The torsion constant is a geometrical property of a bar’s cross-section which is involved in the relationship between angle of twist and applied torque along the axis of the bar, for a homogeneous linear-elastic bar. The torsion constant, together with material properties and length, describes a advanced mechanics of materials boresi pdf’s torsional stiffness. The SI unit for torsion constant is m4. 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.

For non-circular cross-sections, there are no exact analytical equations for finding the torsion constant. However, approximate solutions have been found for many shapes.

Non-circular cross-sections always have warping deformations that require numerical methods to allow for the exact calculation of the torsion constant. The torsional stiffness of beams with non-circular cross sections is significantly increased if the warping of the end sections is restrained by, for example, stiff end blocks. This is identical to the second moment of area Jzz and is exact.

This is a tube with a slit cut longitudinally through its wall. This is derived from the above equation for an arbitrary thin walled open tube of uniform thickness.