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Re: seaint Digest for 16 Aug 1999

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> From: Mark Gilligan <MarkKGilligan(--nospam--at)>

> The difference between our statements is based on the assumption of the
> buckled shape.  You are assuming that the brace suppresses all
> displacement in the brace in which case your statement is true.

You are probably refering to my comment:
> > If you put in more braces (e.g. reduce your unbraced length), the
> > buckling mode increases (e.g. from 1/2 sine wave to 1 sine wave, etc.).
As you note, this refers to the discrete brace model which is the basis
for the compression column brace model in the design standards.

> On the other hand if you use more braces, each somewhat less stiff, you
> will get a different buckling mode shape that has displacements at the
> bracing points.  Salmon & Johnson 3rd Edition has a figure that shows

> difference between a simple beam and a beam on elastic foundation.  To get

I don't have Salmon & Johnson. However, the elastic foundation model
1) braces closely spaced relative to length and sine wave length
   (this may invalidate the elastic foundation model, here, but that is
     where engineering judgement comes into play.)
2) determine the half wave length that will develop given k, E, I
   (minimize Pcrit)
3) gradually increasing load
   (probably acceptable with a moving load on a bridge)
4) consistent brace stiffness to ensure that buckling occurs as assumed
5) local buckling/yielding does not occur
   (a possibility as you push angle members to higher stress levels)

Obviously, there are practical limits to the quantity of braces and the
structural configuration, to ensure brace design stiffness, that can be
provided. I would consider this a candidate for bracketing solutions
(e.g. lower/upper limits on chord size vs. maximum/minimum braces) to
determine cost/benefit. If Ed is satisfied that the elastic foundation
analysis applies then there may be merit.

In any event, there may be a better way to provide stiff bracing than to
use a simple cantilever.

Paul Ransom, P. Eng.
Burlington, Ontario, Canada
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