고체역학 (Gere) — Torsion: Problem 3.9-1

3.9-1 A solid circular bar of steel (\(G = 80\text{ GPa}\)) with length \(L = 1.5\text{ m}\) and diameter \(d = 75\text{ mm}\) is subjected to pure torsion by torques \(T\) acting at the ends (see figure). (a) Calculate the amount of strain energy \(U\) stored in the bar when the maximum shear stress is \(45\text{ MPa}\). (b) From the strain energy, calculate the angle of twist \(\phi\) (in degrees).