고체역학 (Gere) — Torsion: Problem 3.8-7

3.8-7 A stepped shaft $ACB$ is held against rotation at ends $A$ and $B$ and subjected to a torque $T_0$ acting at section $C$ (see figure). The two segments of the shaft ($AC$ and $CB$) have diameters $d_A$ and $d_B$, respectively, and polar moments of inertia $I_{pA}$ and $I_{pB}$, respectively. The shaft has length $L$ and segment $AC$ has length $a$. (a) For what ratio $a/L$ will the maximum shear stresses be the same in both segments of the shaft? (b) For what ratio $a/L$ will the internal torques be the same in both segments of the shaft?