Determining Plywood Thickness for Rolling Cart to Prevent Warping

[amuron]

I'm trying to build a low profile rolling flat cart. I am running into issues with calculating the material thickness needed to prevent warping, as well as total failure.

The consisits of a 4 foot x 8 foot sheet of plywood of tbd thickness. On the bottom of the cart will be 12 tandem wheel 2" castors spaced equally across the surface. As such, the carts height will remain below 4" from rolling surface to the top.

The cart will be loaded with a fairly uniformly distributed load of 2000 lbs. Each castor is rated at 200lbs. The fairly uniform load is across the total surface, but there will be 12"-18" gaps between points of load contact. This is a lot less safety factor than I'm comfortable with under normal cirumstances. Otoh, the duty cycle will be very low.

What I need to do is determine the proper plywood thickness to use, such that it doesn't warp between castors, nor catastrophically fail. I'm assuming somewhere there exists detailed information on plywood loading vs thickness and species, both static and dynamic. Unfortunately, a quick google seach didn't identify a useful site.

The castors will roll on a maple floor, with 4"X12" floor joists underneath, such that the floor loading should not be an issue.

Its been 20 years + since my statics classes... any help to get my back on track would be appreciated.
Ron

 

[brewnog]

Plywood mechanical properties here:

http://www.matweb.com/search/SpecificMaterial.asp?bassnum=PTSPLY

Should get you started!

 

[FredGarvin]

I'd like to see a picture of what the loading is like. It doesn't make a whole lot of sense to me right now, especially when you say the load will be evenly distributed but with 12-18" gaps.

Anyways, by the sounds of it, the first thing that came to mind is that we'd have to examine the cart as a bunch of plates, not beams. The castors will create a bunch of small plates constrained at the corners. We could possibly treat each plate as a beam, but I think you'd have to add a fudge factor in there. I'll have to consult my Roark's for this one. If you can provide a picture that would be great.

 

[Moonbear]

I'd like to see a picture of what the loading is like. It doesn't make a whole lot of sense to me right now, especially when you say the load will be evenly distributed but with 12-18" gaps.

Anyways, by the sounds of it, the first thing that came to mind is that we'd have to examine the cart as a bunch of plates, not beams. The castors will create a bunch of small plates constrained at the corners. We could possibly treat each plate as a beam, but I think you'd have to add a fudge factor in there. I'll have to consult my Roark's for this one. If you can provide a picture that would be great.

I'm certainly no engineer, but I can see how the arrangement of castors would make a difference in this situation. With 12 castors, I would guess the arrangement would be in rows with 3 spaced along the 4' side and 4 spaced along the 8' side, but for the life of me I can't figure out how that would leave spacing of 12-18" gaps (I can't think of any other configuration that would use 12 castors and keep them somewhat evenly spaced). Even if the castors are placed so that the rows start 6" or so in from the corners, it would leave bigger gaps than that, wouldn't it?

I have some questions that may or may not be important, but since you're venturing into reality and not just in the realm of ideal systems in textbooks...how do those castors attach to the plywood? Do they have flat plates with several screw holes to attach via bolts or screws, or are they of the variety with a post that needs to be inserted into a single hole? Will the attachment of each of those castors create weak areas in the plywood, or leave you with bolt heads protruding through the surface that your 2000lb whatever is going to sit on? This may put more of the weight onto the bolts and directly onto the castors rather than distributing it on the plywood. If the bolts are recessed, then you have to thin out the plywood in places to create those recesses. Or will you have some other form of reinforcement at the attachment locations?

In terms of the floor you're rolling this thing over, what sort of surface does it have? You said maple...is this bare wood, or high polished finished wood? In other words, when you get something with lots of small casters onto it that's carrying a load near the maximum capacity of those casters, the floor surface might make the difference between rolling and sliding. Do you need to worry about damaging the floor? If so, larger wheels or casters will get you over bumps more easily so you can put down another path of plywood over the flooring to protect the floor from a trail of caster marks.

I feel sorry for whoever has the job of pushing this thing across the floor! Hopefully they remember to wear steel-tipped boots and keep their toes out from under the thing...just in case.

 

[Gokul43201]

1. Show us a picture if you can (indicating positions of castors)

2. I think you can get a reasonable approximation (at least a safe upper limit) modeling the sections of the cart-floor as cantilevered beams. Do you have access to any kind of modeling software, like ANSYS or even BEAM ?

3. Why are you limiting yourself to 12 casters of 200 lb capacity ? It looks like the casters will likely fail before the wood, for even a reasonable thickness. The load alone is going to put 170 lbs on each caster, assuming the load is distributed perfectly over the casters. Even without including the weight of the rest of the cart, a slight imbalance of the loading will put some unlucky caster at it's rated maximum load. Yes, there's a factor of safety involved, but with cycling loads, you're sure to kill the bearings in the casters first. At about $12 a pop, you can get yourself some 4" casters rated for about 270 lbs, and I'd buy 13 of them, for a better arrangement.

