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# How to Explain von Mises?3

## How to Explain von Mises?

(OP)
I am incoperating customer comments into a calculation.  The calculation was done in a FEA program using von Mises.  The purpose of the calcuation was to show that the mounting brackets attaching directly to the walls were of sufficient desing to handle the applied loads.  The reviewer is a structural engineer who is use to seeing these calculations done according to allowable tension, bending, flexure and shear.  I am having trouble explaning the concept of von Mises.  Any help in relating the two to one another would be helpful.  Thanks

### RE: How to Explain von Mises?

Not a very good structural engineer if he doesn't understand failure of metals...

Simply put: "The Von Mises yield criteria is a means of predicting yielding in ductile metals under combined loading."

More depth: "The Von Mises yield criteria predicts yielding occurs when the elastic distortion energy in a material reaches a critical value."

Really confuse him: "The Von Mises yield criteria suggests that the yielding of materials begins when the second deviatoric stress invariant reaches a critical value."

### RE: How to Explain von Mises?

Mind you... sometimes there's more to life than von Mises... He may be interested in the directionality of the stress. Materials tend to be stronger in compression than in tension. Perhaps he was merely looking for more information.

### RE: How to Explain von Mises?

(OP)
Thanks flash3780

What I keep getting back from him is "The allowable Bending and Shear stress is lower than the allowable Tension.  Therefor how can I use the allowable tension to justify all forms of loading.

Thanks

### RE: How to Explain von Mises?

Maybe the engineer would like to see a simple calculation for the brackets.  Ask if you could provide hand calculations with maximum shear, bending and tensile stresses determined and related to the material properties. Structural engineers like to relate properties back to accepted limits. If you don't know how to calculate the stresses ask one of your co-workers.

### RE: How to Explain von Mises?

Hi

Hi RoboDroid

Why not ask him to clarify his point.

desertfox

### RE: How to Explain von Mises?

If the spec (according to the structural engineer) doesn't use Von Misses as a failure criteria then you can not use it in this case. Maybe the spec is still using the maximum tensile and the maximum shear failure criteria but those are the rules for the time being.

The same FEA analysis that gave you the Von Misses stress can give you the maximum tensile, compressive and shear stresses in the structure instead just the Von Misses stress (which in fact is calculated from those values).

### RE: How to Explain von Mises?

As structural engineers we are used to looking at uni-directional stress interaction or bi-directional stress interaction.  Von Mises distribution gives an omnidirectional look at the same things.

It has more relevance to planar sections such as plates or membranes, but can be used to isolate critical stress considerations in flanges or webs of beams, independently; or more commonly, a bolted plate or bracket.

### RE: How to Explain von Mises?

(OP)
Ron

Thanks for the insight.

So how would you address his following question of von Mises.

"The allowable Bending and Shear stress is lower than the allowable Tension.  Therefor how can I use the allowable tension to justify all forms of loading."

Thanks

### RE: How to Explain von Mises?

Robo...if I'm understanding your question correctly, you cannot justify comparing only the allowable tension if you have both shear and bending occurring as well.  You have to check all, and you have to check interaction as well (for instance, tension + shear on the same section).  The lower value prevails.

Look at the von Mises results in a uni-directional or bi-directional case and compare those to allowables.  The structural engineer will better understand those as they compare directly to what normally checks.

Post a photo or sketch of the bracket and maybe that will help us to give you a better idea of how to present your results.

Ron

### RE: How to Explain von Mises?

Von Mises stress is a method of working out a single stress value based on three principal stresses. It works well for ductile materials such as steel but not for brittle materials like cast iron. Codes such as BS2573 will give allowables based a principal stress for example bending. In reality most parts see a combined stress such as bending and shear for example. You could calculate combined stress and compare this to Von Mises from your FEA model.

### RE: How to Explain von Mises?

RoboDroid,

It has occured to me that if someone is waving FEA calculated stresses in my face, I can ask them to explain Von Mises stress to me.  This would be a good way to weed out CAD operators.  Could it be that your reviewer is just verifying that you know what you are talking about?

I wish I understood Von Mises better.  Reading up on it again is one of my rainy day projects.

JHG

### RE: How to Explain von Mises?

Robo, I hope this narrative facilitates your explanation to you customer.

In my experience, engineers sometimes seem to forget that material failures cannot be calculated to the umpteenth decimal place.  It is a statistical phenomenon because of too many untractable variables in the microstructure: flaws, inclusions, chemical segregations, surface scratches, etc.  The best we have to go on are empirically failure theories.  In 1913, Professor von Mises came up with a pretty good one.  It predicts yielding, not catastrophic failure.

I think of the VM criteria as relating 3-d loading back to a uniaxial condition.  Plug in the 6 components of the stress tensor into the VM equation.  [Turn the crank]  If the result is less than the yield stress obtained in a unaxial tensile test (i.e. the YS widely published in tables), you're probably good to go.  I believe FEA software does this for the thousand or so points in the grid, assigns colors, etc.  There are other failure criteria such as the Tresca, which are easier to use if you are doing manual calcs and more conservative; also the Lundborg. (BTW, for plasticity, there is the Levy-Mises theory.)  I haven't seen the others used that often in practice.

### RE: How to Explain von Mises?

Chris9 is correct.

Von Mises is a principle stress, that is, wall element stress with shear removed.  We do this in a Mohr's Circle computation where rotation of the element is brought into the principle plane in the absence of shear.

Tresca concerns the shear phenonema.

Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc

### RE: How to Explain von Mises?

Cockroach:
1) From any stress distribution you can of course derive the principal stresses, this has nothing to do with the failure criterion
2) vonMises and Tresca (besides others) are simply two alternative failure criteria, they give hopefully quite close results for any stress pattern, the choice between them being normally dictated by the applicable code
3) All failure criteria, as the name implies, are based on an hypothesis on what type of derived stress component will cause failure when attaining a limit value
4) vonMises is also called the criterion of the maximum octahedral shear stress, so it also concerns shear phenomena! For this criterion the derived stress component is what is called the combined shear stress of vonMises, also called the quadratic invariant or the octahedral shear stress of Ros-Eichinger (names change, but the result is always the same)
5) For Tresca's criterion the derived stress component is the maximum shear stress
6) To visualize the relationship between the two criteria, one can observe that, in the space of the principal stresses, for vonMises the locus of the acceptable stress states is a circular cylinder (Wikipedia), and for Tresca is an hexagonal cylinder, the hexagon being inscribed in the circle. So the two will give, as necessary, quite close results, and one could say that Tresca is safer than vonMises (though this is a completely different debate).

prex
http://www.xcalcs.com : Online engineering calculations
http://www.megamag.it : Magnetic brakes and launchers for fun rides

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