Polar Area Moment Of Inertia

[brieffiniteelementnet]

Polar Area Moment Of Inertia

[ArtemRash]

It is very interesting to solve the problem of torsion constants determining
(https://www.researchgate.net/publication/225387731_Warping_shear_stresses_in_nonuniform_torsion_by_BEM for example)

[epsi1on]

From Torsion Constant on Wikipedia:

In 1820, the French engineer A. Duleau derived analytically that the torsion constant of a beam is identical to the second moment of area normal to the section Jzz, which has an exact analytic equation, by assuming that a plane section before twisting remains planar after twisting, and a diameter remains a straight line. Unfortunately, that assumption is correct only in beams with circular cross-sections, and is incorrect for any other shape where warping takes place.

Ref: Archie Higdon et al. "Mechanics of Materials, 4th edition"

[epsi1on]

Fixed in commit 9de5042

[epsi1on]

It is very interesting to solve the problem of torsion constants determining
(https://www.researchgate.net/publication/225387731_Warping_shear_stresses_in_nonuniform_torsion_by_BEM for example)

Is there any simpler method?

[ArtemRash]

It is very interesting to solve the problem of torsion constants determining
(https://www.researchgate.net/publication/225387731_Warping_shear_stresses_in_nonuniform_torsion_by_BEM for example)

Is there any simpler method?

I'm afraid not. A simpler method is to determine the torsion constants "It" based on standard formulas (see earlier, for example). These formulas, unfortunately, apply only to individual cross-sectional shapes. The universal method is nontrivial.