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# Re: Rigid frame deflections (again)

• To: seaoc(--nospam--at)seaoc.org
• Subject: Re: Rigid frame deflections (again)
• From: James_F_Fulton(--nospam--at)rohmhaas.com (James F Fulton)
• Date: Thu, 22 Jan 1998 15:37:39 -0500

```Kate, when you asked the questions earlier this month, some responses
indicated that you could refer to Kleinlogel's book and find formulas for
rigid frame DEFLECTIONS.  I've got a copy of the 2nd American Edtion, Second
Printing (1964), and in that edition at least, there are only equations for
frame forces and moments--no deflections. I looked in a couple of other
references on my shelf (incl Roark) and can find no DEFLECTION formulas for
rigid frames. I would be interested in knowing if and where others find
deflection formulas for rigid frames.

I've got a copy of the Interchange article, and I used slope-deflection
theory to derive the equation given there for the pinned=end frame. However,
based on my derivation, the equation in Interchange is incorrect in that the
factor in the denominator times Ibm should be "1" , not "2", which
incidentally is what you quoted in your original note.  (You remember, the
one where you did not want to use a "fancy shmancy" \$\$ computer program for
these "small and uncomplicated" frames)  Well, it looks to me that
defermining frame deflections, as opposed to forces and moments, for even
simple rigid frames is not trivial and there does not appear to much
information (equations) for these structures in the texts either. So a
computer program appears to be the way to go, even for a statically
determinant frame, if one's interest include deflections.

______________________________ Reply Separator _________________________________
Subject: Rigid frame deflections (again)
Author:  seaoc(--nospam--at)seaoc.org at Internet
Date:    1/21/98 7:35 PM

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)
where    P = load
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

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