고체역학 (Gere) — Torsion: Problem 3.9-10

3.9-10 A thin-walled hollow tube AB of conical shape has constant thickness \(t\) and average diameters \(d_A\) and \(d_B\) at the ends (see figure). (a) Determine the strain energy \(U\) of the tube when it is subjected to pure torsion by torques \(T\). (b) Determine the angle of twist \(\phi\) of the tube. Note: Use the approximate formula \(I_p \approx \pi d^3 t / 4\) for a thin circular ring; see Case 22 of Appendix E.