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Partially Tapered Column Analysis

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I am looking at an analyzing an existing building that consists of pre-manufactured rigid frames with a ‘partially tapered’ column on the one side.  What I mean by “partially tapered” is that the column is tapered from 0’ to 30’ up and then above that it takes on a uniform depth from 30’ to 45’.  I’ve seen these all over before, but I’ve never analyzed one until now.

 

So I started with 3rd edition LRFDI’m mainly using Appendix F and G to check the girder.

 

But here’s my question: If I look at this column in a piecewise fashion, what do I use for K of the two segments. It seems like the K for the bottom section would have to be larger than 2.0 because the WHOLE column should have a K of 2.0.   

 

Alternately, If I look at this as one big tapered member 45’ tall with a K=2.0, is it really fair to use the KL/r at the base of the taper?  I don’t think so.  Is the 5/3 factor in EQN A-F3-3 an adjustment for the fact that we use the KL/r of the smaller end?

 

 

 

Brian S Bossley, PE

Ventura Engineering

7610 Olentangy River Rd

Columbus, OH 43235