Von Misses Failjre Theory

[SALTRAM4567777]

Hi!
I am a little bit confused.
We have failure theory Von Misses to check if our member has yielded or not .
We also have a bending theory i.e M/I= Stress/y
If I am designing a beam and I am very sure that it will fail by yielding
Will both bending tbeory amd von misses give same result?
I just want to know the difference.

 

[r13]

I find this article is an interesting read. Link

 

[hardbutmild]

Keep in mind that von Mises is applicable for steel, but usually is not applicable for other materials.

 

[r13]

Will both bending tbeory amd von misses give same result?

I believe it depends on how sensitive is your beam regarding to shear deformation, and localized failure.

 

[Mohanlal0488]

The equation you have presented only considers bending, you would need to consider bending about both axis, axial and shear effects. The total fibre stress for a beam will be the same as the Von Mises as stresses. The process for getting the total fibre stress in a beam is simplistic since it is a 1D element.

There are other failure mechanisms apart from yielding which need to be considered.

 

[MegaStructures]

Von Mises yield criterion gives a scalar magnitude value that represents the combined stress state in a member from varying stress directions. Tension from bending is one of the components that go into the von mises formula, so if no other stress exists they will be the same. Keep in mind shear and moment will not act at the same “extreme fiber” on most beams. I would rarely ever use Von Mises criterion for beam design

“Any idiot can build a bridge that stands, but it takes an engineer to build a bridge that barely stands.”

 

[JoshPlumSE]

Will both bending theory and von misses give same result?

I assume you're talking about doing a FEM analysis of your beam and checking the Von Mises stresses from this analysis. Is that correct?

If so, then they MIGHT give the same result if you confine the problem sufficiently. If you're calculating your stresses based on bending theory, then you need to take into account WHERE your stresses are coming from....bending, shear, torsion, warping, weak axis effects. If you constrain your model so that torsion, warping and weak axis effects are negligible then they should be pretty close in terms of stress calculations. Provided, of course, that your FEM model has been sufficiently meshed. Even then there are items in bending theory that are mostly true that are not 100% true (plane sections remain plane, and such) which would be a cause for minor differences.

Even if the two results matched up nicely, the question then becomes what type of safety factor is appropriate on the loading, and what sort of material safety factors are appropriate for the failure method. Also, is there any chance of buckling and slenderness effects. Remembering that residual stresses and such cause code formulas to indicate buckling at much lower stress levels than pure bending theory would predict.