고체역학 (Gere) — Axially Loaded Members: Problem 2.4-1

2.4-1 The assembly shown in the figure consists of a brass core (diameter \(d_1 = 6 \text{ mm}\)) surrounded by a steel shell (inner diameter \(d_2 = 7 \text{ mm}\), outer diameter \(d_3 = 9 \text{ mm}\)). A load \(P\) compresses the core and shell that both have a length \(L = 85 \text{ mm}\). The moduli of elasticity of the brass and steel are \(E_b = 100 \text{ GPa}\) and \(E_s = 200 \text{ GPa}\), respectively. (a) What load \(P\) will compress the assembly by \(0.1 \text{ mm}\)? (b) If the allowable stress in the steel is \(180 \text{ MPa}\) and the allowable stress in the brass is \(140 \text{ MPa}\), what is the allowable compressive load \(P_{\text{allow}}\)? (Suggestion: Use the equations derived in Example 2-8.)