4. My back of envelope calculation says that the required plywood thickness is very small. Even with just a 1/4" thick board, you'll be pretty safe. With a 1/2" or 3/4" board, you'll get a huge (really huge) safety factor. And a 1" thick board adds about 100 lbs to your load, so you might not want to overdo the thickness, unless you settle for better casters.

 

[amuron]

I made up a pdf file showing the basic concept.
http://tinyurl.com/4b85d

It is a polished wood floor which I don't want to damage. Otoh, I'm really height constrained, so large castors create a whole other set of engineering problems...

Otoh, failure is not an option, and I don't like being so close to manufactuers limits. My other thought would be to have a steel frame work fabricated, and then use huge castors on the periphery.

My background is EE, and physics, not mechanical. As such, Roarkes is a new one to me. It sounds like a great reference to have around.

Thanks
Ron

 

[brewnog]

Wow, moonbear in the engineering forum, there's a sight for sore eyes!

Steel framework sounds like a FAR better plan; you would then have room to have much bigger castors on all four corners. Don't forget to do your sums assuming that only three (NOT FOUR!) castors are on the floor at anyone time; floors are not flat.

 

[Moonbear]

Wow, moonbear in the engineering forum, there's a sight for sore eyes!

LOL! I have a history of dating engineers, does that count? And I watched a roommate tearing her hair out over statics problems back in college...surely I learned some of that from her muttering aloud about the problems. Honestly, I just couldn't resist this topic when I saw it on the forum list...it sounded far too intriguing to pass over. Engineering, that's just using common sense to build stuff, right? (Just kidding, just kidding...*ducks to avoid casters being thrown*)

Steel framework sounds like a FAR better plan; you would then have room to have much bigger castors on all four corners. Don't forget to do your sums assuming that only three (NOT FOUR!) castors are on the floor at anyone time; floors are not flat.

I keep getting these pictures in my head of those shopping carts with one wheel that wants to go the wrong way, or hits a speck of dirt on the floor and screeches to a halt. From all my adventures with carts (albeit for pushing around much smaller loads than this), I'd say if you hit an uneven spot on the floor where only three casters touch the floor, there is the very real possibility you'll only have two of the three on the floor (two diagonal corners) at anyone time while the cart teeters between the two remaining casters. Does it make sense to have 8 casters on a steel frame? One on each corner and one centered on each side, just to add a safety factor and a bit more stability? I'm not thinking about distribution of loads even so much as avoiding wobbling across potentially uneven floors.

 

[brewnog]

Engineering, that's just using common sense to build stuff, right?

Hell yes!

I'd say if you hit an uneven spot on the floor where only three casters touch the floor, there is the very real possibility you'll only have two of the three on the floor (two diagonal corners) at anyone time while the cart teeters between the two remaining casters.

Yes, but I think the castor people assume that this only happens momentarily (where a three-wheel loading situation could be over a long period of time) and that their castors can withstand momentary excess load. Either that or it's accounted for in their factors of safety. The point is, when specifying castors for a four-wheeled product, you assume just three wheels.

 

[Gokul43201]

The point is, when specifying castors for a four-wheeled product, you assume just three wheels.

You can ensure contact with all casters by means of independent suspensions. While this still does not ensure equal loading on all casters, it does improve things some, at the cost of money and design simplicity.

 

[FredGarvin]

It just occurred to me...if you are interested in height savings as well as load carrying capacity, have you looked at the roller tracks used in heavy machinery moving? Why reinvent the wheel if you don't have to?

For example, McMaster-Carr has quite a few to choose from.

P/N: 2735T3 (6000 Lbf capacity)
P/N: 2764T2 (2000 Lbf capacity)
P/N: 2730T8 (2000 Lbf capacity)

If you were going to go with something like that you could double them up to get the size and then, possibly a piece of 3/4" plywood as a base. All of the load carrying would be in the purchased bases and not really in the plywood.

P.S. I found something that comes close to the loading and boundary conditions of your square plate in Roark's. The big thing is to find a useable value for yield of plywood. I used the link to Matweb that Brewnog provided, but the rupture value was so low that the thickness worked out to close to 6 inches. That's way too high. I know a 1" ply would handle this loading, I just have to find reliable numbers to use. As soon as I find some I will post the result.

 

[amuron]

I hadn't thought of that... great idea, and less expensive than 12 castors. I would sacrifice some of the low profile criteria, but I think the extra 2" would be worth it.

I will continue to follow this discussion, as its cool information no matter what.
Ron