고체역학 (Beer) — Stress and Strain—Axial Loading: Problem 2.53

2.53 Solve Prob. 2.52, assuming that portion AB of the composite rod is made of aluminum and portion BC is made of steel. Reference (Prob 2.52): A rod consisting of two cylindrical portions AB and BC is restrained at both ends. Portion AB is made of steel (\(E_s = 29 \times 10^6 \text{ psi}, \alpha_s = 6.5 \times 10^{-6}/^\circ\text{F}\)) and portion BC is made of aluminum (\(E_a = 10.4 \times 10^6 \text{ psi}, \alpha_a = 13.3 \times 10^{-6}/^\circ\text{F}\)). Knowing that the rod is initially unstressed, determine (a) the normal stresses induced in portions AB and BC by a temperature rise of \(70^\circ\text{F}\), (b) the corresponding deflection of point B. Geometry from Fig. P2.52: Portion AB: \(L_{AB} = 24 \text{ in.}\), diameter \(d_{AB} = 2\frac{1}{4} \text{ in.}\) Portion BC: \(L_{BC} = 32 \text{ in.}\), diameter \(d_{BC} = 1\frac{1}{2} \text{ in.}\)