Study of Torsional and Stiffness Properties of the RC Buildings with Shear wall and Steel Bracing with Lateral Loadings

: The equivalent static analysis and response spectrum analysis were performed for sixteen different models with different positioning of lateral load resisting systems in building. For the development of seismic response curve of the represented model is presented in tabular form and graphically shown in figure. Seismic response curve has been generated according to the response spectra curve of IS 1893:2016. The following parameters are compared between Equivalent Static Method and Response Spectrum Method with different positions of shear wall, braces and combined system in each model.


Introduction
As the Indian subcontinent lies in the boundary of the Eurasian and Indian plates the probability of earthquakes affecting the performance of any structure is very high. Structures are susceptible to collapse during moderate to strong ground motion which trigger huge losses to the human society in terms of lives and economy. The seismic design of building structures is typically conducted to satisfy the life safety using modern design codes. The design codes have been finalized conducting a number of studies including the seismic hazard analysis. RC Moment-Resisting Frames are the modeling system that are used all over the world, these systems are mainly used because of their ductility, speed and the simplicity in construction. Usually these type of buildings are designed as per procedures that are clearly based on seismic design codes. Beams and columns are assembled in a rectilinear way forming a Moment resisting frame, and beams are tightly connected to the columns. Rigid frame action mostly provides the resistance to the lateral forces that is because of the development of bending and shear force in the frame members and joints Depending upon the structure of the joint the Moment frame can't dislocate sideways without bending the beams or columns under the rigid beams-column joints. Properly built and complex buildings with shear walls have shown very good performance for many earthquakes in the past. In high seismic regions shear walls need special detailing. Also steel bracings in Rc buildings are used to resist the lateral loading now days. To make strong and ductile RC buildings normally shear walls and steel bracings are used [1]. The continuity of the frame also increases resistance to gravity loading by reducing the positive moments in the girders. The advantages of a rigid frame are the simplicity and convenience of its rectangular form.
foundation level was assumed fixed and meshing of the shell element i.e. slab and shear wall was done. Concrete grade of M 25 and steel (rebar's) of grade Fe 500 as material for beam, slab, shear wall, M 30 for column and structural steel of Fy 250 for X-braces were assigned. Slab and shear wall were modeled as shell element with slab having rigid diaphragm in each story level. Each model was designed as per IS 1893 load combinations for linear static and response spectrum method with soil type ii and seismic zone IV. The size of columns is 625 mm x625mm and size of beam is 600x400 in each models are considered. In the models the thickness of shear wall is 400mm. and other parameter and configurations are as shown in figure 1 and table 1.      Type I  Type II  Type III  Type IV  Type V Values of storey stiffness in bracing system along X-direction by the action of seismic force for all locations of shear walls using ESM and RSM are tabulated and plotted in figure. By analyzing these values, it can be concluded that type-II model of shear wall system has higher value of storey stiffness than that of other types (positions) by RSM but the same result is for type-IV model by using ESM. The decreasing order of storey stiffness by ESM are type-IV, type-II, type-III, type-I and type-V respectively and that by RSM are type-II, type-IV, type-III, type-I and type-V respectively. Type-II and type-IV curves in both methods of analysis and type-I and type-V curves in ESM nearly coincide with each others. In RSM, type-I and type-III curves nearly coincide at their peaks with each other. It can be concluded that the type (location of shear wall) with higher stiffness shows lesser deflection and vice versa.  Diaphragm maximum to average drift ratio in all types (locations) of shear wall system along Xdirection by the effect of seismic force is presented in tabular form and graphically using ESM and RSM as shown in figure above. It is observed that for all types, the ratio by ESM is greater than that by RSM.

Diaphragm Maximum to Average Drift Ratio
In overall, type-I position has lesser value of diaphragm maximum to average drift ratio than that of other positions. The decreasing order of maximum value of the ratio in all types are as type-V, type-IV, type-III, type-II and type-I respectively. It can be concluded that the location of the shear wall with smaller value of diaphragm maximum to average drift ratio contributes less torsional susceptibility.

