Contact Area of Steel Wheel on Concrete Slab 5

[waytsh]

Hi All,

I have a situation where I am designing a slab-on-grade which will have large steel container dumpsters stored on it. These are the large dumpsters that are mounted on the back of trucks and used by recycling and garbage companies. The containers are on steel wheels which are 11" wide and will roll across the slab as they are slid off the truck. Can anyone give me some guidance on how to calculate the contact area for this type of wheel?

Thanks!

 

[SlideRuleEra]

waytsh - The diameter of the wheel is in important factor, and of course the roughness of the concrete. Investigation to determine the contact area for railroads (steel wheels on steel rails) was performed over a century ago. The contact area for this application is very small, well under 1 square inch per wheel. Here is a 1910 Engineering News Record report on that work:

http://books.google.com/books?id=ef...=onepage&q=contact area of steel wheel&f=true

For your application, I would suggest just making a judgment estimate: perhaps 1/4", as measured around the circumference of the wheel. Of course the worst case condition would be to assume a true point load - for designing the slab, I would like just do that.

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[MrHershey]

For most applications, contact area is based on tire pressure and load applied. Contact area ends up being load divided by tire pressure to maintain equilibrium between tire and pavement.

For hard/solid tires this becomes a little trickier since there's no 'pressure'. 'Designing Floor Slabs on Grade' by Ringo & Anderson points to a couple of engineering reports published by Goodyear in the 1980s called 'Over-the-Road Tires Engineering Data' and 'Off-the-Road Tires Engineering Data' and suggests that these test reports estimate an equivalent pressure for hard/solid tires of 180 psi to 250 psi. I've used 250 psi for hard rubber tires since the 250 psi results in a lower contact area (higher load concentration) than the 180 psi. Would imagine the same could be down for metal wheels, though may want to check the engineering reports to make sure. Hard rubber wheels are somewhat ubiquitous. I'm not sure that steel wheels are, aside from trains.

 

[GregLocock]

Unles you are concerned with spalling failure at the contact patch, and experience does suggest that is not an issue, then the contact area makes no odds to the slab design due to Saint Venants theorem.

Cheers

Greg Locock


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[Archie264]

SlideRuleEra,

Wow, 1 square inch per wheel? That's a surprise. But then, on second thought, they were steel wheels that were being studied. Interesting. Thanks.

 

[JAE]

waytsh - check out this article - very close to what you are looking at:

http://www.burnsmcd.com/BenchMark/Article/Contact-Mechanics

 

[waytsh]

Thank you all for the input. Using the PCA method the slab is getting very thick. It would be in the range of 14" if I use a contact area of 10 square inches. Any smaller on the contact area and I am off the chart. Of course the owner just admitted he was very conservative in the wheel loads he had given me. He is going back to get a more accurate number. Do you think I should be using something other than the PCA method when dealing with steel wheels? I have been scanning literature from the Army Corps but haven't found anything yet.

 

[JAE]

Did you check the article I linked? It has a design example.

 

[boo1]

Design of Machine Elements, M. F. Spotts, 6th ed, pp 443
Contact cylinder and flat surface, fig 9-9
a=1/2 width of contact area, P1=load/axial inch
a=1.076*sqrt(((P1*R(E1+E2))/(E1*E2))

 

[waytsh]

JAE, sorry i missed that. I must have been typing up my post when you posted. Thanks.

 

[hokie66]

More important than the thickness design is the toughness of the slab. The authors of the paper referenced by JAE state that armoring was required for the application they studied. Steel fibre concrete increases toughness markedly, but whether that would be sufficient without surface armoring, I don't know.

 

[GregLocock]

"will roll across the slab as they are slid off the truck"

I suggest a site visit. That sounds a rather optimistic description of most operations off the back of a truck.

Cheers

Greg Locock


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[Ron]

Abrasion and scraping of the concrete, as hokie66 noted, are the most significant issues. I agree that steel fibers should be used to increase the toughness of the concrete.

While the B&M articles gives some good theory, I think it overestimates the contact stress. If those values were correct, roll-off containers would damage something every time they are rolled onto the concrete. Not the case.

I would consider a 1/4" wide x width of the wheel as a reasonable contact area, since both the steel and the concrete are elastically deforming and such deformation allow the load contact area to enlarge.

As for thickness design, consider the wheel as a point load and design for shear. Steel wheels do not act like tires and therefore the typical pavement design techniques are not appropriate.

