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Limitations of Von Mises Equation

Limitations of Von Mises Equation

Limitations of Von Mises Equation

(OP)
Hello,

I just finished reading thread404-160050: Von Mises /Maximum distortion theorem? and I learned alot regarding the use of von Mises equivalent stress equation.  My simple question revolves around a 4" pipe that is pressurized and has an external load on it.  (See the attached sheet for hand calculations.  This is just a hypothetical example for discussion purposes.) The equivalent stress is lower than the hoop stress.  

Question 1: Although we tend to use the von Mises equation to find a combined stress, is there ever a case where the von Mises value will exceed a hoop stress or bending stress value?

Question 2:
What other methods are used to find combined stress?   

RE: Limitations of Von Mises Equation

#1 - yes, look at the other side (compression side) of the pipe.

#2 - Er, well, Mohr's circle (or 3d transform equations) to find principal stresses if normal and shear stresses are known.

RE: Limitations of Von Mises Equation

The Von Mises assumes that distortion energy causes failure and that volumetric expansion and contraction have no influence on failure.

This was witnessed by applying a hydrostatic pressure (all faces of a tensor are equal) and failure did not occur for ductile metallics.  

So in other words, if you have a major component of stress, the other components may "hurt" or "help" depending on their directions and magnitudes (also witnessed by the equation).

In the aerospace industry, a more common approach to stress interaction is the use of an "R ratio".  You would create something like:

R1=sigmax/Ftu
R2=tauxy/Fsu

R1^2 + R2^2 = 1 would indicate failure

Depending on test data, the square terms could be linear,cubic, or other.  Niu and Bruhn books have some popular forms.

Brian
www.espcomposites.com

RE: Limitations of Von Mises Equation

Having looked at your work, I doubt you have a correct solution depending on the end load reaction.  Remember that there is a longitudinal stress associated with pressure containment inside your pipe.

I would suggest the Hencky Equation, which is the triaxial state of stress associated with hoop, radial and longitudinal loading, then apply your external loads.  If the longitudinal stress turns out to be low for 800 psi internal pressure, then yes, this would reduce to the solution you have found to within a margin of uncertainty (error).

Lots of threads in this, I did post a solution sometime ago so you may need to surf for that thread.

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

RE: Limitations of Von Mises Equation

i think the problem is a pipe carrying pressurised water, so no end-caps, no axial load in the pipe.

yes, von mises combined stress for bi-axial tension is lower than either tension stress ... consider poission's effects ...

as btrueblood noted, look at the combined stress at the top of the pipe, combining hoop tension with axial compression.  this will be higher than the hoop stress.

you also might want to consider the shear stresses, but these peak at the na (zero bending stress) but will combine with the hoop stress.

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