고체역학 (Beer) — Stress and Strain—Axial Loading: Problem 2.71

2.71 The homogeneous plate \(ABCD\) is subjected to a biaxial loading as shown. It is known that \(\sigma_z = \sigma_0\) and that the change in length of the plate in the \(x\) direction must be zero, that is, \(\epsilon_x = 0\). Denoting by \(E\) the modulus of elasticity and by \(\nu\) Poisson’s ratio, determine (a) the required magnitude of \(\sigma_x\), (b) the ratio \(\sigma_0 / \epsilon_z\).