고체역학 (Gere) — Torsion: Problem 3.9-9

3.9-9 Derive a formula for the strain energy \( U \) of the cantilever bar shown in the figure. The bar has circular cross sections and length \( L \). It is subjected to a distributed torque of intensity \( t \) per unit distance. The intensity varies linearly from \( t = 0 \) at the free end to a maximum value \( t = t_0 \) at the support.