Load Distrubution for Truck Scales

Well, a quick reality check:
Figure 85,000 lbs/ 18 tires x 2 tires = 9444 lbs on a set of dual wheels.
Figure that is put on a 11.5" x 24" wide span, treat as uniform load.
Then M=1/8x9444x11.5" = 13,576 in-lbs.
Then stress = 13,576 x 1/8"/(1/12x(1/4)^3x24) = 54,303 psi if I've done it right.
So yes, 1/4" plate doesn't sound promising here, and an analysis that gives you lower capacity might be right on.
This might just result in the plate sagging between supports while it continued to support the load. If that's acceptable, build it that way and design it as a catenary. Otherwise, thicker plate is in order. Or possibly heavy grating.
You can juggle the numbers some treating it as a fixed span or considering the bending stiffness of the beam flanges, but still, it's a lot of load on that area.
As a first approximation, I would consider that the tire contact pressure is about equal to the tire pressure which is around 85-100 psi. Also, I would design for a considerable amount of overload on a truck scale.
Some trailer wheels are on bogeys (not sure if that's the right term), where the whole set of wheels can swivel, which ought to equalize the weight on twin axles. Others use those air springs. With those air springs, if you run one axle up on a raised platform, it may transfer all the trailer weight to that one axle. So depending on your geometry, you may have higher wheel loading than you ever would on flat pavement.

You should take a closer look through your local highway design code. The Canadian code gives maximum wheel load of 88 kN = 20,000 lbs (I'm pretty sure that's it, can't confirm right now). I agree that 1/4" does not sound quite right.

Do you have access to AASHTO LRFD specifications? It provides guidance on orthotropic design and tire contact areas. If you don't have one, may not be necessary to spend $384 for it. What JStephen wrote is similar to the AASHTO approach for contact area & tire pressure. See the attached sketch for how AASHTO would apply the wheel loads on an orthotropic design (this is for the HS20 portion of HL-93 loading). Your tire pressure would be 40 psi (8 kips/200 square inches).

The specifications allow you use other trucks and states that the Length of the contact area (inches) =6.4 x Gamma x(1 + IM/100), where Gamma is a Load Factor (1.0 would be conservative; 1.3 would be the factor for the Service II condition; IM = dynamic allowance, aka impact, 0 to 10% would be appropriate given the low speed. Width of the contact area (inches) = P/0.8, where P= wheel load.

If you're using an 85K truck, I assume that's the legal limit in your state, get a copy of the maximum axle loads from the DOT.

AASHTO permits the use of the AISC Orthotropic Design Manual for simplified analysis. Regarding material thickness the code states:

"For orthotropic decks, the web thickness of rolled beams or channels and of closed ribs in orthotropic decks shall not be less than 0.25 in., the deck plate thickness
shall not be less than 0.625 in. or four percent of the larger spacing of the ribs, and the thickness of closed ribs shall not be less than 0.1875."

However, we're not talking about a bridge so you might have some wiggle room, assuming you could make 1/4" work.

I think I need clarify. This steel platform is already in use by the company that makes and sells the scales. This isn't something I'm designing, I'm just doing analysis. Many of these have been built and are in use. I know it works. So I don't need to check it against a truck, I need to figure out the maximum load it can support.

The way NIST Handbook 44 defines a concentrated load capacity is, 2 axles 4' apart with a wheel spacing of 8'. This is similar to the AASHTO design tandem, except that tandem has a wheel spacing of 6' with the axles spaced at 4'.

Bridgebuster, I was using the same figure from the 6th Edition. I was approximating the wheel load as a point load, not using a tire pressure. Since the length of the contact area parallel to the beam is only 10", that would only decrease the applied moment by a small amount (as compared to a point load). But what the heck I'll try it.

I was using the tire patch width of 20" and then using the design charts in the AISC Orthotropic Design Manual. From the design charts in Appendix I, I calculate that with the wheel centered over the beam, the load per beam/rib is 0.625P, where P is the wheel load. Then I calculated the section properties and the moment capacity and solved for P. Multiply P x 4 wheels, and that is the concentrated load capacity according to Handbook 44. I calculated a wheel load of 13.56 kips which gives me a concentrated load capacity of 54.2 kips or 27.1 tons. The problem is the concentrated load capacity of the scales is probably at least 40 tons. I am still waiting on the manufacturer to get me that number, but a quick google search of similar portable scales reveals that 40 tons or greater fairly normal. The scale modules are 20' to 24' long. The platform is only 10' long.

Since the scale and the platform are built the same way, it makes no sense that the platform has a lower capacity when the span length is half as long. Either I'm screwing up the wheel load distribution or I'm calculating the capacity of the section wrong. I just am not sure which one it is.

OSUCivlEng:
Why don’t you provide a sketch, with dimesnions, of how these platforms (ramps ?) are framed, how they relate to the 20' wide by 24' long scale section and the direction of travel. Include a section through the platform. I am not at all clear on which way the W10x19 beams which are 11.5" o/c actually span in relation to the direction of travel. Then we would know how to apply the wheel loads to this deck structure. Jstephen’s calcs. contemplate the beams spanning parallel the truck axles, and he is checking the stress in the deck pl. Your last post seems to indicate that the beams are spanning 10' in the direction of travel, perpendicular to the truck axles, and you have a wheel point load, or point loads, on the beam. You’ve got to clear this up or we’re just guessing and playing 20 questions here. You also have to talk about how the beams are framed at their ends and how they are braced and welded to the deck pl. Then you can start to talk about the actual built-up sections, etc. In terms of deck pl. span, I would certainly consider (11.5" - [2x2" half flanges]) = 7.5" as the clr. span of the deck pl. At the max. stress point on the deck pl. (@ center line of a beam), it also has the top flg. working as a short canti. This is an extension of Jstephen’s calcs. and I think he mentioned this possibility. If you are checking the beam spanning ability, you at least have the WF beam, plus the deck pl. acting as a built-up section. What is the .625P from the Handbook 44, where does that come from? I don’t have that handbook. Is the concentrated load cap’y. on the sale really 40 tons, or is that the total cap’y. of the scale or scale section? I suspect you are missing something

