고체역학 (Gere) — Axially Loaded Members: Problem 2.5-8

2.5-8 A plastic bar \(ACB\) having two different solid circular cross sections is held between rigid supports, as shown in the figure. The diameters in the left- and right-hand parts are \(50 \text{ mm}\) and \(75 \text{ mm}\), respectively. The corresponding lengths are \(225 \text{ mm}\) and \(300 \text{ mm}\). Also, the modulus of elasticity \(E\) is \(6.0 \text{ GPa}\), and the coefficient of thermal expansion \(\alpha\) is \(100 \times 10^{-6}/^\circ\text{C}\). The bar is subjected to a uniform temperature increase of \(30^\circ\text{C}\). (a) Calculate the following quantities: (1) the compressive force \(N\) in the bar; (2) the maximum compressive stress \(\sigma_c\); and (3) the displacement \(\delta_C\) of point \(C\). (b) Repeat part (a) if the rigid support at \(A\) is replaced by an elastic support having spring constant \(k = 50 \text{ MN/m}\) (see figure part b; assume that only the bar \(ACB\) is subject to the temperature increase).