Problem $2$: The gas tank is made from A$-36$ steel and has an inner diameter of $2\mathrm{.}0$m$,$ as shown in Figure $3.$ If the tank is designed to withstand a pressure of $4\mathrm{.}5$ MPa $,$ determine the minimum required wall thickness to the nearest millimeter using $($a$)$ the maximum shear stress theory, and $($b$)$ the maximum distortion energy theory. Apply a factor of safety of $1\mathrm{.}8$ against yielding.

Figure $3.$ The stationary gas tank