K value of side-sway columns 1

The k values are a function of the boundary or restraint conditions. They assist engineers in determining the elastic Euler buckling load.

The P-Delta is a method of analysis capturing the second order effects. This method supercedes the moment magnification method.

Neither the P-Delta nor the moment magnification analysis replaces the Euler equation for buckling or critical load (stress). Rather one of the methods is compared to the Euler buckling load. to determine if the column selection is safe.

Take for example a column with a intial imperfection, we don't modify the K value just because of the additional lateral deflection.






Regards,
Qshake

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Often frames with sidesway can have an effective K of 2... think of it as a column twice as long with the point of no rotation at the middle of this longer column... for example.

Dik

I'd chime in here and second what Qshake says.... the k factor and Pdelta effects are dealing with two different things as stated.

I agree. The k factor will still be greater than 1. However, if a P-Delta analysis is performed, only Equation H1-3 needs to be checked (I am assuming 1989 ASD design), because Equations H1-1 and H1-2 amplify moments to account for P-Delta effects. For concrete design, the same logic would apply--moments would not need to be magnified.

DaveAtkins

It is depends why you want K factor?

If you want only to get the magnified moment ,apply P-Delta analysis with K=1 and what ever the k value it is not going to effect because it is relating to the lateral deflection of your column.

But if you like to get some thing relating to K like Slenderness ratio limit or lateral torsional buckling, you have to take the actual K factor and consider the magnified moment from p-Delta if required .

Regards

i agree completely with DaveAtkins

Thanks for the input!

From AISC 2005, Chapter C, it seems that under certain circumstances K=1.0 can be used in strength design of columns in a side-sway frame.

I haven't thoroughly read AISC 2005.

See attached link to AISC Modern Steel Construction December 2002 for more on this question.

Forgot the link!

well that article is perfect but i do not understand a phrase in this article


"However, frame buckling capacity can be determined if the second-order analysis is taken incrementally to the limit."


what incrementally to the limit mean?

I guess the "incrementally" here means the analysis iteration with P-Delta option. The stiffness matrix will be updated with the step-by-step load increase.

The answer by Dr. Louis F. Geschwindner makes me more confused. Actually, in accordance with CISC S16-94, there isn't a word saying with P-Delta analysis K value can be simply 1.0 anywhere. The code distinguishes beam and column although we can name both "beam-column" in actual structure. For beams K=1.0 (SAP2000 gives a default value K=1.0 for all beams, also there isn't a K required in calculation of Mr in S16-94), end moments will include the 2nd-order effect, which is obtained either by a P-Delta analysis option or by a moment magnification factor (old formula). For columns which are prone to buckling, as per Clause 9.3.3, K will be determined by either Appendix B and C. Appendix B gives the column K values, ranging from 0.65 to 2.0. Appendix C is for K value of columns in a continuous frame with side-sway prevented. In another word, S16-94 removed the K value chart for columns of side-sway permitted frame. This creates a room for confusion.

In real design, I still use the old approach: check the column strength with K values according to the support conditions, which can be definitely larger than 1.0. On the other hand, P-Delta analysis is not usualy my choice to trade off the K value. Quote a few words from a SAP2000 manual: "A well designed building should not have significant P-Delta effects. Analysis with and without the P-Delta effects will yield the magnitude of the P-Delta effects separately. If those lateral displacements differ by more than 5% for the same lateral load, the basic design may be too flexible and a redesign should be considered."

I hope AISC can make the issue clearer.