P$3$Ans:$($a$)10\mathrm{.}533$MPa,$25\mathrm{.}125$MPa,$-4\mathrm{.}014$MPa,$($b$)26\mathrm{.}2$MPa,$9\mathrm{.}50$MPa;$8\mathrm{.}33$MPa;$17\mathrm{.}83$MPa;$13\mathrm{.}08$MPa; $($c$)2\mathrm{.}29,2\mathrm{.}1,($d$)2\mathrm{.}29$

A pressurized pipe with an outside diameter of $355$ mm and a wall thickness of $10$ mm is subjected to an axial force Px $=$

$22$ kN and a torque T $=7\mathrm{.}3$ kN$-$m as shown in figure a$.$ The internal pressure in the pipe is $1,500$ kPa. The ultimate failure

strength in tension is $60$MPa and in compression is $-20$MPa.

$($a$)$ calculate and present combined stress state on the outer surface of the pipe on the standard plane stress element,

$($b$)$ determine: principal stresses, maximum in$-$plane shear stress, average stress, and absolute maximum shear stress on

the outside of the cylindrical surface of the pipe. Draw all applicable stresses on a wedge element $($wedge element

template is in Canvas Class$\_1\_$Plane$\_$Stress$\_$Review$\_$ES$\_202.$pdf file under Class $1)$

$($c$)$ determine the factor of safety predicted by the maximum normal$-$stress theory of failure

$($d$)$ determine the factor of safety predicted by the Mohr$$s failure criterion

$($e$)$ on common or separate axis draw the stress envelope$($s$)($failure diagram$($s$))$ for both theories indicating all

stress values as well as the load line$($s$).$

figure $($a$)$