고체역학 (Gere) — Torsion: Problem 3.7-12

3.7-12 The shaft $ABC$ shown in the figure is driven by a motor that delivers $300\text{ kW}$ at a rotational speed of $32\text{ Hz}$. The gears at $B$ and $C$ take out $120\text{ kW}$ and $180\text{ kW}$, respectively. The lengths of the two parts of the shaft are $L_1 = 1.5\text{ m}$ and $L_2 = 0.9\text{ m}$. Determine the required diameter $d$ of the shaft if the allowable shear stress is $50\text{ MPa}$, the allowable angle of twist between points $A$ and $C$ is $4.0^\circ$, and $G = 75\text{ GPa}$.