Gere & Goodno — Torsion: Problem 3.4-8

3.4-8 Two sections of steel drill pipe, joined by bolted flange plates at B, are being tested to assess the adequacy of both the pipes. In the test, the pipe structure is fixed at A, a concentrated torque of \(500 \text{ kN} \cdot \text{m}\) is applied at \(x = 0.5 \text{ m}\), and uniformly distributed torque intensity \(t_0 = 250 \text{ kN} \cdot \text{m/m}\) is applied on pipe \(BC\). Both pipes have the same inner diameter \(d = 200 \text{ mm}\). Pipe \(AB\) has thickness \(t_{AB} = 15 \text{ mm}\), while pipe \(BC\) has thickness \(t_{BC} = 12 \text{ mm}\). Find the maximum shear stress and maximum twist of the pipe and their locations along the pipe. Assume \(G = 75 \text{ GPa}\).