고체역학 (Gere) — Torsion: Problem 3.9-6

3.9-6 A cantilever bar of circular cross section and length $L$ is fixed at one end and free at the other (see figure). The bar is loaded by a torque $T$ at the free end and by a distributed torque of constant intensity $t$ per unit distance along the length of the bar. (a) What is the strain energy $U_1$ of the bar when the load $T$ acts alone? (b) What is the strain energy $U_2$ when the load $t$ acts alone? (c) What is the strain energy $U_3$ when both loads act simultaneously?