고체역학 (Beer) — Stress and Strain—Axial Loading: Problem 2.72

2.72 For a member under axial loading, express the normal strain \(\epsilon'\) in a direction forming an angle of \(45^\circ\) with the axis of the load in terms of the axial strain \(\epsilon_x\) by (a) comparing the hypotenuses of the triangles shown in Fig. 2.43, which represent respectively an element before and after deformation, (b) using the values of the corresponding stresses \(\sigma'\) and \(\sigma_x\) shown in Fig. 1.38, and the generalized Hooke’s law.