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# Center of rigidity

## What is center of rigidity?

Answer: Center of rigidity is the stiffness centroid within a floor-diaphragm plan. When the center of rigidity is subjected to lateral loading, the floor diaphragm will experience only translational displacement. Other levels are free to translate and rotate since behavior is coupled both in plan and along height. As a function of structural properties, center of rigidity is independent of loading. Certain building codes require center of rigidity for multistory-building design-eccentricity requirements.

For a given floor diaphragm, center of rigidity is calculated through the following process:

• Case 1 applies a global-X unit load to an arbitrary point, perhaps the center of mass, such that the diaphragm rotates Rzx.
• Case 2 applies a global-Y unit load at the same point, causing rotation Rzy.
• Case 3 applies a unit moment about global-Z, causing rotation Rzz. These three load cases are shown in Figure 1:

Figure 1 - Center of Rigidity

• Center of rigidity (X,Y) is then computed as X = -Rzy / Rzz and Y = Rzx / Rzz.

During analysis, ETABS automatically calculates this coordinate for each floor diaphragm. The diaphragm assignment must be present in the model. Center of rigidity and center of mass are then displayed by selecting Display > Show Tables > Analysis > Results > Structural Results > Centers of Mass and Rigidity > OK.

Also Make sure to check option to calculate Diaphragm Centers of Rigidity via Analyze > Set Load Cases To Run...