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Re: AISC Appd'x 'B' - Effective width

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> From: richard lewis <rlewistx(--nospam--at)juno.com>
> 
> I am designing a steel box beam subject to 3 axis of bending, torsion and
> shear.  It is 36" x 8" and I hope to make it from 1/4" plate.  Since the
> b/t of the 36/0.25 is too slender I must use Appd'x. 'B'.  My question
> has to do with calculating the effective width 'be'.  What does the 'f'
> stand for?  It appears to me it is the combined compressive stress on the
> section.  Are the stresses based on the gross section, or the reduced
> section?  The code is not clear.  It says use the properties as specified
> in Appd'x. B5.2 which could be reduced section properties or gross
> section properties.  If it is the reduced section then this appears to be
> an iterative process.

f = "(axial plus bending stresses)" = "the level of uniformly
distributed stress to which the element would be subjected based upon
the design of the member".

In ASD 9th, page 5-131, second paragraph from the bottom, it is quite
clear about application. If you properly apply the form factor Qa and
reduction factor Qs, you do not need to iterate.

Otherwise, iterate or use a reduced section to meet limits of B5.1. It
is noted that "the limits provided in Sect. B5.1 is unnecessarily
conservative" when the max UDL stress is much less than allowable or the
b/t ratio is much higher than given in B5.1 - both are typical when
local buckling controls. Section B5.1 is actually based on achieving
yield (allowable) stresses and would be conservative for all lesser
stress conditions.

AISI Cold Formed Manual (without increase due to effects of cold
forming) describes the scenario pretty well in their analysis and
commentary.

You may achieve adequate results after two iterations and probably 3
max. It's the result of a "wandering centroid." Note that each reduced
section is valid only at a particular point on the structure where a
particular stress condition exists - move left or right and things
change. A rigorous analysis of the structure becomes VERY complicated.

The flip side is to do the analysis with the particular plate or element
Fy limited to a value (say Fy') which would permit the plate to be fully
effective (e.g. f=0.60*Fy' at which be = b). This reduces conservative
response and effort. Above this stress, you start to iterate. It can
also give you some idea of the sensitivity of the final result.

Alternately, you could stiffen the compressive element and all the
uncertainty goes away.

-- 
Paul Ransom, P. Eng.
Civil/Structural/Project/International
Burlington, Ontario, Canada
<mailto:ad026(--nospam--at)hwcn.org> <http://www.hwcn.org/~ad026/civil.html>

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