dhengr, the platform is 10' long by 13' wide. The W10x19s span 10' and the trucks travel parallel to the beam span. I'm sorry I just assumed that everyone would understand the direction of traffic is parallel to the beam span. NIST is the National Institute for Standards and Technology. NIST Handbook 44 is the Specifications, Tolerances, and Other Technical Requirements for Weighing and Measuring Devices. Handbook 44 defines the concentrated load capacity as "a capcity rating of a vehicle or axle-load scale, defining the maximum load applied by a group of two axles with a centerline spaced at 4 feet apart and an axle width of 8 feet". The beams are welded to a channel running perpendicular to them. The channel has a couple of anchor bolts that connects it to a concrete foundation. I am treating the beams as simply supported since the channel is free to rotate. The 10x19s are braced at midspan (5').

Using that tandem axle configuration, the AISC Design Manual for Orthotropic Steel Plate Deck Bridges, and the AASHTO wheel patch area of 20"x10" I calculated that 0.625 x the wheel load is distributed to each W10x19 beam when the wheel is centered over the beam. When the wheel load is centered between beams, I calculated that it's 0.45 x the wheel load. Again this comes from Appendix I of the AISC Design Manual for Orthotropic Steel Plate Deck Bridges. I also calculated the section properties according to the same AISC manual.

With all that said I neglected to multiply 0.625 x the wheel load, which I am calling P, in the moment calculation. Taking that into account, I recalculated a concentrated load capacity of 57.8 tons which is much more reasonable.

Sketch.

OK here are some sketches. Have at it

OSUCivlEng:
It never ceases to amaze me that OP’ers. assume we can see what they are looking at, we can see the details too, and that we can conjure up the yield strength of the materials used, etc. Look at the cookbooks for general knowledge and understanding of the problem, and the truck dimensions, wheel loads, etc. The cookbooks are: NIST Handbook 44, AASHTO, AISC Design Manual for Orthotropic Steel Plate Deck Bridges; then put them down and go back to the basics. You said you weren’t designing scales or orthotropic bridges, you wanted to check the max. cap’y of this platform/bridge section. You still haven’t explained where the .625P comes from, particularly who derived the .625 or the .45, and how? And, if you don’t know, maybe you shouldn’t be using them. For your problem, the 20"x10" wheel patch represents two tires, a dual set, and is a little suspect. Why not measure a few trucks for actual tire and load patch location and size, and use these avg. values, they are pretty std. on most std. trucks. The 8' c. to c. of wheel patches in you first sketch looks a little suspect, since most std. trailers are about 100" (8'-4") wide, and the outside width of the wheels isn’t greater than that, not your 8' + 20". The 4' axle spacing is about right for a std. truck, but that can vary too, 4 to 4.5 is common. I think Bridgebuster’s sketch is more accurate. Given an 80k or 85k GVW, the tire loads will be about 80k/18 wheels, maybe with some small safety factor added. Many times the tire load on the front axle will be a little higher than the tire load on the rear axles. And, the front tires are about 6.67' c. to c. wide. You have to know the welding and connection details and the strengths (Fy) of the various elements. They must all pass the test. Then look to the AISC Design manual for how to treat the various design issues.

Go back to your Engineering Mechanics (Statics) and Strength of Materials text books and study them. The 11.5" beam spacing is very close to the c. to c. spacing of the two tires on a dual set, study that a bit. It looks like the two tires on a dual set will either load two beams or the deck pl. btwn. two beams, check both conditions. Still on your first sketch, if you lower the two axles so the lower axle is only 6" +/- above the lower channel, this will give you the max. reaction/shear on a beam. Your exact sketch, axle spacing and location, will give you one likely near max. moment on the beam. The max. moment will probably be with one axle at the center of the beam span. Move the axles around a bit and see if you can get a larger moment on the beams. The section properties of the beams are based on a built-up section, the WF plus the deck pl. if welding allows. You probably do not want any yielding, check deflections, you pick the safety factors.

I'm sorry, but your reading comprehension is poor. If you would actually read what I wrote (3 times) you will see that I am bound by NIST Handbook 44 to use the axle and wheel combination that my sketch shows.

Furthermore 20" x 10" is directly from AASHTO and what it recommends for orthotropic decks. I am guessing you don't do a lot of bridge design, so that's why you think it's suspect.

Again if you read what I wrote you would see that I wrote "I was using the tire patch width of 20" and then using the design charts in the AISC Orthotropic Design Manual. From the design charts in Appendix I, I calculate that with the wheel centered over the beam, the load per beam/rib is 0.625P, where P is the wheel load." and "When the wheel load is centered between beams, I calculated that it's 0.45 x the wheel load. Again this comes from Appendix I of the AISC Design Manual for Orthotropic Steel Plate Deck Bridges.".

I calculated section properties per the AISC Ortho. Manual, but hey I already mentioned that as well.

Actually explaining what I did to you multiple times makes me feel pretty confident with the way I approached the problem. Sorry if I am sounding arrogant, but next time I will think twice before posting a particular problem on here. Especially if it deals with design specifications that most people don't normally use.