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Re: Lateral Brace Deflection

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> From: "Ed Fasula" <tibbits2(--nospam--at)>
> I know that many use a factor of 0.02 of the design load on a compression
> member to brace it, but what kind of deflection criteria should be used?

There is good theory and testing to support this limit. However, as you
note, it is inadequate to rely on strength without stiffness since the
force in the brace is developed through deflection. If your restraint is
not stiff enough, then the brace, regardless of strength, is inadequate.

> I'm bracing the top chord of a bowstring truss for a bridge (discussed
> earlier on this list) with a diagonal fastened to an outrigger.  The
> outrigger extends 6' out, so it will deflect close to an inch under the 3
> kip vertical reaction from the brace (using a TS6x6x9/16).  With a 10' high
> truss, that's  about 1.5" lateral movement of the top chord (2L6x4x5/8 LLH).
> That's the center brace.  Each following brace would move successively less.
> So, I guess you could look at it as 100'*12/1.5 = 800; L/800 deflection.  I
> don't want to over-simplify it here, but I'm guessing that most people
> aren't doing P-delta analysis in each case, and there is some conventional
> approach.  I haven't been able to find a discussion of it in any of my
> books...unless I suppose a unbraced frame analogy could be made.

You should actually consider the length between two adjacent braced
spans instead of the full length (e.g. L'=2*10 with braces at 10'
instead of 100') and the relative deflections between them. The other
braces must be considered ineffective if you use the full length. At
L'/span', what P-delta restraint load is generated? Is it larger than
the 2% rule of thumb load? If so, iterate to find the new deflection of
the outrigger and the new P-delta load. If not, maybe you can stop

Don't forget to consider the cumulative effect of fabrication and
construction tolerances in determining the initial delta. Add to the
load deflection in each iteration.

What happens to the rest of your structure when this outrigger is
loaded/deflects? What is providing the support to the outrigger? Does
the same outrigger extend out the opposite side to support another
compression chord? You may find that your cumulative relative
stiffnesses are much lower than you anticipate: k = 1/(1/k + 1/k + 1/k
...) The net result is closer to your lowest stiffness in a series load
path and the L/800 that you calculate may be unconservative.

P-delta analysis should be done where it is required. It will depend on
the buckling modes that you are trying to prevent or enforce.

As you add more braces, to reduce the braced length and increase the
buckling strength of the braced member, the stronger/stiffer each of
your bracings must be! Catch-22! It may be more economical to increase
the braced member and increase the unbraced length. Other conditions may
affect this decision.

Check these books:
Effective Length and Notional Load Approaches to Assessing Frame
Stability: Implications for American Steel Design, ASCE, 1997

Guide to Stability Design Criteria for Metal Structures, T.V.Galambos,
John Wiley and Sons.

SSRC may have other publications available:
Structrual Stability Research Council
Lehigh Universtiy
13 E Packer Avenue
Bethlehem, PA 18015 USA

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