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# RIGID DIAPRAGM - Center of Rigidity

• To: seaint(--nospam--at)seaint.org
• Subject: RIGID DIAPRAGM - Center of Rigidity
• Date: Tue, 03 Nov 1998 09:26:04 -0800

```The so-called "center of rigidity" is a function of the stiffnesses of the
members at a given level (including the columns and walls immediately
below) and of those of all levels above. In your example, levels 6 through
10 would have the same center of rigidity, but levels 1 through 5 would
have different centers of rigidity from each other (slightly) as well as
different from level 6 through 10 (potentially significantly). The reason
the lower levels would differ from each other is that as you go down the
structure, the effects of the stiffnesses of the upper levels become more
and more diluted relative to the stiffnesses of the lower levels.
Three-dimensional finite element analysis take these effects into account
automatically. If you are doing a two-dimensional analysis or a hand
analysis you will have to calculate this manually. The most common manual
procedures ignore the stiffnesses of the levels above, and consider only
the stiffnesses of the elements immediately below, and are only rough
approximations.

RAM International

>
>In computing the center of rigidity, will I consider the floor below? the
floor
>above? or both? Say for a ten story building, say the column size , beam size
>and shear wall thickness are all the same for the first five floors, and
>another set members for the next five floors, does that mean that on the
lower
>five floors, it will have the same center of rotation and on the last five
>floors, it will also rotate on another location center of rotation? Does
it not
>differ from floor to floor even if the member sizes are the same?
>
>Alex Gutierrez
>
>

```