A spherical pressure vessel has a diameter $($d$)$ of $200$ mm and is subjected to internal

pressure $(P).$ The thickness of $(t)$ the steel sheet is $1\mathrm{.}25$ mm and design factor of $1\mathrm{.}5$ is

required. Find the allowable pressure to initiate yielding if the vessel is formed from

$($a$)$ Cold$-$drawn AISI $1030($Use non$-$conservative theory$).$

$($b$)$ Cast iron grade $30($Use brittle Coulomb$-$Mohr theory$).$

NOTE:

The in$-$plane shear stresses are zero.

The membrane stresses are ${}_x={}_y=\frac{Pd}{4t}$ and the through$-$thickness stress is ${}_z=-P$