Von Mises & Concrete 1

[Splitrings]

Does the Von Mises stress have an application in concrete? I am specifically looking at a notch in a vertical wall of a cylindrical tank. The intent of this tank is that it be watertight. Its easy to reinforce in both principle directions within a few inches of the edge of the notch. Obviously I am more concerned with tensile stresses than compressive stresses. Is it reasonable to assume that anywhere your Von Mises stress exceeds the tensile stress of the concrete you will form a crack? I am only looking at plane stresses and not including normal stresses.

 

[structSU10]

max/min principle stresses are more critical for concrete structures, as you are looking at a brittle material and von mises is better used for ductile materials.

 

[rickfischer51]

And, there is no such thing as a negative von mises stress, so you cant determine where tensile stresses are positive or negative simply by looking at von mises stress.

Rick Fischer
Principal Engineer
Argonne National Laboratory

 

[johnbridge231]

von misses stresses are for ductile materials only and don't have any sense for concrete.

Analysis and Design of arbitrary cross sections
Reinforcement design to all major codes
Moment Curvature analysis

http://www.engissol.com/cross-section-analysis-design.html

 

[Splitrings]

My intent is to look for areas where the extreme fiber is at or above its tensile strength. I am not concerned about designing principle reinforcing based on Von Mises stresses. As we all know the area of concrete below the tensile reinforcing is assumed cracked in singly reinforced beam. This doesn't mean the structure fails but this cracking is of concern when designing watertight structures. ACI 350 addresses this by reducing the allowable steel stress to certain levels well below 0.9fy. It seems to me anywhere your Von Mises stress is greater than the concretes tensile stress, it likely cracks. I realize Von Mises doesn't indicate a tensile or compression failure but it is easy to determine with other FEA output where the stresses are tensile. I don't buy the concept that Von Mises only applies to ductile materials. A stress is a stress and all materials whether ductile or brittle have an ultimate stress at which they fail. If the material is isotropic, Von Mises should apply.

 

[jhardy1]

"If the material is isotropic, Von Mises should apply."

No, isotropy is only one key assumption of the von Mises Yield Criterion - other critical assumptions are that the it applies to linearly elastic, ductile materials, with a defined yield point, with essentially the same yield strength in tension and compression. Concrete is not ductile, and its tensile strength is MUCH lower than its compressive strength, so it violates two of most fundamental assumptions inherent in the formulation. (And reinforced concrete is not isotropic anyway, as its tensile strength is locally concentrated in the rebar.)

Look at the shape of the von Mises Yield Surface here:

http://en.wikipedia.org/wiki/File:Tresca_stress_2D.png

That is NOT the shape of the stress-strain curve that we usually apply to concrete!

Even putting aside the theory for a moment (which I would NOT advise!), in practical senses, von Mises Stresses can be quite misleading for concrete. Consider a typical symmetric reinforced concrete beam in pure bending - the post-processor will show von Mises stresses are the same value on the top and bottom faces (suggesting that the top and bottom faces are equally critically loaded), but the bottom (tensile) face will be heavily cracked long before the top face is anywhere near its compressive strength.

As others have stated, I suggest you use the Maximum Principal Stress to indicate where tensile stresses are significant, and the Minimum Principal Stress to indicate where the concrete matrix is heavily stressed.

http://julianh72.blogspot.com

 

[rickfischer51]

The von mises stress has nothing to do with crack initiation. It is an indication of the onset of plastic flow. Go back to your strength of materials book and follow the derivation. It has to do with the observation that a hydrostatic compressive stress results in no failure. Such a stress is termed dilitational, that is, a stress that causes a change in volume. From this it was concluded that yielding must be due only to deviatoric stresses, that is, stresses that cause a change in shape. They (Huber, Henkey, and von Mises) took the total strain energy, subtracted the dilatational strain energy, and got the deviatoric strain energy. The math trail from that lead to the von Mises stress formula. But, concrete does not yield, so I think its safe to say that its deviatoric strain energy is zero, and that the von Mises stress is meaningless for concrete.

A stress is NOT a stress. Yes, all materials have a "stress" at which they fail, but different materials fail by widely different mechanisms, and so the measure of that mechanism is different. Do you really believe that concrete, mild steel, high density polyethyene and carbon fiber composite, for instance, all behave the same and can be analyzed in the same way? The con Mises stress is not a real stress. It is a stress convention. It is a quantity made up from real stresses that is used as a criteria for a specific type of failure. You might want to take a look at "Failure of Materials in Mechanical Design" by Collins. He deals with faiure criteria and how and when to apply them in chapter 6.


Rick Fischer
Principal Engineer
Argonne National Laboratory