Problem $2(30$ pts$.)$

A cylindrical tank is $15$ ft long with an outer diameter of $5$ ft and a wall thickness of $0\mathrm{.}90$ inches. The tank is made of steel with $\backslash (\backslash$mathrm$\{$E$\}=29\backslash$times $10^\{6\}\backslash )$ psi $.$ The gage pressure in the container is increased from zero to $250$ psi $.$

a$)$ Determine the hoop stress and longitudinal stress on the wall of the container. Clearly indicate which stress is which.

b$)$ Determine the maximum shear stress, indicating if the maximum shear stress is in$-$plane or out$-$of$-$plane.