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DAM- Appendix 7 Application to Step Columns

DAM- Appendix 7 Application to Step Columns

DAM- Appendix 7 Application to Step Columns

Does appendix 7 allow K-factors for step-columns to be set = 1.0 for the upper and lower segments?  

RE: DAM- Appendix 7 Application to Step Columns

Toad -

I don't think step columns are ever officially mentioned. But, this is a good example where the DA method (with K=1.0) will probably be better / more reliable for ensuring stability than a K factor.  

I'd use K = 1.0, but set the unbraced length as the distance between bracing... even if that is greater than the segment length.  

There is another method to use for calculating the buckling capacity of this type of member. The method of successive approximations.  This is described in the AISC design guide (number 25?) for tapered members.  The method comes from one of Timoshenko's books (Elastic Stability?). And, the example that Timoshenko gives in his book is a stepped column.   

RE: DAM- Appendix 7 Application to Step Columns

I have been using the method for getting K-factors from Design guide 7 and AIST Tech Report 13 for years now.
I was just curious about DAM because K-factors for step columns can become a real pain as the factors are load dependent and therefore sometimes you have different K-factors for different load combinations.  

RE: DAM- Appendix 7 Application to Step Columns

I had a thread (see here thread507-288365: Built-up / Reinforced - Stepped Column) regarding the analysis of stepped members a while bac. It was a question on using the newmark method, which I believe is a successive approximations approach however I didn't understand on how to account for inelastic buckling. As the newmark method (I thought) would give you the elastic buckling.
Does DG7, the AIST Tech Report 13, or DG25 discuss this?


RE: DAM- Appendix 7 Application to Step Columns

I'm not going to pretend to fully understand all the theory behind inelastic buckling. The only way I have ever understood on how to tackle stepped columns was effective length factors (K).   

RE: DAM- Appendix 7 Application to Step Columns

The method of successive approximations that I mentioned is definitely an elastic buckling method. So, it will give you part of the answer.  

The concepts of Direct Analysis Method (reducing the flexural stiffness of the members based on the axial loading) are what allow a typical elastic analysis (with P-Delta for 2nd order effects) to approximate the inelastic buckling of the member or frame. It's not perfect, but I'd argue that it's good enough.  And, it is relatively simple compared to trying to get the "true" inelastic buckling values for this member or frame.  


RE: DAM- Appendix 7 Application to Step Columns


Good call. Such a simple concept yet I get it confused time and time again.

I think really the confusion (for me) lies with in the fact of using the B1-B2 method which I relate to effective length method. I forgot that B1-B2 is just the 2nd order analysis part of the DAM  (Add notional loads to account for initial imperfections, 2nd order analysis, and reduce stiffness to account for axial loads - ?)

In my thread I was referring to columns which were pinned and gravity only. In this case K=1 would be conservative (I believe)and basically you would use the Newmark Method (numerical method I believe to be similar to a successive approx.) to find your elastic buckling strength then use the elastic buckling strength equation Pe=pi^2*E/(L/r)^2 to find L/r then from there you would determine which equation AISC E3a or E3b to use.


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