고체역학 (Gere) — Torsion: Problem 3.8-2

3.8-2 A solid circular bar $ABCD$ with fixed supports at ends $A$ and $D$ is acted upon by two equal and oppositely directed torques $T_0$, as shown in the figure. The torques are applied at points $B$ and $C$, each of which is located at distance $x$ from one end of the bar. (The distance $x$ may vary from zero to $L/2$.) (a) For what distance $x$ will the angle of twist at points $B$ and $C$ be a maximum? (b) What is the corresponding angle of twist $\phi_{max}$?