Gere & Goodno — Axially Loaded Members: Problem 2.5-17

2.5-17 A copper bar $AB$ with a length $0.635\text{ m}$ and diameter $50\text{ mm}$ is placed in position at room temperature with a gap of $0.2\text{ mm}$ between end $A$ and a rigid restraint (see figure). The bar is supported at end $B$ by an elastic spring with a spring constant $k = 210\text{ MN/m}$. (a) Calculate the axial compressive stress $\sigma_c$ in the bar if the temperature of the bar only rises $27^\circ\text{C}$. (For copper, use $\alpha = 17.5 \times 10^{-6}/^\circ\text{C}$ and $E = 110\text{ GPa}$.) (b) What is the force in the spring? (Neglect gravity effects.) (c) Repeat part (a) if $k \rightarrow \infty$.