고체역학 (Beer) — Principal Stresses Under a Given Loading: Problem 8.25

8.25 The solid shafts $ABC$ and $DEF$ and the gears shown are used to transmit 20 hp from the motor $M$ to a machine tool connected to shaft $DEF$. Knowing that the motor rotates at 240 rpm and that $\tau_{\text{all}} = 7.5\text{ ksi}$, determine the smallest permissible diameter of (a) shaft $ABC$, (b) shaft $DEF$.