Problem $1$: An AISI $1030$ cold drawn steel thick$-$walled pressure vessel has an outside diameter

$OD=10$ in and wall thickness $t=0\mathrm{.}25in.$ What maximum internal pressure can this tube withstand

$($Assume $p_O=0)$ if the maximum normal stress and maximum shear stress should not to exceed

$75\%$ of the minimum yield strength of the material?

${}_t=\frac{r_i^2{p}_i}{r_o^2-r_i^2}(1+\frac{r_o^2}{r^2})$

${}_r=\frac{r_i^2{p}_i}{r_o^2-r_i^2}(1-\frac{r_o^2}{r^2})$

${}_l=\frac{p_i{r}_i^2}{r_o^2-r_i^2}$

$($a$)$ Tangential stress

distribution