7 Replies Latest reply on Feb 26, 2013 3:46 AM by Leo Zhou

    how to estimate the results of high pressure pipe

    Leo Zhou

      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!

        • Re: how to estimate the results of high pressure pipe
          Matthew Jackson

          Hi Leo,


          What you are dealing with here is not as simple as adding a pressure to the inside of the cylinder, you are wanting to perform a thick walled pressure vessel analysis according to Lames theory.


          The stress results you are wanting to plot are the circumfrential or hoop stresses, can you describe the dimensions of the cylinder?



            • Re: how to estimate the results of high pressure pipe
              Leo Zhou

              Hi Matthew,

                      Thanks for your reply. Yes, I'm trying to analysis a thick walled pressure vessel. i just begin to use simulation and i don't know how to do it.

                       The dimensions of the cylinder are as follows: inner diameter φ10mm,outer diameter φ30mm, length 50mm; material ANSI 304,yield strength 206Mpa.  I fixed one end of the cylinder, only add a pressure of 150Mpa in it. The result of stress is show in von mises.



            • Re: how to estimate the results of high pressure pipe
              Matthew Jackson

              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.


              Set Up.png


              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).




              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:


              Radial Stress.png


              Hoop Stress.png


              As you can see, the values correlate very well.


              I hope this helps you.