Figure 7. Storey Stiffness Along X-Direction in Bracing System (RSx) by RSM
Values of storey stiffness in bracing system along X-direction by the action of seismic force for all locations of steel braces using ESM and RSM are tabulated and plotted in figure. By analyzing these values, it can be concluded that type-II model of bracing system has higher value of storey stiffness than that of other types (positions) by RSM but the same result is for type-IV model by using ESM. The decreasing order of storey stiffness by ESM are type-IV, type-II, type-III, type-I and type-V respectively and that by RSM are type-II, type-IV, type-III, type-I and type-V respectively. Type-II and type-IV curves in both methods of analysis and type-I and type-V curves in ESM nearly coincide with each others. In RSM, type-I and type-III curves nearly coincide at their peaks with each other. It can be concluded that the type (location of bracing) with higher stiffness shows lesser deflection and vice versa.  Diaphragm maximum to average drift ratio in all types (locations) of bracing system along X-direction by the effect of seismic force is presented in tabular form and graphically using ESM and RSM as shown in figure above. It is observed that for all types, the ratio by ESM is greater than that by RSM. It is seen that type-I position has lesser value of diaphragm maximum to average drift ratio than that of other positions. The decreasing order of maximum value of the ratio in all types are as type-V, type-IV, type-III, type-II and type-I respectively. It can be concluded that the location of the steel braces with smaller value of diaphragm maximum to average drift ratio contributes less torsional susceptibility. Type-II position of bracing has better performance against torsion than that of all other types except of type-I.

Figure 11. Storey Stiffness Along X-Direction in Combined System (RSx) by RSM
Values of storey stiffness in combined system along X-direction by the action of seismic force for all locations of combined system using ESM and RSM are tabulated and plotted in figure. By analyzing these values, it can be concluded that type-II model of combined system has higher value of storey stiffness than that of other types (positions) by RSM but the same result is for type-IV model by using ESM. The decreasing order of storey stiffness by ESM are type-IV, type-II, type-III, type-I and type-V respectively and that by RSM are type-II, type-IV, type-III, type-I and type-V respectively. Type-II and type-IV curves in both methods of analysis and type-I and type-V curves in ESM nearly coincide with each others. In RSM, type-I and type-III curves nearly coincide at their peaks with each other. It can be concluded that the type (location of combined system) with higher stiffness shows lesser deflection and vice versa.    X-direction diaphragm maximum to average drift ratio in all types (locations) of combined system by the effect of seismic force is presented in tabular form and graphically using ESM and RSM as shown in figure above. It is observed that for all types, the ratio by ESM is greater than that by RSM. It is seen that type-I position has lesser value of diaphragm maximum to average drift ratio than that of other positions. The decreasing order of maximum value of the ratio in all types are as type-V, type-IV, type-III, type-II and type-I respectively. It can be concluded that the location of combined system (shear walls + steel braces) with smaller value of diaphragm maximum to average drift ratio contributes less torsional susceptibility. Type-II position of the combined system has better performance against torsion than that of all other types except of type-I. Bracing Combined than that of Response Spectrum Method. Also it can be seen that model with shear wall system has higher stiffness than other system models. Shear wall, combined, bracing and bare frame system respectively have decreasing order of storey stiffness values. This storey stiffness can play a major role for lateral stability of the structure. Having higher stiffness, it shows lesser deflection & drift and vice versa.

Figure 17. X-Direction Diaphragm Max to Avg Drift Ratio in Type-I System (RSx) by RSM
Diaphragm maximum to average drift ratio along X-direction in Type-I position of all the system due to seismic force effect is presented in tabular form and graphically using ESM and RSM as shown in figure above. It is observed that for all system, the ratio by ESM is greater than that by RSM. It is observed that shear wall system has lesser value of diaphragm maximum to average drift ratio than that of other systems by both RSM and ESM. Bare frame, bracing, combined and shear wall have decreasing order of the ratio. So, it can be concluded that shear wall system contributes less torsional susceptibility than other systems.

