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# Torsional Constant

• To: seaint(--nospam--at)seaint.org
• Subject: Torsional Constant
• From: Roger Turk <73527.1356(--nospam--at)compuserve.com>
• Date: Wed, 26 Feb 2003 09:32:24 -0500

```Nels,

>From Roger L. Brockenbrough and Bruce G. Johnston's USS Steel Design Manual,
for a rectangular cross section:

fsubs = T * Gamma * t/J

where,   fsubs = torsional shear stress
T = Torque
t = thickness
Gamma = a factor based on height/thickness ratio

and,     J = b*t^3/3 - 2 * Psi *t^4

where,   b = height of rectangle
Psi = a factor based on height/thickness ratio

(Penciled in my book is the notation that 2*psi*t^4 term accounts for the
loss of volume in ends of membrane analogy.)

For b/t approaching 4,

fsubs = Tt/J

and,  J = b * t^3/3 - .21 * t^4

For b/t = 4, 2 * psi = .2101, and
gamma   = 0.9970

For b/t = infinity, 2 * psi = .2101, and
gamma   = 1.0000

HTH

A. Roger Turk, P.E.(Structural)
Tucson, Arizona

Nels Roselund 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

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