Westergaard - slab on grade - contact area of tire

[ajk1]

To use the Westergaard expressions for slab on grade flexural stress due to concentrated load, I need to know the contact area of the slab on which the load is applied. For a vehicle tire, the contact area of the tire with the pavement is sometimes taken as the wheel load divided by the tire pressure. Exampe: 6000 pound wheel load and 100 psi truck tire pressure gives a contact area of 60 square in inches with the pavement. Is this correct, and if not is there any other general formula? The problem seems to be that for higher wheel loads such as say 12,000 pounds and 100 psi tire pressure, the contact area is 120 square inches, which my sense tells me is too large.

 

[ajk1]

Thanks Hokie66, I do realize that there is a practical coordination problem with the contractor. In fact he has already indicated pretty much what you stated. His attitide is that if the forklift has 4 wheels with big tires, there is no need to do any calculations, although he is clear that he is not going to accept responsibility for cracking the pavers. That means that we cannot ok the driving of a forklift onto the granite pavers, unless we can show that a solid tire forklift is unlikely to crack the pavers. I am painfully aware that the calculations are not anywhere near precise. Different calculation procedures (such as PCA charts vs Westergaard equations) give quite significantly different results.

If I apply the Westergaard equation with the loaded area at the paver surface I get a given loaded area (53 square inches at 100 psi tire pressure), but if I spread the load down to mid-thickness of the 2.5" thick granite paver at a 2 vertical to 1 horizontal spread, I get a much larger loaded area. Using the former area I get a safety factor against cracking of 1.4 but using the latter procedure I get a safety factor of 1.9. I would be comfortable with 1.9, but I am doubtful of 1.4, knowing as I do (from lift-off tests when the pavers were installed two years ago) that not all pavers are fully in contact with their setting beds. Do you think that spreading the load down to mid-thickness of the paver is valid, when applying Westergaard equation?

 

[Ron]

ajk1...I'm not sure Westergaard would be the right approach since you are using pavers. The lateral stress at the bottom of the paver is going to be quite high and the interface with the grout bed will suffer at the least...

With high lifts and probably reasonably high loads, I would certainly warn the owner about sudden failure of a paver and the danger potential of that.

Take a look at elastic layer analysis. You can model the layers with their properties and determine stresses and strains at any point.

 

[ajk1]

Hi Ron - any suggestion for elastic layer analysis software?

 

[Ron]

ajk1...most of them are derived from the original ELSYM 5 software produced in the 70's. There are a few proprietary ones with Windows interfaces from the old DOS, but I have not seen one that I particularly like.

The better one that I've seen in the last few years is available free from the State of Washington DOT. It is called EverSTRESS and is easy to use. I've checked its accuracy manually as much as I could and it appears to be on target.

If you want to do it manually using elastic layer techniques, Yoder and Witczak's "Principles of Pavement Design" has a reasonably good treatment of the subject and examples.

 

[ajk1]

Thanks Ron. That is very helpful. I will pursue it. Much appreciated.

 

[ajk1]

Ron - I notice that EverSTRESS is intended for flexible asphalt pavements...I do not think the granite paver would be flexible...more like rigid pavement...so maybe ELSYM5 is the software to use?

 

[Ron]

ajk1...that shouldn't make a difference. The layers are still "elastic". The layers are defined by material properties and stiffness of the whole section does not matter much...the only caveat to that is that if you have flexible layers over an ending "hard" layer like a flexible pavement with a rock subsurface within a few feet of the top of pavement, you will need to make sure that is noted in the layer properties.

Enter the material properties for each layer without regard to what that layer is. Typically, for pavement evaluation, Poisson's ratio of concrete is 0.15.

 

[ajk1]

Ron - thanks for this information. I am much indebted to you for this. I will give it a try. I did notice this afternoon when I went to Home Depot, that they had a small forklift there and it said on the tire the infltion pressure was 45 psi, but it could only lift to 10 feet. We need a lift to 15 feet so that forklift would not be appropriate, but it has got me to thinking perhaps the tire pressure on some forklifts is not so high.