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# Re: Rigid frame deflections (again)

• To: <seaoc(--nospam--at)seaoc.org>
• Subject: Re: Rigid frame deflections (again)
• From: "T" <vicpeng(--nospam--at)vtcg.com>
• Date: Wed, 21 Jan 1998 18:37:50 -0800

```I haven't done the math yet but I wonder if the individual beam to col
stiffnesses are the same for both frames then the more the drift is a
function of individual col stiffness ( i.e. very stiff cols and not-so-stiff
beams) it seems that the frame will tend to have less rigidity the longer
the beam is.  In the ridiculous case where beam to col stiffness tends to
zero the cols will act more and more as isolated elements. ????
-----Original Message-----
From: Kathleen A. O'Brien <wildwoman1(--nospam--at)compuserve.com>
To: SEAOC Forum <seaoc(--nospam--at)seaoc.org>
Date: Wednesday, January 21, 1998 5:29 PM
Subject: Rigid frame deflections (again)

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

```