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# RE: P-Delta

• To: <seaint(--nospam--at)seaint.org>
• Subject: RE: P-Delta
• From: "Bill Allen" <T.W.Allen(--nospam--at)cox.net>
• Date: Wed, 7 Apr 2004 07:05:53 -0700

```I recently attended an AISC seminar where the presenter discussed "leaning
columns". As he presented it, the horizontal component of the load on the
leaning column turns into a horizontally applied force in the LFRS.
Therefore, the base shear will be greater than the applied loads.

For example, let's say you have a one story building, 15 ft tall and. Based
on an applied lateral force of 20k the LFRS deflects 4.5 inches. In the same
line, you have a "leaning column" with a 50k load on it. The horizontal
component of the vertical load is 50k * [(4.5)/(15*12)] = 1.25k. According
to this rationale, the P-Delta analysis *should* consider 20 + 1.25 = 21.25k
lateral load on the LFRS even though there is only a 20k *applied* lateral

I think a "quick" check would be to multiply the sum of all the gravity
loads on all "leaning columns" in the system by the drift slope (deflection
divided by the height). That should give you the global additional force the
LFRS needs to resist in a P-Delta analysis as well as the incremental base
shear you would see in such an analysis.

T. William (Bill) Allen, S.E. (CA #2607)
ALLEN DESIGNS (http://www.AllenDesigns.com)
San Juan Capistrano, CA

:-----Original Message-----
:Sent: Tuesday, April 06, 2004 8:22 AM
:To: seaint(--nospam--at)seaint.org
:Subject: P-Delta
:
:John Peterson wrote:
:
:"When looking at individual frames in the small model, with only the
:wind loads applied in one direction (also the innate mass load, which
:would be the "P" of P-delta), the horizontal reactions at the base are
:greater than the applied story forces for each direction.  I modeled one
:of the end frames using Visual Analysis 4.0 and did not get the same
:results as I did with RAM despite using the P-delta analysis.  The
:reactions added up to the applied loads in VA.  I contacted RAM to see
:if I was interpreting their program incorrectly and the representative
:stated that since I used the P-delta calculation, the building is no
:longer in static equilibrium and will have base horizontal reactions
:greater than the applied lateral loads."
:
:
:John,
:If you're doing a static (not dynamic) analysis, the frame as a whole
:still has to be in static equilibrium.  The only explanation that makes
:any sense (aside from simple roundoff error) is the idea put forth by
:Craig Leech, that the software is applying a "small disturbing load" (or
:words to that effect) to generate a lateral displacement, then
:forgetting to take it out.
:
:Leaner columns can't defy statics--the reactions of the whole building
:still have to add up to the lateral forces applied to it.  If the RAM
:rep actually said that, he should be made to take his licensing exam
:again.
:
:TKDA
:St. Paul, Minnesota
:
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