Gere & Goodno — Analysis of Stress and Strain: Problem 7.2-15

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.)