고체역학 (Beer) — Transformations of Stress and Strain: Problem 7.157

7.157 The following state of strain has been determined on the surface of a cast-iron machine part: \[ \epsilon_x = -720 \mu, \quad \epsilon_y = -400 \mu, \quad \gamma_{xy} = +660 \mu \] Knowing that \(E = 69 \text{ GPa}\) and \(G = 28 \text{ GPa}\), determine the principal planes and principal stresses (a) by determining the corresponding state of plane stress [use Eq. (2.27), Eq. (2.34), and the first two equations of Prob. 2.73] and then using Mohr’s circle for stress, (b) by using Mohr’s circle for strain to determine the orientation and magnitude of the principal strains and then determining the corresponding stresses.