Center of Rigidity and Center of Shear in Wall-Frame Systems

In case of torsion in buildings, additional earthquake forces affect the structure and internal forces and displacements increases. For this reason, it is important to place the bearing systems in the plan as much as possible to reduce the torsion effect. To minimize torsion effects, the center of mass and center of rigidity should be as close as possible. Although most of the existing earthquake seismic codes do not require the determination of the center of rigidity in the analysis phase of the structures, it is important to determine the center of rigidity in terms of reducing the torsional effects. In practice, the concepts of center of rigidity and shear center are sometimes confused and found to be incorrect. Particularly in the structural system of wall-frame, due to the different behavior of wall and frame, the center of rigidity varies from the story to story even if the dimensions of the walls and frames are constant throughout the height of the structure. In such buildings, the center of rigidity may even go out of plan on some storey. In this study, firstly the concepts of center of rigidity and shear center in multi-storey buildings are briefly explained. An approach was then proposed to find the center of rigidity and the shear center. The presented approach was applied on two examples taken from the literature and the results were compared with the literature and ETABS software and the suitability of the presented method was demonstrated.