Problem $2(10$ points$).$ A closed$-$ended thin$-$walled cylindrical pressure vessel has an average diameter of $8$ in and a wall thickness of $0\mathrm{.}08$ in $.$ Determine the internal pressure necessary to initiate yielding. Assume that the vessel is made of a ductile material with $S_{yt}=36$ksi and $S_{yc}=54$ksi, and consider a factor of safety, $n=2\mathrm{.}5.$