고체역학 (Gere) — Analysis of Stress and Strain: Problem 7.2-20

7.2-20 Solve the preceding problem for \(\sigma_x = 11 \text{ MPa}\) and \(\sigma_y = -20 \text{ MPa}\) (see figure). Reference to Problem 7.2-19: At a point on the surface of an elliptical exercise machine, the material is in biaxial stress with \(\sigma_x = 9.7 \text{ MPa}\) and \(\sigma_y = -6 \text{ MPa}\), as shown in the figure part a. The figure part b shows an inclined plane \(aa\) cut through the same point in the material but oriented at an angle \(\theta\). Determine the value of the angle \(\theta\) between zero and \(90^\circ\) such that no normal stress acts on plane \(aa\). Sketch a stress element having plane \(aa\) as one of its sides and show all stresses acting on the element.