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Re: k for compression members of frames with sidesway

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>Do you know of any documentation regarding
>the k = 1.0 if a P-delta analysis is performed?

I posed your question to Lou Geschwindner, who is AISC's new Vice President
of Engineering and Research. His reponse is below.


Your question is one with which engineers regularly struggle and I hope I
can provide a useful answer. The first, and perhaps most important, issue
has to do with looking at and combining provisions from two different
specifications. The AISC, CISC and other steel design specifications will
all accommodate stability issues differently and it is imperative that the
provisions within a single specification are used consistently. The approach
taken in the AISC specification is to use effective length for column axial
capacity and a second-order moment magnification for checking bending
capacity. Alternatively, the engineer could choose to do a second-order
analysis but it must be done correctly and that is usually the place where
misunderstandings occur.

The Canadian code uses a different approach to stability and second-order
effects (the notional load approach). Thus, their statement that the
effective length factor may be taken as 1.0 when a second-order analysis is
used is inappropriate for use with the AISC Specifications at this time.

When carrying out a second-order analysis one must be sure to address both
system buckling and moment amplification. The second-order analysis
procedures in a typical computer program will determine the magnitude of the
moments in the displaced equilibrium configuration corresponding to the
applied loads. They will not determine the buckling capacity of the frame.
However, frame buckling capacity can be determined if the second-order
analysis is taken incrementally to the limit. This requires more than just
checking the box in the software program for a second-order analysis.

It should also be noted that a second-order incremental approach can have
some potential problems. If the frame to be analyzed has no lateral load and
no sway under gravity load, a second-order analysis will yield the same
results as a first-order analysis, thus saying nothing about column capacity
or any second-order moments.

So, using a typical second-order analysis at ultimate load will permit the
elimination of the code-specified moment amplification factor from the
interaction equation but will not permit the use of K=1.0. A second-order
analysis under ultimate load taken to the limit will determine the buckling
capacity of the system and that will negate the need to use a K-factor to
determine that capacity.

A paper I published in the Proceedings of the 2000 North American Steel
Construction Conference, "A Practical Look at Frame Analysis, Stability and
Leaning Columns"  may be of help to you and a paper of the same title that
should be published soon in the AISC Engineering Journal will provide some
additional discussion and should also be of assistance. If you still have
questions on this topic I would be happy to hear from you again.

Louis F. Geschwindner
Vice President, Engineering and Research
American Institute of Steel Construction

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