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# Re: Torsional Constant

• To: seaint(--nospam--at)seaint.org
• Subject: Re: Torsional Constant
• From: Scott Maxwell <smaxwell(--nospam--at)engin.umich.edu>
• Date: Tue, 25 Feb 2003 14:30:46 -0500 (EST)

Yes, the torsional constant is the same as the polar moment of interia if
it is a circular section.

This is not true for non-circular sections.  From the Feb. 1965 ASCE
Structural journal article titled "Torsion of Structural Shapes":

"The polar moment of inertia would be the torsion constant for noncircular
sections, also, if the resultant shear stress were everywhere proportional
in magnitude to the distance from the center of twist and directed at 90
deg to radial lines.  The torsional constant of a noncircular section is
always less that the polar moment of inertia - increasingly so as a
section becomes less and less compact."

The article then goes onto give the following formula for St. Venant's
solution to the torsional constant for a rectangular section:

J = b*t^3/3 - 2V*t^4

The 2V value is given by a table in the article and is a function of the
b/t ratio.  For your case (b=8" and t=3/8"...b/t=21.33333), the value of
2V in the table would be 0.2101.

Further, the maximum torsional stress would be given by:

tau(sub m) = M*gamma*t/J

where M is the torsional moments, t is thickness, J is from above and
gamma is from the same table as 2V. For your case, gamma would be about
1.00 (for b/t of 4 gamma is 0.9970 and for b/t of infinity it is 1.00).

The second part of the torsional constant equation is due to "end effects"
(that is how I describe it in my notes from an advanced steel course that
I took that included torsion).

HTH,

Scott
Ypsilanti, MI

On Tue, 25 Feb 2003, Nels Roselund, SE wrote:

> I'm using Section F1 of the AISC Manual, 3rd edition, to analyze a 3/8" x 8"
> rectangular plate in bending about its major axis: it is subject to lateral
> torsional buckling.
>
> J is defined as the torsional constant.  Where is the method of determining
> the value of J stated in the manual?  J is the polar moment of inertia of a
> section in "Roark's Formulas for Stress and Strain" -- is that also the
> definition of J used here?
>
> Nels Roselund
> Structural Engineer
> South San Gabriel, CA
> njineer(--nospam--at)att.net
>

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