# Re: P-Delta Analysis(clarification)

• To: seaint(--nospam--at)seaint.org
• Subject: Re: P-Delta Analysis(clarification)
• From: Daryl Richardson <h.d.richardson(--nospam--at)shaw.ca>
• Date: Sun, 03 Feb 2002 00:23:16 -0700
```Scott,

Don't apologize for your earlier reply; it was excellent as are most
(all?) of your replies.  Not only that, it actually got me thinking.
The following is the result.

There are two distinctly separate non linear structural effects which
apply to structures made up of rigid (not catenary, for example)
elements and loaded within the linear elastic range.  One is the effects
of applying the loads to the deflected structure; this is solved by
using a p-delta analysis.  The second is the effect of axial loads on
the rotational stiffness of bending elements; this must be accommodated
by modifying the rotational (4EI/L) stiffnesses of the bending
elements.  These two effects are independent of one another and must be
handled separately in the analysis.  It also follows that the effects
will be different for different load cases.

The change in the rotational stiffness of an element is a function of
P/Pc, where P is the axial load and Pc is the critical buckling load.
After 25 years of not using this analysis I've forgotten whether this is
a linear function or not (in fact, I'm fairly sure that it is not; I
think it might be the square or even higher order power of the ratio).
The value of the function will, of course, be different for each axis.

If you like playing around with the analysis there is a simple
procedure which might tell you whether the non linear rotational
stiffnesses are likely to have any significant impact on the design.  It
works for special cases and might be useful as a "sensitivity analysis"
for other load cases.  The procedure consists of changing (reducing) the
axial strain so determined.  The special cases of course are: the ratio
P/Pc is the same for both column axes; or it is a two dimensional
problem.  Note: you could also change the I values for x and y
directions separately and not add the thermal load but this may take
more data entry or foul up the program data base.

That's what you get when I start thinking;  my head hurts too.

Happy Groundhog Day, Scott.

Regards,

H. Daryl Richardson

Haan, Scott M. wrote:
>
> "They look at each degree of freedom as not depending on the other degrees
> of freedom."
>
> Sorry, I was baffling with BS.  A diaphragm works by making stuff deflect
> together. I was thinking of mass, damping and stiffness for dynamics or
>
> 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: Haan, Scott M.
> Sent: Saturday, February 02, 2002 1:41 PM
> To: 'seaint(--nospam--at)seaint.org'
> Subject: RE: P-Delta Analysis(clarification)
>
> "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
> load in the stiffness calculations.
>
> 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
>
> _________________________________________________________________
>
> ******* ****** ******* ******** ******* ******* ******* ***
> *   Read list FAQ at: http://www.seaint.org/list_FAQ.asp
> *
> *   This email was sent to you via Structural Engineers
> *   Association of Southern California (SEAOSC) server. To
> *   subscribe (no fee) or UnSubscribe, please go to:
> *
> *   http://www.seaint.org/sealist1.asp
> *
> *   Questions to seaint-ad(--nospam--at)seaint.org. Remember, any email you
> *   send to the list is public domain and may be re-posted
> *   site at: http://www.seaint.org
> ******* ****** ****** ****** ******* ****** ****** ********
>
> ******* ****** ******* ******** ******* ******* ******* ***
> *   Read list FAQ at: http://www.seaint.org/list_FAQ.asp
> *
> *   This email was sent to you via Structural Engineers
> *   Association of Southern California (SEAOSC) server. To
> *   subscribe (no fee) or UnSubscribe, please go to:
> *
> *   http://www.seaint.org/sealist1.asp
> *
> *   Questions to seaint-ad(--nospam--at)seaint.org. Remember, any email you
> *   send to the list is public domain and may be re-posted
> *   site at: http://www.seaint.org
> ******* ****** ****** ****** ******* ****** ****** ********

******* ****** ******* ******** ******* ******* ******* ***
*   Read list FAQ at: http://www.seaint.org/list_FAQ.asp
*
*   This email was sent to you via Structural Engineers
*   Association of Southern California (SEAOSC) server. To
*   subscribe (no fee) or UnSubscribe, please go to:
*
*   http://www.seaint.org/sealist1.asp
*
*   Questions to seaint-ad(--nospam--at)seaint.org. Remember, any email you
*   send to the list is public domain and may be re-posted