Torsion

Abstract

In the problem of simple torsion of a circular shaft examined in Section 4.2, we obtained the following formulas for the displacements v and w in the lateral plane:

$$v=-\alpha xz w=\alpha xy$$

(8.1)

and found that the axial displacement u is always zero. In a general case of a noncircular cross section, however, the axial displacements are nonzero and, in accordance with Saint-Venant’s hypothesis, can be presented in the form

$$u=\alpha S(y,z)$$

(8.2)

The function S(y, z) considers the deplanation of the cross section and is called Saint-Venant’s torsion function.