고체역학 (Gere) — Axially Loaded Members: Problem 2.6-12

2.6-12 A plastic bar of diameter \(d = 32 \text{ mm}\) is compressed in a testing device by a force \(P = 190 \text{ N}\) that is applied as shown in the figure. (a) Determine the normal and shear stresses acting on all faces of stress elements oriented at (1) an angle \(\theta = 0^\circ\), (2) an angle \(\theta = 22.5^\circ\), and (3) an angle \(\theta = 45^\circ\). In each case, show the stresses on a sketch of a properly oriented element. What are \(\sigma_{\text{max}}\) and \(\tau_{\text{max}}\)? (b) Find \(\sigma_{\text{max}}\) and \(\tau_{\text{max}}\) in the plastic bar if a re-centering spring of stiffness \(k\) is inserted into the testing device, as shown in the figure. The spring stiffness is 1/6 of the axial stiffness of the plastic bar.