고체역학 (Gere) — Torsion: Problem 3.4-13

3.4-13 The nonprismatic, cantilever circular bar shown has an internal cylindrical hole from 0 to \(x\), so the net polar moment of inertia of the cross section for segment 1 is \((7/8)I_p\). Torque \(T\) is applied at \(x\) and torque \(T/2\) is applied at \(x = L\). Assume that \(G\) is constant. (a) Find the reaction moment \(R_1\). (b) Find internal torsional moments \(T_i\) in segments 1 and 2. (c) Find \(x\) required to obtain twist at joint 3 of \(\phi_3 = TL/GI_p\). (d) What is the rotation at joint 2, \(\phi_2\)? (e) Draw the torsional moment (TMD : \(T(x), 0 \le x \le L\)) and displacement (TDD : \(\phi(x), 0 \le x \le L\)) diagrams.