6 Capacity curves and seismic performance level of buildings with modeling of shear walls as retrofitting scheme
After modeling the shear walls with proper arrangement without disturbing the purpose of parking as shown in Fig. 4.15, performance of the building is determined. This is represented by the capacity curve and hinge formation pattern. Fig 4.16 to Fig 4.21 show the comparison of pushover curve for without retrofitted models and building with modeling of shear walls as retrofitting scheme. From the comparison of pushover curve it is seen that performance of the soft storey building is modified with the provision of shear walls at comers of outer periphery of soft storey level.

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