고체역학 (Gere) — Axially Loaded Members: Problem 2.4-17

2.4-17 A bimetallic bar (or composite bar) of square cross section with dimensions \(2b \times 2b\) is constructed of two different metals having moduli of elasticity \(E_1\) and \(E_2\) (see figure). The two parts of the bar have the same cross-sectional dimensions. The bar is compressed by forces \(P\) acting through rigid end plates. The line of action of the loads has an eccentricity \(e\) of such magnitude that each part of the bar is stressed uniformly in compression. (a) Determine the axial forces \(P_1\) and \(P_2\) in the two parts of the bar. (b) Determine the eccentricity \(e\) of the loads. (c) Determine the ratio \(\sigma_1/\sigma_2\) of the stresses in the two parts of the bar.