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RE: question on K factors and P-delta analysis

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Clifford,

My ASD general finite element program has the following note concerning
P-Delta analysis:

1. In 2d structures, analyze them in 3d and enter a small destabilization
force perpendicular to the plane of the structure.
2. Keep K=1.0 unless the elements are subdivided.  In this case, enter K
factor such that the K*L longitude of the sub-element is equal to the length
of the undivided element.

I have always wondered how a small perpendicular force should be defined.  I
have tried structures that passed with wind but not seismic forces.  Seems
subject to interruption.

HTH

Ronald A. Hill, P.E.
HILL Consulting Engineering
PO BOX 26525
Birmingham, Alabama 35260 USA
Phone: 205-823-4784
FAX: 205-823-4145
email: ronhill(--nospam--at)hillce.com
http://www.hillce.com
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-----Original Message-----
From: Clifford Schwinger [mailto:clifford234(--nospam--at)yahoo.com] 
Sent: Tuesday, October 07, 2003 8:15 AM
To: seaint(--nospam--at)seaint.org
Subject: question on K factors and P-delta analysis


I've heard people say that when you do a second-order
analysis on a moment frame, you can use a K-factor of
1.0 for the column design.  I'm trying to find an
explanation of this concept, and I am trying to find
out whether the idea of using K=1 when you do a
second-order analysis is correct or not.

I don't understand how doing a second-order analysis
to compute the P-delta moments would allow you to
automatically toss the K-factor out the window (and
use K=1). 

As I understand it, the K-factor is a modification you
make to the Euler buckling equation to adjust that
equation to account for column end conditions
different from the ideal pinned-pinned ends assumed
for the "perfect" Euler column.

I have a copy of a book called "Is Your Structure
Suitably Braced".   This publication is a compilation
of papers from a 1993 conference organized by the
SSRC, AISC, AISI and MBMA.  In the back of the book is
a transcript of a panel discussion where someone asked
the following question:

What is your recommendation on the K-factor when a
second-order elastic analysis is performed?  Can K be
taken as 1.0 in all these cases?

Dr. Joseph Yura (one of the panelists) responded as
follows:

"If you are using the AISC Specification, and you are
using a second-order elastic structure analysis, you
must use a K-factor.  The SSRC Third Edition indicated
that you can do a K=1.0.  If you check the Fourth
Edition, you'll see that's been removed and you still
must use a K factor because the checks that we had
done indicated that in high gravity load situations,
that procedure will not cut it."

Surfing the internet for the source of the "you can
use K=1 when you do a second-order analysis" concept,
I found a paper by Dr. Edward Wilson (of CSI?) titled "Geometric Stiffness
and P-Delta Effects".  In that paper he says: 

".The application of the method of analysis presented
in this chapter should lead to the elimination of the
column effective length (K-) factors, since P-Delta
effects automatically produce the required design
moment amplifications.  Also, the K-factors are
approximate, complicated, and time-consuming to
calculate.  Building codes for concrete and steel now
allow explicit accounting of P-Delta effects as an
alternative to the more involved and approximate
methods of calculating moment magnification factors
for most column designs."

(Here is the url to the paper:
www.comp-engineering.com/downloads/technical_papers/CSI/11.pdf

So now I am really confused.

Section C1.2 in the Third Edition AISC Manual says:

"In structures designed on the basis of elastic
analysis, Mu for beam-columns..shall be determined
from a second order elastic analysis or from the
following approximate second order analysis procedure:
 Mu =  B1 x Mnt + B2 x Mlt."

A similar methodology to the one in the AISC Manual is specified in ACI
318-02-318 for concrete structures.

The way I see it, engineers have the option of
accounting for P-delta effects by either doing a
second-order analysis or by computing the moment
magnification factors as described in the AISC Manual
or ACI 318, but whichever method is used (for
computing P-delta moments) you still have to use the appropriate K-factor. 

I'm confused by the comment made by Dr. Yura  (see
above) where he said that SSRC Third Edition said to
use K=1 but the SSRC Fourth Edition said to use the
actual K-factor. Was the Third Edition incorrect, or
did something else change when the Fourth Edition was published.

What is the theory (please explain in simple terms so
that my aging mind can understand) that would allow
you to ever use K=1 for an unbraced moment frame when
you do a second-order analysis?

Here's an example that's reinforcing my "brain-lock"
on this issue:

Let's say you have a single cantilevering "flag-pole"
column with an axial load and horizontal load applied
at the top of the column. You compute the first-order
moment and deflection. You then compute the
second-order moment and deflection, and then design
the cantilevered column using K=2.  Is there any way
you could ever use K=1 on a cantilevered column just
because you did the second-order analysis?

A similar example is where you have a moment frame
with two identical columns with perfectly pinned bases
and connected to an infinitely rigid beam at the top. 
Each column has an identical axial load and there is a
single horizontal load applied at the top of one of
the columns acting parallel to the beam span.  This
example is virtually identical to the previous
cantilevered flag-pole example except that the
cantilevering flag-pole columns are upside down. How
could you ever justify using K=1 just because you do a second-order
analysis?

I would be most grateful if someone could explain
where the "you can use K=1 when you do a second-order
analysis" idea came from and whether or not it is a
structural engineering "urban legend".  There must
have been some justification to the K=1 concept if it
was in the SSRC Third Edition.

Thanks.

Cliff Schwinger


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