고체역학 (Gere) — Torsion: Problem 3.8-11

3.8-11 A circular bar $AB$ with ends fixed against rotation has a hole extending for half of its length (see figure). The outer diameter of the bar is $d_2 = 76\text{ mm}$, and the diameter of the hole is $d_1 = 61\text{ mm}$. The total length of the bar is $L = 1270\text{ mm}$. (a) At what distance $x$ from the left-hand end of the bar should a torque $T_0$ be applied so that the reactive torques at the supports will be equal? (b) Based on the solution for $x$ in part (a), what is $\phi_{max}$, and where does it occur? Assume that $T_0 = 10\text{ kN}\cdot\text{m}$ and $G = 73\text{ GPa}$.