Westergaard - slab on grade - contact area of tire
Westergaard - slab on grade - contact area of tire
(OP)
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.






RE: Westergaard - slab on grade - contact area of tire
RE: Westergaard - slab on grade - contact area of tire
A follow up:
1. What is the air pressure in truck and fire engine tires? Is it 100 psi, or more than that? I think I once saw 125 psi written in the sidewall of a truck tire.
2. When evaluating the Westergaard expressions for interior and edge loads, I find that the flexural stress in the slab-on-grade increases with increasing wheel load up to a certain load, and then starts decreasing, which seems rather counter-intuitive. I suppose this arises because of how the increasing contact area of the tire plays out in the Westergaard formulae. I wonder if this is right, or perhaps there should be some range beyond which the Westergaard formulae should not be used. Have you found this when using the Westergaard formulae?
3. Is a safety factor of 2.0 appropriate for the permissible stress for the occasional heavy vehicle (such as fire engine) on the slab on grade (only other vehicles would be bobcat snow plough and the occasional maintenance vehicle), when using cracking stress of 9 x square root of f'c? This is less than a 1.5 load factor divided by 0.65 phi factor = 2.3, but I feel that a safety factor of 2.0 may be justified because the slab on grade is not a life safety issue.
4. I suppose that an f'c at 90 days can be used in the calculations since there is little possibility of a heavy vehicles driving on the slab on grade before 90 days.
RE: Westergaard - slab on grade - contact area of tire
Westergaard theory assumes a consistent deflection "bowl". Edge and corner conditions interrupt the "bowl". The closer you get to the edge, the more likely there will be reversing curvature.
A safety factor of 2 in appropriate since if the flexural stress is less than 1/2 the allowable stress, there is no need to consider repetition of load.
RE: Westergaard - slab on grade - contact area of tire
Personally, I would have no problem using SF = 1.5, and could probably argue for 1.3, without any phi factor.
RE: Westergaard - slab on grade - contact area of tire
RE: Westergaard - slab on grade - contact area of tire
http://road-transport-technology.org/Proceedings/2... Note: average contact pressure measured in this paper was usually within a few PSI of tire pressure. Maximum pressure was considerably higher.
http://www.performancesimulations.com/fact-or-fict...
http://www.eng-tips.com/viewthread.cfm?qid=298728
RE: Westergaard - slab on grade - contact area of tire
Looks like it is getting complicated, but thanks and much appreciated. I will study what you have sent. If you have a simple approximate way of calculating the contact area, that is conservative (i.e gives less contact area than actual), that might suffice for my purposes. How about the information that the standard truck tire is generally inflated to 110 psi...is that correct?
RE: Westergaard - slab on grade - contact area of tire
The max. contact area allowed under AASHTO is 10"x20"....which is actually quite large. Most contact areas will be in the 60 to 80 sq. in. area range.
RE: Westergaard - slab on grade - contact area of tire
On a related matter, is there any way of calculating the contact area for solid rubber tires that are on some vehicles such a fork lifts?
RE: Westergaard - slab on grade - contact area of tire
You could go over to one of the automotive fora and ask there.
RE: Westergaard - slab on grade - contact area of tire
1. Is a "cushion tire" a solid rubber tire?
2. If so, how can I estimate the approximate contact area so that I can apply the Westergaard equations to calculate the stress in slab-on-grade? The tires are on a forklift truck that is going to be lifting 3300 pounds (1500 kg) and the maximum front axle single wheel load under this condition is 5300 pounds (2400 kg). The tire size is 22x12x16 which I guess to mean 22" (559 mm) outside diameter and 12" (305 mm) wide tire? I am considering "guesstimating" 4"x12" = 48 square inches pavement contact area.
3. Can the cushion tires be temporarily removed from the forklift and replaced with pneumatic tires inflated to say only 50 psi (which would give a contact area roughly 110 square inches?
RE: Westergaard - slab on grade - contact area of tire
RE: Westergaard - slab on grade - contact area of tire
RE: Westergaard - slab on grade - contact area of tire
Richard A. Cornelius, P.E.
WWW.amlinereast.com
RE: Westergaard - slab on grade - contact area of tire
As for my immediate problem of the forklift, I am aware as suggested by dicksewerrat that we could possibly go to the forklift rental company and ask if we can go measure the tire contact area, but it would not be easy because I believe that the tires have a deep indented pattern to the tread, in which case the contact area is not simply the contact length times width. Perhaps the tire manufacturer has data on the contact area, but it is a long shot; would have been nice if there were an approximate means of calculating it.
Thanks Denial for the caution about the safety of pneumatic tires on forklifts. I will check whether fork lifts can have pneumatic tires, and if they can, perhaps they should not be inflated to as low a pressure as 50 psi. I was hoping that pneumatic tires at 50 psi was the solution, but maybe not, in which case have to think more about what to do!
RE: Westergaard - slab on grade - contact area of tire
RE: Westergaard - slab on grade - contact area of tire
Try these for info:(most of the spec sheets give tire size and load distribution)
http://nissanforklift.com
http://www.mit-lift.com/_mit/index.cfm/north-ameri...
http://www.cat-lift.com/_cat/index.cfm/north-ameri...
http://www.hyster.com/north-america/en-us/
RE: Westergaard - slab on grade - contact area of tire
This is very useful. Thanks for your help. Unfortunately there is still one piece of information missing, namely the tire pressure for pneumatic tires (or the tire contact area for non-pneumatic tires). I have a tire manufacturer's data sheet giving the tire pressure for different size tires, but I don't know if that would be universal or particular to that manufacturer. Also need a 15 foot lift height, so these generally don't lift that high. The Genie Telehandler 5519 might be ideal, as it has a long wheelbase, leading me to think the front axle load may perhaps be less than other forklifts, and it can lift to 15 feet, but their data sheet lacks the basic information needed to calculate the axle load. Although they have an engineer, he does not call me back, at least not yet.
RE: Westergaard - slab on grade - contact area of tire
RE: Westergaard - slab on grade - contact area of tire
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?
RE: Westergaard - slab on grade - contact area of tire
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.
RE: Westergaard - slab on grade - contact area of tire
RE: Westergaard - slab on grade - contact area of tire
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.
RE: Westergaard - slab on grade - contact area of tire
RE: Westergaard - slab on grade - contact area of tire
RE: Westergaard - slab on grade - contact area of tire
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.
RE: Westergaard - slab on grade - contact area of tire