Problem $8\mathrm{.}2\mathrm{.}9$

A spherical stainless$-$steel tank having a diameter of $26$ in$.$ is used to store propane gas at pressure of $2075$ psi. The properties of the steel are as follows: yield $$tress in tension, $140,000$ psi; yield stress in shear, $65,000$ psi; modulus of elasticity, $30106$ psi; and Poisson's ratio, $0\mathrm{.}28.$ The desired factor of safety with respect to yielding is $2\mathrm{.}8.$ Also, the normal strain must not exceed $1250{10}^6.$

$($a$)$ Determine the minimum permissible thickness $t_{\text{m}\text{i}\text{n}}$ of the tank.

$($b$)$ If the tank thickness is $0\mathrm{.}30$ in $.$ and normal strain is measured at $990106,$ what is the internal pressure in the tank at that point?