고체역학 (Gere) — Analysis of Stress and Strain: Problem 7.2-11

7.2-11 The polyethylene liner of a settling pond is subjected to stresses \(\sigma_x = 2.5 \text{ MPa}\), \(\sigma_y = 0.75 \text{ MPa}\), and \(\tau_{xy} = -0.8 \text{ MPa}\), as shown by the plane-stress element in the figure part a. Determine the normal and shear stresses acting on a seam oriented at an angle of \(30^\circ\) to the element, as shown in the figure part b. Show these stresses on a sketch of an element having its sides parallel and perpendicular to the seam.