고체역학 (Gere) — Torsion: Problem 3.8-10

3.8-10 A circular bar $AB$ of length $L$ is fixed against rotation at the ends and loaded by a distributed torque $t(x)$ that varies linearly in intensity from zero at end $A$ to $t_0$ at end $B$ (see figure). (a) Obtain formulas for the fixed-end torques $T_A$ and $T_B$. (b) Find an expression for the angle of twist $\phi(x)$. What is $\phi_{max}$, and where does it occur along the bar?