고체역학 (Gere) — Analysis of Stress and Strain: Problem 7.2-25

7.2-25 At a point on the web of a girder on an overhead bridge crane in a manufacturing facility, the stresses are known to be $\sigma_x = -30\text{ MPa}$, $\sigma_y = 12\text{ MPa}$, and $\tau_{xy} = 21\text{ MPa}$ (the sign convention for these stresses is shown in Fig. 7-1). A stress element located at the same point in the structure (but oriented at a counterclockwise angle $\theta_1$ with respect to the $x$ axis) is subjected to the stresses shown in the figure ($\sigma_b$, $\tau_b$, and $14\text{ MPa}$). Assuming that the angle $\theta_1$ is between zero and $90^\circ$, calculate the normal stress $\sigma_b$, the shear stress $\tau_b$, and the angle $\theta_1$.