고체역학 (Gere) — Axially Loaded Members: Problem 2.6-13

2.6-13 A plastic bar of rectangular cross section (\(b = 38\text{ mm}\) and \(h = 75\text{ mm}\)) fits snugly between rigid supports at room temperature (\(20^\circ\text{C}\)) but with no initial stress (see figure). When the temperature of the bar is raised to \(70^\circ\text{C}\), the compressive stress on an inclined plane \(pq\) at mid-span becomes \(8.7\text{ MPa}\). (a) What is the shear stress on plane \(pq\)? (Assume \(\alpha = 95 \times 10^{-6}/^\circ\text{C}\) and \(E = 2.4\text{ GPa}\).) (b) Draw a stress element oriented to plane \(pq\) and show the stresses acting on all faces of this element. (c) If the allowable normal stress is \(23\text{ MPa}\) and the allowable shear stress is \(11.3\text{ MPa}\), what is the maximum load \(P\) (in the positive \(x\) direction), which can be added at the quarter point (in addition to thermal effects given) without exceeding allowable stress values in the bar?