고체역학 (Beer) — Torsion: Problem 3.56

3.56 Solve Prob. 3.55, assuming that the shaft AB is replaced by a hollow shaft of the same outer diameter and 25-mm inner diameter. Reference Problem 3.55: Two solid steel shafts ($G = 77.2 \text{ GPa}$) are connected to a coupling disk B and to fixed supports at A and C. For the loading shown, determine (a) the reaction at each support, (b) the maximum shearing stress in shaft AB, (c) the maximum shearing stress in shaft BC. Given data from Fig. P3.55: Applied torque at disk B: \(T_B = 1.4 \text{ kN}\cdot\text{m} = 1400 \text{ N}\cdot\text{m}\) Length of shaft AB: \(L_{AB} = 200 \text{ mm} = 0.2 \text{ m}\) Length of shaft BC: \(L_{BC} = 250 \text{ mm} = 0.25 \text{ m}\) Outer diameter of shaft AB: \(d_{o, AB} = 50 \text{ mm} \rightarrow c_2 = 25 \text{ mm} = 0.025 \text{ m}\) Inner diameter of shaft AB (for 3.56): \(d_{i, AB} = 25 \text{ mm} \rightarrow c_1 = 12.5 \text{ mm} = 0.0125 \text{ m}\) Diameter of solid shaft BC: \(d_{BC} = 38 \text{ mm} \rightarrow c_{BC} = 19 \text{ mm} = 0.019 \text{ m}\) Modulus of rigidity for steel: \(G = 77.2 \text{ GPa} = 77.2 \times 10^9 \text{ Pa}\)