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RE: effective length factor for sway moment

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My copy of the Column Research Council's "Guide to Design Criteria for Metal
Compression Members", edited by Bruce G. Johnston, John Wiley & Sons, August
1967, presents the equations for K as a function of Ga and Gb for both
"sidesway prevented" and "sidesway not prevented" frames.  The equations are
such that the can be solved via spreadsheet or incorporated easily into a
computer program.  This reference also explains how the alignment charts
were developed in 1959 by L.S. Lawrence "for incorporation into the Boston
Building Code".

The alignment charts allow generalization to the solution of the 4th order
differential equation defining the elastic stability of a column for varying
degrees of rotational and translational restraints at the ends.  If you'd
like a nice math refresher (assuming you're a masochist), the standard
reference for derivation and solution of the DE is "Theory of Elastic
Stability", by Timoshenko and Gere, published by McGraw-Hill.  My copy is
the 2nd edition, dated 1961.

When included in new editions of the AISC code, recent work sponsored by
SSRC and AISC as presented in AISC's current "Bracing for Stability"
seminars will make changes in how we use the alignment charts to help assess
frame stability, but will not eliminate them as a useful design tool.

Hope this helps.

John W. Woollen, P.E.
Project Manager

Pegasus International, Inc.
PO Box 82209
Lafayette, LA 70598
Phone:		Direct (337) 314-8013, (337) 232-7777
Fax:		(337) 984-6188
Pager:		(337) 231-3246
Email:		jwoollen(--nospam--at)

-----Original Message-----
From: Bill Polhemus [mailto:bill(--nospam--at)]
Sent: Tuesday, April 03, 2001 10:40 AM
To: seaint(--nospam--at)
Subject: RE: effective length factor for sway moment

This may sound horribly ignorant--because it is, "ignorance" being defined
by Webster as "a ack of knowledge or awareness of a particular thing"--but I
do not know how one arrives at a "K factor" using computer structural

I have always assumed that this could be done using e.g. "slope-deflection",
but never found any reference that would easily allow me to calculate it,
and so I have continued in my ignorance. (I even purchased an edition of the
"Guide to Stability of Metal Structures" ed. by Galambos once, in hope of
learning how this was to be done, but that reference is primarily
theoretical, and I got no further enlightenment from it. I have also perused
the various materials design standard texts such as Salmon and Johnson, but
they discuss the topic only briefly, refer you to the "alignment charts" and
move on to design topics.

I seems like the theoreticians want to leave it to the applied-design folks
for a fuller explanation, and the design folks want to refer back to the
theory guys in turn.

So, I'd LOVE for someone to assuage my ignorance, or at the very least point
me in the direction of sources that can.


William L. Polhemus, Jr., P.E.
Polhemus Engineering Company
Katy, Texas
Phone 281-492-2251
Fax 281-492-8203

-----Original Message-----
From: Peter Higgins [mailto:76573.2107(--nospam--at)]
Sent: Tuesday, April 03, 2001 10:18 AM
To: INTERNET:seaint(--nospam--at)
Subject: effective length factor for sway moment

Message text written by INTERNET:seaint(--nospam--at)
>For frames NOT restrained against sidesway (drift), regardless of whether
not you have fully or partially restrained joints, K will always be > 1 and

can be much greater than 2, 3, or even 4.

(Simple sketches will show that this is true.)<

Not to nit pick too much, but there are cases of columns in a "sway
permitted" frame which will have a K<1. Yura in his seminars demonstrated
some. You might also dive into "Effective Length and Notional Load
Approaches for Assessing Frame Stability" by the ASCE Structural Institute.

Once again, as others have mentioned, K factors (not just their nomograms)
were introduced in the "pre computer" days. We really have much better
tools now, and should use them.

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