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Re: Partially Tapered Column Analysis

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> From: "Brian S Bossley" <BSBossley(--nospam--at)>

> 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.

This sounds like the column was designed for a crane bracket or maybe a
clearance issue. This is quite common.

> 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.

k=2 is worst case, despite the changes along the length.
Since there is flexibility at the haunch, the actual k<2.
Conservatively, same k for the full length.

> 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

It is common to use the section properties at the section being
assessed. It is conservative to use the minimum properties between
lateral brace points. This requires you to assess a LOT of sections for
each load case - custom software helps.

I recall that there is a commercial product for analysis of tapered
member frames for about $5000. Probably ASD 9th, only. Be cautious.

R. Paul Ransom, P. Eng.
Burlington, Ontario, Canada
<mailto:ado26(--nospam--at)> <>

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