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Pressure vessel - Von Mises Stress

Pressure vessel - Von Mises Stress

Pressure vessel - Von Mises Stress

(OP)
I've got a small cylinder of 3 in. OD, 2. in ID running a pressure of 2000 psi. I am familiar with hoop and longitudinal stress calculations. How do I calculate the von Mises stress?

 

RE: Pressure vessel - Von Mises Stress

von mises (or the maximum distortion energy theory) is simply a manner of combining the stresses as vectors (either component or principal) to create a scalar.  Check out the wikipedia http://en.wikipedia.org/wiki/Von_Mises_stress to see the formulation.

Now, for a tough question, why are you needing to calculate the von mises stress?  What will you do with this scalar?

RE: Pressure vessel - Von Mises Stress

For a cylinder with isotropic behavior you can estimate the following biaxial state of principal stresses;

Sigma 1 = PR/t
Sigma 2 = PR/2t
And sigma 3 = 0

Using the von mises approach to calculate an effective stress under the given conditions;

Sigma e = von mises equation

Plug in the values for the principal stresses and calculate sigma e

If sigma e is less than the tensile yield strength, no permanent deformation will occur.

RE: Pressure vessel - Von Mises Stress

There has been a tremendous amount of threads posted in the mechanical section of this forum.  You can trace the development of the triaxial state of stress by the Von Mises-Hencky Theory there.

To answer your question directly, a pressure vessel 3.0 OD X 2.0 ID holding 2000 psig would have a maximum stress of 6235.38 psi on it.

Taking into account significant digits, I would report 6200 psi as Von Mises-Hencky stress.

Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada

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