Question

If a cylindrical steel pressure vessel has a 400-mm inner radius and 8-mm-thick walls. Find the change (mm) in the inner radius when the vessel is pressurized to 1.2 MPa. Use E = 200 GPa and v = 0.3 for steel.

Answer 1

Given, Diameter D = 400mm, Thickness t = 8mm, Pressure = 1.2MPa,

Modulus of Elasticity E = 200 GPa x 1000 = 200000 MPa, Poisson ratio = 0.3

We must find the change in diameter

We know that circumferential stress or hoop stress =

And Longitudinal stress =

Strain in Major axis, that is circumferential strain or hoop strain,

From the basic stress strain theory, we know that

Now substituting the values of and

Solving the equation, we get

From basic definition of strain,

Substituting the value of in the above equation we get

                      OR

Now input the numeric values in the equation to get the

Change in diameter = = 0.051mm

Final inner radius of cylinder is = = 400 + 0.051 = 400.051 mm