고체역학 (Beer) — Torsion: Problem 3.30

3.30 (a) For a given allowable shearing stress, determine the ratio \( T/w \) of the maximum allowable torque \( T \) and the weight per unit length \( w \) for the hollow shaft shown. (b) Denoting by \( (T/w)_0 \) the value of this ratio for a solid shaft of the same radius \( c_2 \), express the ratio \( T/w \) for the hollow shaft in terms of \( (T/w)_0 \) and \( c_1/c_2 \).