고체역학 (Gere) — Analysis of Stress and Strain: Problem 7.2-16

7.2-16 Solve the preceding problem for a plate of dimensions \(100 \text{ mm} \times 250 \text{ mm}\) subjected to a compressive stress of \(2.5 \text{ MPa}\) in the long direction and a tensile stress of \(12.0 \text{ MPa}\) in the short direction (see figure). (From 7.2-15): A rectangular plate of dimensions \(75 \text{ mm} \times 125 \text{ mm}\) is formed by welding two triangular plates (see figure). The plate is subjected to a tensile stress of \(3.5 \text{ MPa}\) in the long direction and a compressive stress of \(2.5 \text{ MPa}\) in the short direction. Determine the normal stress \(\sigma_w\) acting perpendicular to the line of the weld and the shear stress \(\tau_w\) acting parallel to the weld. (Assume that the normal stress \(\sigma_w\) is positive when it acts in tension against the weld and the shear stress \(\tau_w\) is positive when it acts counterclockwise against the weld.)