 

[dik]

Ron et al:
I've always use 1/2" for steel to concrete assuming the concrete 'yields' a tad with the modular ratio of steel to concrete (I've never found a source for the 1/2")... same sort of approach... one of the best uses for steel fibres due to their added 'toughness'...

I've had problems with hardening the surface due to spall and it may have been the application... traprock, due to the general deeper embedment seems to work a tad better...

Dik

 

[Archie264]

Hokie66, others,

What is surface armoring? Thanks.

 

[dik]

Armouring is providing a tough surface to resist abrasion and/or damage. It can be accomplished by using traprock, metallic and non-metallic hardeners and some proprietary materials. I've even seen embedded steel rail sections used for 'real heavy' loads...

dik

 

[Archie264]

Thanks, dik.

 

[dhengr]

Waytsh:
This is going to produce a very high concentrated bearing stress on the conc. It is most certainly going to be a crushing/pulverizing action on the conc. and it is most likely to be occurring in some fairly confined areas of the overall slabs. In day to day usage, damage is minimized by putting a couple 2x10's down for the rollers to ride on and these can be thrown away when damaged badly enough. This is called a Hertz bearing stress problem and the material in the M.F. Spotts text book that boo1 suggested is from this type of analysis. But, this type of analysis is somewhat suspect when one of the materials is conc.

Can you define this application any better? Will you ever see loaded containers, or is this just storage space for light weight (empty) or new containers? The cross-truck spacing btwn. the rollers is always the same, a function on the truck chassis center sills or the lifting/loading/tilt frame rail spacing; the width of the container boxes is always the same too. So, you could place these containers in a fairly consistent fashion. Could you embed a pair of 15" channels, or some such, toes up, in the conc. slab to act as guide rails/troughs for each container in this parking space/area? Maybe a .5" thk. by 11"+ wide pl. with two side pls. .75" x 1.5" high welded to the sides and with shear studs on the bottom. This would give you a 1" deep by 11"+ wide guide way/trough for each container wheel.

Can you control and organize the container storage system so the whole bldg. doesn’t need this slab treatment? There are several different forms of armoring a slab, and a number of people here on E-Tips who probably know more about the subject, off the tops of their heads, than I do. The iron fillings troweled into the top surface of the slab are a good hardening and abrasion resistance method, but probably not deep enough or strong enough for your application. Talk with some contractors who do this type of flat work. Steel plates welded to embeds in the slab. But, these might tend to buckle, washboard under your type of loading, if too thin. You could buy raw steel plates, 6 or 8' wide by 20' long, tack weld them to some floor embeds, near a wall and back the containers onto these at random withwise. It seems I’ve seen where they embedded a steel gridwork/grating, almost like very heavy duty floor grating into the top of the slab, with conc. filling the voids to give a level surface.

 

[racookpe1978]

Many appropriate comments above, but two fundementals are missing:

Compression strength of concrete is nominally 3000 psi (it can be specified higher with fibres inside and more cement in the mix, etc.) but steel wheels are "nominally" 36,000 and could go as high as 70,000 psi. On a dumpster, you'd probably not see very high ratings.

So, across the bottom little arc of an 11 inch wide curved wheel pressing down into a flat concrete surface, will not the concrete move 10x further than the wheel?

Assume 3000 psi concrete: The concrete will deform until the area in that little arc length across the bottom of the wheel is large enough to accomodate all of the weight of the dumpster on that wheel: Thus, if 30,000 lbs on an 11 inch wide wheel is resisted by 3000 psi concrete, then (approximately) the area across that arc must (at maximum) be 30000/3000/11 = .9 inch wide. That assumes a 60,000 lb dumpster has all of its weight on 2x wheels. If only 3000 lbs are on the 11 inch wide wheel, then the concrete could deflect only if there were 0.1 inch arc touching.

Go to a dumpster site and Get on your hands and knees with a small steel ruler and LOOK! Look for abrasion wear (scrapes and rips and gouges) and for compression wear and cracking: Where does it occur, how are the dumpsters handled in real life and where is the damage occurring - and not occurring.

 

[oldestguy]

I have a question. With all this theory and results of loads on blocks, has anyone ever gone to an active dumpster area and compared any damage conditions of the concrete to concrete test data, such as the cylinder tests during construction or cores taken later? How about semi trailers being parked with the dollies sitting on a concrete slab? Somehow in my experience there never has been any commotion brought to my attention about damage done by these wheels or slabs breaking under loads.