Consider a pressure vessel made of steel designed to hold high pressure steam at $20$ Bar $(1$ Bar $=0\mathrm{.}1$ MPa$)$

The pressure vessel is cylindrical in shape. The steel plate used to make the cylindrical pressure vessel has a

thickness of $12$ mm and the cylinder is $2$ m long. The diameter of the pressure vessel is $1$m$.$

$1)$ Compute the longitudinal and hoop stresses in the pressure vessel

$2)$ Use Mohr's circle to:

a$.$ Determine the maximum principal stresses

b$.$ Maximum shear stress

$3)$ If steel has an elastic modulus of $200$GPa and a Poisson's ratio of $0\mathrm{.}3,$ what are the longitudinal and

circumferential strains in the pressure vessel? Note, consider the role of both longitudinal and hoop

stresses on the strain. Ignore the effect of temperature.