Steel Bearing Strength - Hertzian Stress 1

[phamENG]

AISC 360-10, J7a - Bearing Strength. The surfaces in contact are limited to a stress of 1.8F_y. Commentary is silent on the reason. I've found a few old threads - mostly mechanical engineering forum - discussing limits on Hertzian Stress. They vary from as high as 5.5F_y for point contact in an Italian code to 1.8F_y as that is when "plastic flow takes place," but most limit it at 2F_y.

Anyone know if that's the source for the AISC limitation? Any insights into AISC's decision making process for 1.8?

Thanks.

 

[WARose]

I've never been sure either. I've always believed it was to limit indentation to what would be expected for the normal surface roughness. (I.e. within AISC tolerances.)

 

[phamENG]

Thanks for responding, WARose. I was beginning to despair, so I didn't save the URL, but I did come across an old DOT report from the railroads discussing contact stress of steel wheels on steel rails. They discussed the same plastic flow phenomenon, and it seems all that means is the development of minute plastic deformation near the surface at the point of contact. So if you do that repeatedly, you can develop a crack and end up with either a low cycle fatigue failure or progressive failure

I'd still like to know for sure where this comes from, but from what I've found so far it seems plausible that the AISC provision is limited the Hertzian (contact) stress to prevent even shallow plastification of the bearing surface(s).

Also, I realize that I should have put this in the AISC Code Issues section - my apologies.

 

[kingnero]

Just for my information, as I have dealt with this many years ago, but even then I did not fully understand everything that goes together with Hertzian contact stresses:
What stress exactly do you want to compare with the yield strenght of the base material(s)? As there are compression forces, tensile stresses, shear stresses, octahedral stresses (if I remember correctly ?)
Point of highest stress was several millimeters below the surface in my case, and was about 10-20% higher than the tensile strength of the base material (it was a pearlitic steel, without a clearly defined yield strength value).

 

[phamENG]

kingero - I believe that it's really just as you say, looking at the point of max stress which is just below the surface. The 1.8*Fy*Ap limit (Ap = projected contact surface area) is a simplification. In reality, you're compressing the material, which is causing orthogonal tension, but that tension is confined, and so on through the complex 3 dimensional stress distribution.

 

[phamENG]

Found this nifty document, in case anyone else is curious about Contact Mechanics.

 

[KootK]

Neat. I wonder if I'll every have occasion to use the word "tribology" again. It would be a shame if I looked it up for nothing.

Tribology. The study of friction, wear, lubrication, and the design of bearings; the science of interacting surfaces in relative motion.

 

[kingnero]

If you're going ro read up on it, I can recommend Engineering tribology by Stochowiak.

@ phamEng, good luck!

 

[RPMG]

The manual says,
In general, the bearing strength design of milled surfaces is governed by the limit state of bearing (local compressive yielding) at nominal loads, resulting in a stress of 0.9Fy. adequate safety is provided by post-yield strength as deformation increases.

I interpret that to mean that the compessive stress is OK from 0 to 0.9Fy (service), and overstressed 0.9 to 1.8Fy and expected to fail above 1.8Fy.

 

[phamENG]

KootK - I agree. I'm tempted to specialize in contact mechanics just so I can call myself a "Tribologist."

Thanks for the recomendation and encouragement, kingnero.

RPMG - I'm not sure...though you get localized yielding at 0.9Fy, I'm not sure if I'd call it overstressed at 1.8Fy. Even though the material starts to yield, you don't have sufficient deformation to get "plastic flow" which I take to mean permanent deformation of the contact region. Greater than 1.8Fy and you get permanent deformations that can compound overtime and lead to a progressive failure or low cycle fatigue fracture.

 

[RPMG]

I'm not speaking about behavior. I'm strictly just interpreting the code as:
[ul]
[li]Fy/Ω = 1.8Fy/2.0 = 0.9Fy. Per AISC, it is NG at 1.8Fy.[/li]
[li]Beyond 0.9Fy, AISC states that Adequate safety is provided by post-yield strength... So, 0.9 to 1.8Fy range is the factor of safety, at service level loads.[/li]
[/ul]

 

[phamENG]

Ok - understand where you're coming from now. I agree entirely with the code interpretation.

Thanks everyone.

 

[phamENG]

For the sake of posterity, I thought I'd add a quick note to this. I'm looking at another contact stress problem and a light bulb just went off.

For the general case of a rigid sphere being pressed into an elastic half space (think ball bearing on a really wide and thick steel plate), the worst case stress that the material experiences is shear (and it experiences it at a depth equal to about half width of the contact area). For steel on steel, the ratio of shear stress to contact stress is about 0.31, or roughly 1/3. What's the limit for shear stress compared to yield? 0.6. So, if the shear stress is 1/3 of contact stress, then it would follow that the contact stress is limited to 3 x 0.6F_y...1.8F_y! Conveniently, that's the limit in J7. It also explains why the resistance factor/safety factor are equivalent to those used in the shear equations.

This probably should have been obvious from the start, but it wasn't. Hopefully this helps anyone else looking around for info on this.