A thin$-$walled vessel is subject to an internal pressure of $228\mathrm{.}48$bar

and an external positive torque $($Right Hand Rule$)$ of $3565$Nm$.$

The vessel wall$-$thickness is $4$mm and its external diamter is $251$mm$.$

The vessel is made from a ductlie metal with a Yield Strength of $592\mathrm{.}28$MPa, Using clockwise positive polar co$-$ordinates:

Determine for an element of stress on the external surface:

the Maximum in$-$plane Principal Stress $($Answer in MPa only$).$

the Minimum in$-$plane Principal Stress $($Answer in MPa only$).$

the Tresca in$-$plane Effective Stress $($Answer in Pa only$).$

the von Mises in$-$plane Effective Stress $($Answer in MPa only$).$

the Maximum in$-$plane Shear Stress $($Answer in Pa only$)$

Select the $5$ correct answers from the list below$/$:

Question $1$Answer

a$.$

$971\mathrm{.}971089549754$

b$.$

$69503625\mathrm{.}585644$

c$.$

$1082\mathrm{.}25235079752$

d$.$

$277\mathrm{.}397548828712$

e$.$

$138\mathrm{.}698774414356$

f$.$

$278014502\mathrm{.}342576$

g$.$

$833\mathrm{.}118076756932$

h$.$

$208\mathrm{.}048161621534$

i$.$

$69503625\mathrm{.}585644$

j$.$

$347518127\mathrm{.}92822$

k$.$

$721\mathrm{.}501567198349$

l$.$

$208510876\mathrm{.}756932$

m$.$

$555\mathrm{.}412051171288$

n$.$

$1110\mathrm{.}82410234258$

o$.$

$841\mathrm{.}751828398074$

p$.$

$208510876\mathrm{.}756932$

q$.$

$694\mathrm{.}26506396411$

r$.$

$104255438\mathrm{.}378466$

s$.$

$139007251\mathrm{.}171288$

t$.$

$139007251\mathrm{.}171288$

u$.$

$346\mathrm{.}74693603589$

v$.$

$962\mathrm{.}002089597798$

w$.$

$416\mathrm{.}096323243068$

x$.$

$173759063\mathrm{.}96411$

y$.$

$601\mathrm{.}251305998624$