Semi Trailer Reaction Loads 1

[marcleblanc12]

Has anyone ever tried to solve for reaction loads on a semi trailer that has tandem axles? I've been treating it as a statically indeterminate beam to get my 3 reactions (at the kingpin and each of the axles).

I've been solving this using Clapeyron's theorem (3 moment equation) and I keep getting a very high value for one axle and a negative value on the second axle.

Here's what I'm basically trying to solve:

A trailer 45 ft long loaded with 80,000 lbs evenly distributed over the entire length. The trailer has two tandem axles spaced 5 ft apart at the back and a kingpin at the front. Using the 3 moment equation I get a reaction of 25,940 lbs at the kingpin (seems normal) but then I get 96,234 lbs at the first axle (more than the weight of the trailer) and then -44,294 lbs at the rear axle (a negative number).

This may work out mathematically, but in reality I know that these loads on the tandem axles are not the case. Has anyone else come across this before? I've tried solving this using a few different methods and still arrive at the same thing. I've done other statically indeterminate beams that have worked out to reasonable loads, but for some reason when I try to do these trailers with multiple axles close together, the reaction loads seem very odd. I've tried this on trailers with 2, 3 and even 4 axles and it still gives me the same weird results.

It seems that when I add up the reactions from the tandem axles and divide by two I get 25,970 lbs per axle (for this example), which seems closer to what I should be getting although I'm sure they're not equal. Let me know if any of you have come across this situation and figured out how to solve it.

 

[rb1957]

is the tandem axle mounted on a bogie, so there's a single point of attachment to the trailer ?

are you modelling the two tires (of the tandem) as "rigid" grounds ? or as springs (which the tires really are) ?

another day in paradise, or is paradise one day closer ?

 

[JStephen]

Either both axles are on a pivot, or they both have air-loaded springs- but they are not both just rigidly attached to the trailer. You either need to treat both as spring supports (if you know or can determine the spring constants) or perhaps assume both are the same regardless of displacement.
Even if both were rigidly attached to the trailer, you'd have some spring action from the axles and tires.

 

[TehMightyEngineer]

Agreed, the tandem axle should roughly distribute load to all the axles on the tandem roughly equally.

Ian Riley, PE, SE
Professional Engineer (ME, NH, VT, CT, MA, FL) Structural Engineer (IL, HI)

 

[Guest090822]

Does your situation require that you can’t just use the standard AASHTO HS20 truck loading?

 

[Ron]

As others noted, the tandem acts as a group with the reaction taken at the center of the group and then distributed to each axle. Typical distribution for an evenly distributed load of 80 kips is about 20 kips on each rear tandem axle, about 15 kips on each of the tractor tandem axles and about 10 kips on the front axle of the tractor. This keeps the guys at the weigh station off your back! It can get pricey in fines if the weight distribution is out of range!

 

[marcleblanc12]

What I'm after is checking the design of the beams for the trailer. So I'm basically treating it as a statically indeterminate beam to get my reaction loads and then plot my shear and bending moment diagram. Like I said, when I have multiple axles close together on one end it's giving me weird results for some reason. (A very high reaction and a negative reaction which I know is not actually the case)

 

[rb1957]

yes, but like we've said either the tandem axles are on one bogie (whence 1 reaction point for the trailer, hence determinate), or there are two separate closely spaced axles (indeterminate). If the latter you will get your "odd" answer if you model the two supports as rigid points (which would be the typical model for a beam) BUT in your case you need to model these as spring supports (since the tires and suspension are not rigid). This will allow the beam to deflect slightly between the two points and distribute the load between them, probably 55:45 maybe 60:40.

another day in paradise, or is paradise one day closer ?

 

[marcleblanc12]

Ah! I'm going to see if I can find the spring rate of these axles. That should solve my problem!

 

[JStructsteel]

Why re-invent the wheel, was this trailer not designed for that load in the first place?

 

[marcleblanc12]

I was asked to check someone else's design that's all. By someone else's design, I mean somebody just drew one up without really designing it. That being said, does anyone know what to use for a live load on semi trailers? I've been using 50% of the dead load as a live load, but I'm not sure if that's accurate.

 

[3DDave]

Considering the shape that roads are in and the way truckers operate - about 200% of dead load would seem reasonable.

 

[JStephen]

I don't know how that's normally handled.
Basically, you need to know "What's the biggest bump this trailer will be subjected to while hauling the rated load". But I'm not aware that vehicle manufacturers publish that kind of information.
Fatigue could be a limiting factor in design rather than just static strength.
I've seen similar issues come up in bicycle design- it seems obvious to use finite element and just analyze the heck out of the thing until you realize you don't know ANY of the applied loads.

 

[CANPRO]

The link below has some good info on securing loads and impact forces. Might help you define your design loads.

http://ccmta.ca/images/publications/pdf/cargo_driver_handbook.pdf

 

[rb1957]

You're checking someone else's sketch … use either some industry standard code (ask a trailer designer) or use your own and "state your assumptions".

another day in paradise, or is paradise one day closer ?

 

[BridgeSmith]

We use an increase factor on the truck loading applied to the bridges we design of 30-33% for the effects impact. Don't know whether the effect of the load to the trailer would be similar, but it could give you a starting point.

With respect to your dead and live load, I'll just say our typical design practice would consider only the self weight of the trailer as "dead load" and what goes on the trailer as "live load" (and as you might have guessed, dynamic effects are termed "impact loading"), just in case you're looking for guidance on load (increase) factors. For instance, Load and Resistance Factor Design (LRFD) takes the nominal (expected) loads and typically factors dead load by 1.25 and live load by 1.75, because load applied is much more variable than the load of components of the structure. In your case what can be put on the trailers is not nearly as well defined as the weight of the trailer itself.

 

[dhengr]

Marcleblanc12:
The king pin on the std. trailer is generally fixed in its longitudinal location on the trailer. The fifth wheel assembly on the tractor is adjustable longitudinally on the back of the tractor chassis to allow for some axle loading adjustment. As mentioned above, the rear tandem or tri-axle on the trailer is arranged such that the axle loads are about equal in a static situation. Google ‘semi trailer, bogies,’ and start looking and reading. Do you actually work someplace where they have a vague idea what they are doing when it comes to on-highway trail design and building which meets federal and state stds. and reqr’mts? This whole thing sounds like a futile exercise in the blind leading and checking the blinder-n-dumber, and if all else fails maybe the internet can design it for us. The various states pretty well dictate legal axle loading and you should certainly design up to (somewhat over) those limits, as a min., if you want to sell your trailers. The two rear axles on many trailers, when contained within one bogie also have a slide capability which allows longitudinal adjustment, again, to adjust trailer and tractor axel loadings. Most of these trailers are designed as simple beams/frames, with considerable cross trailer load distribution capability. They have center sills, and/or side sills, and cross framing members, some combination of these depending upon the types of loadings they will see. Then, you look at any special load conditions on an individual basis, on that basic framing system. You obviously can’t have a negative axle loading or you need a pilots license, not a truck drivers license.