# RE: P-Delta Analysis(clarification)

• To: "'seaint(--nospam--at)seaint.org'" <seaint(--nospam--at)seaint.org>
• Subject: RE: P-Delta Analysis(clarification)
• From: "Haan, Scott M." <HaanSM(--nospam--at)ci.anchorage.ak.us>
• Date: Sat, 2 Feb 2002 13:40:39 -0900
```"My question why we don't consider the axial load in the calculation of
stiffness which is more correct ."

So are you asking why the rotational and translational stiffnesses in
American finite element modeling programs do not consider axial load affects
or are you asking why a textbook moment frame drift approximation formula
does not include axial effects.

Most moment frame buildings have more drift from translation then from
building curvature unless they are super tall. Curvature (effects of columns
squashing and stretching) adds up as you go up a tall building, so the
higher you go the more drift is affected by "flexural" effects then by
racking. Approximate formulas for moment frame drift are pretty accurate for
short buildings. Ommitting axial stiffness from the analysis of a short
moment frame building actually does not affect the results very much.

American building codes assume people are using software that does
structural analysis in the elastic range.  Most programs used for design are
doing stuff in the elastic range and consider rotational stiffness and
translational stiffness to be independent on axial effects. They look at
each degree of freedom as not depending on the other degrees of freedom. I
can't remember what that  is called. If you don't use these assumptions
there is not a closed form solution for your stiffness matrix and you need
to iterate or do something more difficult.

Most modeling programs [anything that is not free] will include axial
stiffness in the calculations. They calculate how much columns stretch on
the upwind building face and squash on the downwind face and in this way the
effects of translational displacement from building curvature are included
in diaphragm displacements. It is more accurate to let a program
automatically include P-Delta effects then to use more approximate methods.

Scott M Haan P.E.
Plan Review Engineer
Building Safety Division
Development Services Department
Municipality of Anchorage
http://www.muni.org/building
phone:907-343-8183
fax:907-249-7399
mailto:haansm(--nospam--at)ci.anchorage.ak.us

-----Original Message-----
From: maaz siddig ibrahim [mailto:maaz_siddig(--nospam--at)hotmail.com]
Sent: Saturday, February 02, 2002 6:42 AM
To: seaint(--nospam--at)seaint.org
Subject: P-Delta Analysis(clarification)

Dear Sherman/William :

I mean by the beam stiffness and the (beam/column) stiffness that:
I have checked some software uses the stiffness of the beam considering only

the bending deformations or the bending and the shear deformations without
considering the effect of the axial load in the rotational and translation
stiffness ,this what I means by the beam stiffness ,The other one
(beam/column) stiffness is used when we consider the effect of the axial

The P-Delta analysis is equal to : when we use the transltional stiffness (
Stt=(S1+S2+2*T)/h^2-P/h ) [where : P is the axial load ]
but the rotational stiffnesses S1 & S2 should calculated considering the
increased .
My question why we don't consider the axial load in the calculation of
stiffness which is more correct .

Thanks
Engineer: Ma'az Siddig Ibrahim.
U.A.E Abu Dhabi
maaz_siddig(--nospam--at)hotmail.com

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