고체역학 (Beer) — Torsion: Problem 3.100

3.100 A torque \( T \) is applied to the 20-mm-diameter steel rod \( AB \). Assuming the steel to be elastoplastic with \( G = 77.2 \text{ GPa} \) and \( \tau_Y = 145 \text{ MPa} \), determine (a) the torque \( T \) when the angle of twist at \( A \) is \( 25^\circ \), (b) the corresponding diameter of the elastic core of the shaft.