고체역학 (Gere) — Axially Loaded Members: Problem 2.4-19

2.4-19 A horizontal rigid bar of weight \(W = 32 \text{ kN}\) is supported by three slender circular rods that are equally spaced (see figure). The two outer rods are made of aluminum (\(E_1 = 70 \text{ GPa}\)) with diameter \(d_1 = 10 \text{ mm}\) and length \(L_1 = 1 \text{ m}\). The inner rod is magnesium (\(E_2 = 42 \text{ GPa}\)) with diameter \(d_2\) and length \(L_2\). The allowable stresses in the aluminum and magnesium are \(165 \text{ MPa}\) and \(90 \text{ MPa}\), respectively. If it is desired to have all three rods loaded to their maximum allowable values, what should be the diameter \(d_2\) and length \(L_2\) of the middle rod?