Why the Location of Center of Rigidity Changes for Each Story Even for Symmetric Structures?
The center of rigidity is the center of resistance of a floor or diaphragm against lateral forces. It is the stiffness centroid located within a floor-diaphragm plan. If the lateral forces are applied at this center, the floor diaphragm will experience only the translational displacement (i.e. no rotation). Other levels are free to translate and rotate since the actual behavior is coupled both in plan and along height. The location of center of rigidity is an inherent structural property and has nothing to do with applied loading. The information about its location is important to calculate design-eccentricity while performing code-based seismic analysis.
Beside the analysis results, the ETABS and other structural analysis software also report the center of rigidity as an output. For a given floor diaphragm, the CSI’s analysis reference manual describes the process of calculating the center of rigidity as follows:
Case 1: A unit load is applied to an arbitrary point in global X direction such that the diaphragm rotates about vertical (Z) direction. The rotation of diaphragm (Rzx) is determined.
Case 2: A unit load is applied to the same point in global Y direction such that the diaphragm rotates about vertical (Z) direction. The rotation of diaphragm (Rzy) is determined.
Case 3: A unit moment about global Z direction is applied to the same point. This also causes the rotation of diaphragm about vertical (Z) direction. This rotation (Rzz) is also determined. These three load cases are shown in Figure below.