$(40$ points$)$ The piping assembly shown in the figure, supported by the fixed connection at $A,$ is actually a pressure vessel that contains a fluid stored at a pressure of $400$ psi $.$ The vessel has an outer diameter of $3$ in $.$ and a wall thickness of $\frac{1}{8}in.$ The pressure vessel is made of a new metal alloy, which will rupture if its shear stress exceeds $3000$ psi. A worker inadvertently applies a force of $F=80l{b}_f$ to the handle of the wrench. Calculate the maximum shear stress at a point on the TOP of the pressure vessel at section $a-a$ to determine if the force $F$ will cause the PV to rupture at that point. Include a sketch of the stress element at this point on the pressure vessel.