Torsion and Shear Effects

Abstract

A pure torque is applied to a circular rod of homogeneous isotropic material (figure 4.1a). We shall consider possible deformations that can take place on the section AA. In figure 4.1b it is assumed that the left-hand portion, X, has a convex surface so that the surface of the right-hand portion, Y, must be concave. This is not compatible as may easily be seen by rotating the left-hand portion through 180° about A-A to become Y’ (figure 4.1c). If we now compare b and c, apparently the same torque has produced a concave surface on Y and a convex surface on Y’. Clearly this is impossible. A line that was radial is shown in c assumed deformed into a curve when the torque is applied. A similar argument may be applied to show that this is impossible. The details are left as an exercise for the reader.