The stress distribution of thick wall pipe is non uniform. When i add a pressure of 150Mpa in it, the maximum stress is 300Mpa in inner suface, it's exceed the yield strength of material, but only about 16Mpa outside.Can somebody tell me how to estimate the result? Is this safty ?

Thanks a lot!

Hello Leo,

The calculations you are referring to are a very simple alternative to doing a FEA simulation if you have studied mechanical engineering.

What you have to do is to use Lames equations to calculate the radial and hoop stresses, these are defined as:

Radial Stress (id) = A - B / ri^2 where ri = inner radius (5mm in your case).

Radial Stress (od) = A - B / ro^2 where ro = outer radius (15mm in your case).

The radial stress is also the pressure, therefore in your case inner radial = -150 MPa and outer radial = 0 since you are applying an internal pressure of 150 MPa and nothing to the outer wall.

Knowing the pressures internally and externally and knowing the inner and outer radii you can calculate the constant A and B.

In your case A = 18.75 and B = 0.0042. You can double check these constants by inputting them back into the equation.

Therefore 0 = 18.75 - 0.0042 / 0.015^2.

You can now calculate the internal and external hoop or circumfrential stresses by using the same constants A and B using:

Hoop Stress (id) = A + B / ri^2 = 186.75 MPa (in your case).

Hoop Stress (od) = A + B / ro^2 = 37.42 MPa (in your case).

Like I say, very simple.

In terms of FEA, you are best making the assumption that the strain in the axial direction = 0 and using a 2D simplification and also take advantage of symmetry and only solve for a 1/4 model as shown.

In terms of output stress you need to define an axis in the z-direction through the cylinders diameter i.e. intersection of the x and z planes and use this to define:

SX (X Normal Stress) for the Radial Stress (-150 MPa @ r = 5mm and 0 MPa @ r = 15mm).

and,

SY (Y Normal Stress for the Hoop Stress.

Please note the stress vectors will depend on the plane you have decided to sketch on.

The following images show the radial and hoop stresses calculated by FEA:

As you can see, the values correlate very well.

I hope this helps you.