고체역학 (Gere) — Axially Loaded Members: Problem 2.5-12

2.5-12 A circular, aluminum alloy bar of a length $L = 1.8\text{ m}$ has a slot in the middle half of its length (see figure). The bar has a radius $r = 36\text{ mm}$ and modulus of elasticity $E = 72\text{ GPa}$. The slot has a height $2a = r/4$. If the temperature of the beam is raised uniformly by an amount $\Delta T = 15^\circ\text{C}$, calculate the thermal stress $\sigma_T$ developed in the bar. Assume that $\alpha = 23 \times 10^{-6}/^\circ\text{C}$.