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.

 

[hokie66]

If it is a pneumatic tire, the method you described is correct. The tires on big haulage trucks are very large.

 

[ajk1]

Thanks very much Hokie66.

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.

 

[Ron]

Typical truck tire pressures are going to be 90 to 110 psi, most often 100 to 110 psi.

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.

 

[spats]

In my opinion, a SF of 2 is very conservative, especially for an "occasional heavy vehicle". I've also never seen anybody trying to apply a phi factor for slab-on-grade design. None of the typical design procedures apply a phi factor, as far as I know. Besides, where do you come up with a phi of 0.65?

Personally, I would have no problem using SF = 1.5, and could probably argue for 1.3, without any phi factor.

 

[ajk1]

Thanks spats. The phi=0.65 is from CSA A23.3 Concrete Design which regulates concrete design in Canada (where I live and where the project is). But you are right, this does not apply to non-structural slab on grade. I was coming round on my own to the idea that a safety factor of 1.5 will suffice in my case, so you have helped me make up my mind. Much appreciated.

 

[ACtrafficengr]

The rule of thumb that the contact patch area equals the load on the tire divided by the pressure is innacurate. It disregards the stiffness of the tire itself, including the sidewalls and steel belts.

http://road-transport-technology.or...E TYPES AND ROAD CONTACT PRESSURES - Yap .pdf

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-fiction-tires-1.htm

http://www.eng-tips.com/viewthread.cfm?qid=298728

 

[ajk1]

ACtrafficengr;
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?

 

[Ron]

ajk1....110 is a bit on the high side. I would generally use 100 psi for analysis purposes. Yes, 110 psi is recommended for some tires, but generally you'll see around 100 psi.

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.

 

[ajk1]

Thanks Ron for the information and help. I have written a spreadsheet to evaluate the slab on grade for wheel load at edge, away from edge and at the corner, using the Westergaard equations. Maybe I should build into it a limit of 60 to 80 square inches for the upper limit on the contact area. But I also have to reconsider how the contact area should be calculated, now that ACtrafficengr has drawn to my attention that it is not correct to divide the wheel load by the tire pressue to arrive at the contact area.

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?

 

[ACtrafficengr]

Based on the Road Trasnport Technology article, taking 110 psi as the average pressure for a 100 psi tire might be a good approximation.

You could go over to one of the automotive fora and ask there.

 

[ajk1]

I went to the automotive forum and posted my questions but got no response, so I am back here with perhaps my final questions:
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?

 

[Splitrings]

Not sure it matters, but there isn't a fire truck in my station that runs less than 125 psi in a drive tire. Steer tires are in certainly in the 100-110 psi range.

 

[Denial]

AJK1. I know nothing about tires, and even less about forklifts. However I would have thought pneumatic tires on a forklift would be a definite "no no". Their softness could lead to stability problems when carrying a heavy weight up high.

 

[dicksewerrat]

Why can't you go to the forklift, measure unloaded and loaded contact areas?

Richard A. Cornelius, P.E.

http://WWW.amlinereast.com

 

[ajk1]

Thanks Splitrings for this information on the tire pressure for fire engines. It is very useful because I happen to have another project where I am designing a slab-on-grade for fire engine loading! Looks like I should use 125 psi tire pressue. The fire truck weighs 75,000 pounds, which I assume is the truck with the water in it. Is that the truck that would have 125 psi tire inflation pressure?

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!

 

[ajk1]

I checked and forklifts definitely can come with pneumatic tires. However I have not found anywhere where it says what the pressure in the tire is. Surpisingly hard to find any internet site with the full technical information on forklifts, such as tire pressure, centre of gravity of the unloaded forklift, etc.

 

[Ron]

ajk1....

Try these for infomost of the spec sheets give tire size and load distribution)

http://nissanforklift.com

http://www.mit-lift.com/_mit/index.cfm/north-america/english/

http://www.cat-lift.com/_cat/index.cfm/north-america/english/products/lift-trucks/

http://www.hyster.com/north-america/en-us/

 

[ajk1]

Hi Ron;

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.

 

[hokie66]

I think you are trying to be too precise in your design loading. Whatever forklift you base the design on, the operator of the facility will purchase something else. Make some conservative assumptions based on your research, then go on. Even if pneumatic tires are intended, there will invariably be some hard wheel ones as well, and these are the ones which tear up the joints.