A thin$-$walled vessel is subject to an internal pressure of $224\mathrm{.}34$ bar

and an external positive torque $($Right Hand Rule$)$ of $3514$ Nm $.$

The vessel wall$-$thickness is $4$ mm and its external diameter is $193$ mm $.$

The vessel is made from a ductile metal with a Yield Strength of $508\mathrm{.}87$ 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$/$:

a$.156812890\mathrm{.}769773$

b$.418167708\mathrm{.}719394$

c $51\mathrm{.}6824557050379$

d$.540\mathrm{.}16069684665$

e$.130677408\mathrm{.}974811$

f$.360\mathrm{.}1071312311$

g$.720\mathrm{.}2142624622$

h$.182948372\mathrm{.}564735$

i$.209083854\mathrm{.}359697$

j$.415\mathrm{.}813677179849$

k$.103\mathrm{.}364911410076$

l$.727\mathrm{.}673935064735$

m$.313625781\mathrm{.}539546$

n$.450\mathrm{.}133914038875$

o$.630\mathrm{.}187479654425$

p$.235219336\mathrm{.}154659$

q$.623\mathrm{.}720515769773$

r$.261354817\mathrm{.}949621$

s$.155\mathrm{.}047367115114$

t$.206\mathrm{.}729822820152$

u$.209083854\mathrm{.}359697$

v$.831\mathrm{.}627354359697$

w$.258\mathrm{.}412278525189$

x $519\mathrm{.}767096474811$

y$.365896745\mathrm{.}12947$