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# Rigid frame deflections (again)

• To: SEAOC Forum <seaoc(--nospam--at)seaoc.org>
• Subject: Rigid frame deflections (again)
• From: "Kathleen A. O'Brien" <wildwoman1(--nospam--at)compuserve.com>
• Date: Wed, 21 Jan 1998 19:35:51 -0500

```Guys and Dolls:

Now that I have the Steel Interchange sheet from Modern Steel Construction
(4/93) which shows the quick hand-calc for rigid frame defelction, I have
started using it.

HOWEVER, I have noticed something very odd. Extremeley odd.

The formulas for pinned and fixed bases follow (and please excuse the
crummy formatting):

drift = P*H(squared)/6E  *(H/Icol + L/2Ibm)
H= height of frame
L=span of frame
Icol= I of column
Ibm= I of beam
E=29000ksi

For fixed-at-base frames:

drfit=P*H(cubed)/12EIcol * (3K+2/6K+1)

where   K= Ibm*H/Icol*L
everything else as above

Now here is the strange part. I have two frames along line D in my project.
One has a 17 foot span and the other a 7 foot span (L). Both of  them are
10.5 feet high (H).  And  I am assuming:

P = 1 kip for each frame  (just getting relative rigidities at this point).
Relative rigidity R is the inverse of the drift; i.e. 1/drift

For both fixed and pinned at base calcs, my 7 foot long frame is stiffer
than my 17 foot one.

I have hunted HARD for errors in my calcs and I can't find any. I have done
the calc both by hand and with a spreadsheet and I still get the same
answer: the tall skinny frame is stiffer than the short fat one.

I do not buy this. Has anyone else had this problem? Is it me? Is it the
calcualtion??

Kate O'Brien
Simi Valley, CA

```