고체역학 (Gere) — Axially Loaded Members: Problem 2.5-21

2.5-21 Pipe 2 has been inserted snugly into Pipe 1, but the holes for a connecting pin do not line up; there is a gap s. The user decides to apply either force \(P_1\) to Pipe 1 or force \(P_2\) to Pipe 2, whichever is smaller. Determine the following using the numerical properties in the box. (a) If only \(P_1\) is applied, find \(P_1\) (kN) required to close gap s; if a pin is then inserted and \(P_1\) removed, what are reaction forces \(R_A\) and \(R_B\) for this load case? (b) If only \(P_2\) is applied, find \(P_2\) (kN) required to close gap s; if a pin is then inserted and \(P_2\) removed, what are reaction forces \(R_A\) and \(R_B\) for this load case? (c) What is the maximum shear stress in the pipes, for the loads in parts (a) and (b)? (d) If a temperature increase \(\Delta T\) is to be applied to the entire structure to close gap s (instead of applying forces \(P_1\) and \(P_2\)), find the \(\Delta T\) required to close the gap. If a pin is inserted after the gap has closed, what are reaction forces \(R_A\) and \(R_B\) for this case? (e) Finally, if the structure (with pin inserted) then cools to the original ambient temperature, what are reaction forces \(R_A\) and \(R_B\)? Numerical properties: \(E_1 = 210 \text{ GPa}\), \(E_2 = 96 \text{ GPa}\) \(\alpha_1 = 12 \times 10^{-6}/^\circ\text{C}\), \(\alpha_2 = 21 \times 10^{-6}/^\circ\text{C}\) Gap \(s = 1.25 \text{ mm}\) \(L_1 = 1.4 \text{ m}\), \(d_1 = 152 \text{ mm}\), \(t_1 = 12.5 \text{ mm}\), \(A_1 = 5478 \text{ mm}^2\) \(L_2 = 0.9 \text{ m}\), \(d_2 = 127 \text{ mm}\), \(t_2 = 6.5 \text{ mm}\), \(A_2 = 2461 \text{ mm}^2\)