고체역학 (Gere) — Axially Loaded Members: Problem 2.6-14

2.6-14 A copper bar of rectangular cross section (\(b = 18\text{ mm}\) and \(h = 40\text{ mm}\)) is held snugly (but without any initial stress) between rigid supports (see figure). The allowable stresses on the inclined plane \(pq\) at midspan, for which \(\theta = 55^\circ\), are specified as \(60\text{ MPa}\) in compression and \(30\text{ MPa}\) in shear. (a) What is the maximum permissible temperature rise \(\Delta T\) if the allowable stresses on plane \(pq\) are not to be exceeded? (Assume \(\alpha = 17 \times 10^{-6}/^\circ\text{C}\) and \(E = 120\text{ GPa}\).) (b) If the temperature increases by the maximum permissible amount, what are the stresses on plane \(pq\)? (c) If the temperature rises \(\Delta T = 28^\circ\text{C}\), how far to the right of end \(A\) (distance \(\beta L\), which is expressed as a fraction of length \(L\)) can load \(P = 15\text{ kN}\) be applied without exceeding allowable stress values in the bar? Assume that \(\sigma_a = 75\text{ MPa}\) and \(\tau_a = 35\text{ MPa}\).