고체역학 (Gere) — Torsion: Problem 3.9-11

3.9-11 A hollow circular tube $A$ fits over the end of a solid circular bar $B$, as shown in the figure. The far ends of both bars are fixed. Initially, a hole through bar $B$ makes an angle $\beta$ with a line through two holes in tube $A$. Then bar $B$ is twisted until the holes are aligned, and a pin is placed through the holes. When bar $B$ is released and the system returns to equilibrium, what is the total strain energy $U$ of the two bars? (Let $I_{pA}$ and $I_{pB}$ represent the polar moments of inertia of bars $A$ and $B$, respectively. The length $L$ and shear modulus of elasticity $G$ are the same for both bars.)