Torsion constant

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.

[1] For non-circular cross-sections, there are no exact analytical equations for finding the torsion constant.

Non-circular cross-sections always have warping deformations that require numerical methods to allow for the exact calculation of the torsion constant.

[4] where where where where [7] Alternatively the following equation can be used with an error of not greater than 4%: where This is a tube with a slit cut longitudinally through its wall.

Main quantities involved in bar torsion: is the angle of twist; T is the applied torque; L is the beam length.