How are second order effects and buckling lengths connected?

[bojoka4052]

As I understand it; when we consider second order effects we take into consideration the horizontal forces coming from the applied vertical load deforming the structure contributing to even more buckling and stresses in the structure. Is using buckling lengths the same as taking second order effects into consideration?

 

[skewl]

I have not worked with the term "buckling length" before. Are you are talking about the "effective length" in the Euler buckling equation?

In the case of a column which is able to deflect at the top (and fixed at the bottom), the effective length is 2L. But this wouldn't account for P-Delta effect for example since the Euler buckling equation assumes a "small" deflection. You would have to account for the second-order moment caused by the vertical load acting eccentrically separately (i.e. check the column as a beam-column with compression and bending due to P-delta).

 

[271828]

Using effective buckling lengths isn't the same as taking second-order effects into consideration. They are related, however.

One could accomplish a buckling analysis for a column, frame, or whatever, by building a frame-analysis model, imposing a very small initial displacement in the shape of the anticipated buckling mode, and doing a second-order analysis. Geometrically nonlinear to be more precise. When the load-displacement curve flattens out and tiny increases in load cause large increases in displacement, then that indicates the buckling load.

Buckling analysis with analytical results starting with Euler's formula and effective length factors is a practical way of accomplishing about the same thing as described above. See the AISC Specification Appendix 7, which gives alignment charts for K for frame members, etc.

This is an enormous subject. I've not done it justice at all. I'd recommend studying the AISC Design Guide 28. Also, I find the old B1, B2 Amplified First Order Analysis Procedure to be very good at illustrating what's going on. That's found in the AISC Specification Appendix 8. If you haven't used it before, you might take a look at a structural steel textbook that has a section on frame design.

 

[DaveAtkins]

Yes, an in depth subject. And keep in mind, P-big delta does not cause moment in a column; it adds lateral force to the overall structure. P-little delta adds moment to a column.

DaveAtkins