고체역학 (Beer) — Torsion: Problem 3.62

3.62 A solid shaft and a hollow shaft are made of the same material and are of the same weight and length. Denoting by \(n\) the ratio \(c_1∕c_2\), show that the ratio \(T_s∕T_h\) of the torque \(T_s\) in the solid shaft to the torque \(T_h\) in the hollow shaft is (a) \(\sqrt{1 - n^2}∕(1 + n^2)\) if the maximum shearing stress is the same in each shaft, (b) \((1 - n^2)∕(1 + n^2)\) if the angle of twist is the same for each shaft.