Consider a thin$-$walled tube with close ends and internal pressure p $.$ The wall thickness is

t $,$ the inner radius is r $,$ and the ductile material has a yield strength of Y $.$

i$.$ Derive the expressions for required thickness corresponding to the specified

values of r and the safety factor X against yielding for von Mises and Tresca

criteria. Calculate the percentage difference in the thickness obtained from

the two criteria.

ii$.$ Explain with some analysis how will the result change if the tube is not

considered as a thin tube but a thick$-$walled tube.