Figure 19 Storey Stiffness Along X-Direction in Type-II System (RSx by RSM
Storey stiffness by seismic forces along X-direction for all type-II position systems (models) are plotted and tabulated using ESM and RSM. By analyzing these values, it can be concluded that all the systems of Equivalent Static Method in X-direction have larger maximum value of storey stiffness at G+1 storey than that of Response Spectrum Method. Also it can be seen that model with shear wall system has higher stiffness than other system models. Shear wall, combined, bracing and bare frame system respectively have decreasing order of storey stiffness values. This storey stiffness can play a major role for lateral stability of the structure.  ratio along X-direction in Type-II position of all the system due to seismic force effect is presented in tabular form and graphically using ESM and RSM as shown in figure above. It is observed that for all system, the ratio by ESM is greater than that by RSM. It is observed that shear wall system has lesser value of diaphragm maximum to average drift ratio than that of other systems by both RSM and ESM. Bare frame, bracing, combined and shear wall have decreasing order of the ratio. So, it can be concluded that shear wall system contributes less torsional susceptibility than other systems.

Figure 23. Storey Stiffness Along X-Direction in Type-III System (RSx) by RSM
Values of storey stiffness by seismic forces along X-direction for all type-III position systems (models) are plotted and tabulated using ESM and RSM. By analyzing these values, it can be concluded that all the systems of Equivalent Static Method in X-direction have larger maximum value of storey stiffness at G+1 storey than that of Response Spectrum Method. Also it can be seen that model with shear wall system has higher stiffness than other system models. Shear wall, combined, bracing and bare frame system respectively have decreasing order of storey stiffness values. Table 9. by RSM X-direction diaphragm maximum to average drift ratio in Type-III position of all the system by the effect of seismic force is presented in tabular form and graphically using ESM and RSM as shown in figure above. It is observed that for all system, the ratio by ESM is greater than that by RSM. In overall, shear wall system has lesser value of diaphragm maximum to average drift ratio than that of other systems. It can be concluded that shear wall system contributes less torsional susceptibility than other systems.  are plotted and tabulated using ESM and RSM. By analyzing these values, it can be concluded that all the systems of Equivalent Static Method in X-direction have larger maximum value of storey stiffness at G+1 storey than that of Response Spectrum Method. Also it can be seen that model with shear wall system has higher stiffness than other system models. Shear wall, combined, bracing and bare frame system respectively have decreasing order of storey stiffness values. In summary, shear wall system has higher values of storey stiffness at all stories than that of other systems.  of all the system along X-direction by the effect of seismic force is presented in tabular form and graphically using ESM and RSM as shown in figure above. It is observed that for all systems, the ratio by ESM is greater than that by RSM. In overall, bare frame system has lesser value of diaphragm maximum to average drift ratio than that of other systems using ESM but that for shear wall system using RSM. The decreasing order of the ratio in these three systems by both methods are bracing, combined and shear wall system. It can be concluded that among these three systems rather than bare frame, shear wall system contributes less torsional susceptibility.   The storey stiffness values by seismic forces along X-direction for all Type-V position systems (models) are plotted and tabulated using ESM and RSM. By analyzing these values, it can be concluded that all the systems of Equivalent Static Method in X-direction have larger maximum value of storey stiffness at G+1 storey than that of Response Spectrum Method. Also it can be seen that model with shear wall system has higher stiffness than other system models. Shear wall, combined, bracing and bare frame system respectively have decreasing order of storey stiffness values. In summary, shear wall system has higher values of storey stiffness at all stories than that of other systems.  of all the system along X-direction by the effect of seismic force is presented in tabular form and graphically using ESM and RSM as shown in figure above. It is observed that for all systems, the ratio by ESM is greater than that by RSM. The decreasing order of the ratio in three systems except bare frame by both methods are bracing, combined and shear wall system. It can be concluded that among these three systems rather than bare frame, shear wall system contributes less torsional susceptibility. From above graphs, among all the system, bare frame system has better response for torsional effect up to G+5 storey, after G+5 shear wall is better than all others.

Discussion
Equivalent Static Method (ESM) and Response Spectrum Method (RSM) with different position/locations (type-I, type-II, type-III, type-IV and type-V) of shear wall, steel bracing and combination of shear walls and braces (combined) systems are compared in terms of maximum storey displacement, maximum storey drift, storey shear, overturning moment, storey stiffness and diaphragm maximum to average drift ratio. Following observations were noticed: i. In all types/locations of any system there is no considerable difference in the distance between center of mass and center of rigidity. ii. It is seen that in continuous lateral load resisting system location without corners (i.e. type-II and type-IV) has greater stiffness than that in continuous lateral load resisting system with corners.