A thin$-$walled vessel is subject to an internal pressure of $225\mathrm{.}08$bar and an external positive torque $($Right Hand Rule$)$ of $3563$Nm$.$The vessel wall$-$thickness is $4$mm and its external diamter is $211$mm$.$The vessel is made from a ductlie metal with a Yield Strength of $630\mathrm{.}36$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 correct answers from

Below:

a$.914\mathrm{.}841358388993$

b$.457\mathrm{.}420679194497$

c$.143420473\mathrm{.}99312$

d$.344209137\mathrm{.}583489$

e$.56\mathrm{.}9869802013759$

f$.229472758\mathrm{.}388993$

g$.686\mathrm{.}131018791745$

h$.86052284\mathrm{.}3958723$

i$.28684094\mathrm{.}7986241$

j$.594\mathrm{.}207993127474$

k$.792\mathrm{.}277324169965$

I. $284\mathrm{.}93490100688$

m$.170\mathrm{.}960940604128$

n$.286840947\mathrm{.}986241$

o$.401577327\mathrm{.}180737$

p$.396\mathrm{.}138662084982$

q$.693\mathrm{.}242658648719$

r$.571\mathrm{.}775848993121$

s$.114736379\mathrm{.}194496$

t$.57368189\mathrm{.}5972482$

u$.800\mathrm{.}486188590369$

v$.227\mathrm{.}947920805504$

w$.113\mathrm{.}973960402752$

x$.172104568\mathrm{.}791745$

y$.495\mathrm{.}173327606228$