Question $2(6$ points$)$

You are pondering the stresses that might develop in a pressurized fuselage of an airplane and draw a couple of rough sketches to describe the lift forces from the wings and stabilizers, along with gravity acting on the structure:

a$)(1$ pt$.)$ Write expressions for $F_1$ and $F_2$ in terms of $mg,a,$ and $b.$

b$)(2$ pt$.)$ The material used is a brittle composite with ultimate compressive strength $S_{u_{\text{u}\text{t}\text{c}}}=-500$MPa and ultimate tensile strength $S_{ul{t}_t}=300$MPa. Please draw the linear approximation of the failure envelope on a ${}_1-{}_2$ plot using Mohr's criterion for brittle materials.