Center of Rigidity Calculation

The center of rigidity is defined as a location within a floor diaphragm at which lateral load produce only translational displacement. It is also referred to as the stiffness centroid of a diaphragm. The center of rigidity calculation is carried out only for rigid diaphragms.

For each rigid diaphragm, the program creates three load cases in such a way that:

Load Case 1: a unit load is applied at the mass center in global X-direction and this produces rotation around the Z-axis (Rot_XZ) perpendicular to the diaphragm at the mass center.
Load Case 2: a unit load is applied at the mass center in global Y-direction and this produces rotation around the Z-axis (Rot_YZ) perpendicular to the diaphragm at the mass center.
Load Case 3: a unit moment is applied at the mass center around the Z-axis and this produces a rotation about the Z-axis (Rot_ZZ).

Then,

{C R}_{X} = X_{m} - \frac{{R O T}_{Y Z}}{{R O T}_{Z Z}}

{C R}_{Y} = Y_{m} + \frac{{R O T}_{X Z}}{{R O T}_{Z Z}}

where

CR_X and CR_Y	=	X and Y coordinates of center of rigidity, respectively
X_m and Y_m	=	X and Y coordinates of diaphragm mass center, respectively

The Center of Rigidity report tabulates center of rigidity calculated for each rigid diaphragm. In addition, story (or diaphragm) stiffness values for each rigid diaphragm are printed in the report. The story stiffness is inverse of interstory drift calculated according to a unit load applied at story mass center.