Prob. $1(7\mathrm{.}27)(3)$

A thin$-$walled cylindrical vessel of diameter $d$ and thickness $t$ is under internal pressure varying from $06$ to $2\mathrm{.}8$ MPa continuously.

Given: $d=1\mathrm{.}5m,t=25mm,S_y=250$MPa,$S_u=350$MPa,$S_e=150$MPa. Design Decision:

$($a$)$ Determine ${}_{le}.(1)$

$($b$)$ Determine the factor of safety $n.(2)$

Use: the maximum energy of distortion theory incorporated with the Goodman relation $$ Eqs. $(7\mathrm{.}25),(7\mathrm{.}30)$

Principal stress: ${}_1=\frac{pr}{t},{}_2=\frac{pr}{2t},{}_3=0.$