고체역학 (Beer) — Stress and Strain—Axial Loading: Problem 2.49

2.49 The aluminum shell is fully bonded to the brass core, and the assembly is unstressed at a temperature of 78°F. Considering only axial deformations, determine the stress when the temperature reaches 180°F in (a) the brass core, (b) the aluminum shell. Brass core: \( E = 15 \times 10^6 \text{ psi} \), \( \alpha = 11.6 \times 10^{-6}/^\circ\text{F} \), diameter \( = 1 \text{ in.} \) Aluminum shell: \( E = 10.6 \times 10^6 \text{ psi} \), \( \alpha = 12.9 \times 10^{-6}/^\circ\text{F} \), outer diameter \( = 2.5 \text{ in.} \)