고체역학 (Gere) — Analysis of Stress and Strain: Problem 7.2-2

7.2-2 Solve the preceding problem for an element in plane stress on the bottom surface of a fuel tanker (figure part a); stresses are \(\sigma_x = 105 \text{ MPa}\), \(\sigma_y = 75 \text{ MPa}\), and \(\tau_{xy} = 25 \text{ MPa}\). Determine the stresses acting on an element oriented at an angle \(\theta = 40^\circ\) from the \(x\) axis, where the angle \(\theta\) is positive when counterclockwise. Show these stresses on a sketch of an element oriented at the angle \(\theta\).