Pressure vessel - Von Mises Stress

[cbert]

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?

 

[TGS4]

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?

 

[metengr]

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.

 

[JohnBreen]

Hello,

To answer your question (with no regard to "why") go to B31.3 and look at Chapter IX. Go to paragraph K304.1.2 (note the "K" paragraph) and read the paragraph and especially the notes.

For some background on failure theories you might find this interesting:

http://feaservices.com/fund_struct/fund_struct.html#General 3-D Stress State

Regards, John.

 

[Cockroach]

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