Question

A wire of length l and radius r is clamped at one end. It is twisted at the other end by an angleϕ about its axis.Write the shearing strain produced, in a small area lying in the cross-section at the end at a distance x from the axis.

Answer 1

The figure shows an area A at position x from axis which is parallel to area P at the clamped end. Due to twisting, A goes to A´ by suffering a displacement A A´ ≈ x ϕ relative to P. The separation between the parallel area P and A is l.

Hence shearing strain,