The pressurized pipe shown below is closed from both ends and is subjected to an internal pressure of

$p=5$MPa and a transverse load of $F=1kN$ in the $-z$ direction. The pipe can be thought of a thin

walled vessel with an inside diameter $d_i=2R=200mm$ and a thickness $t=5mm.$

a$)$ Find the stresses acting at the stress element $A$ on the pipe outer surface as shown above.

b$)$ Sketch and label Mohr's circle corresponding to the state of stress at $A.$

c$)$ Determine the principal normal and extreme shear stresses at $A.$

d$)$ Find the principal normal stress and extreme shear stress directions or angles and then sketch the

principal normal and extreme shear stress elements at $A.$

e$)$ What is the maximum shear stress at $A?$