고체역학 (Gere) — Tension, Compression, and Shear: Problem 1.3-18

1.3-18 A stepped shaft \(ABC\) consisting of two solid, circular segments is subjected to uniformly distributed torque \(t_1\) acting over segment 1 and concentrated torque \(T_2\) applied at \(C\), as shown in the figure. Segment 1 of the shaft has a diameter of \(d_1 = 57 \text{ mm}\) and length of \(L_1 = 0.75 \text{ m}\); segment 2 has a diameter \(d_2 = 44 \text{ mm}\) and length \(L_2 = 0.5 \text{ m}\). Torque intensity \(t_1 = 3100 \text{ N}\cdot\text{m/m}\) and \(T_2 = 1100 \text{ N}\cdot\text{m}\). (a) Find reaction torque \(T_A\) at support \(A\). (b) Find the internal torque \(T(x)\) at two locations: \(x = L_1/2\) and at \(x = L_1 + L_2/2\). Show these internal torques on properly drawn free-body diagrams (FBDs).