Square Tube or Rectangular Cross Section, and practical application

[ColonelMonk]

OK, this is quite a rudimentary question, I'm not sure why I'm writing it other than I'm rusty in strength of materials and I've observed some conflicting information that confused what I thought I knew.

Consider two structural tubes, one rectangular and one square.

The rectangular cross section is 5 x 3 x .188" and the square is 4 x 4 x .25. Each have the same weight per foot of 9.42#/ft.

The second moment of area of a cross section is a predictor of the beam's resistance to an applied moment which is independent of the material. So all else being equal, we can evaluate it's future performance by calculating the I...

So I figure these, first using the formulas on paper and then verifying with calculators from engineers edge:

For rectangle section, with assumed load along the "long" direction or "top" of the section: I = 9.61 in^4
For rectangle section, with assumed load along the "short" direction or "side" of the section: I = 4.28 in^4

For square section, with assumed load along either direction: I = 8.83 in^4

OK, so for sanity check, the relationship of the magnitude of I to stress is inverse. Increased I, results in decreased stress. Right?

So with the same amount of steel, the 5x3 tubing is a little stronger loaded from the top, but it's substantially weaker than the square tubing when loaded from the side. Right?

A discussion that I was reading, was talking about I-beams and comments regarding the strength of I-beam coming primarily from the cross-section of the flange. Not entirely, but mostly. A contributor went on to say, that for a given beam, if you needed to strengthen it, you would get more result out of thickening the flange than you would thickening the web, by boxing it in with plates or something.... They used that example, because so many people have done exactly that thinking that they were doing the right thing.

Back to the hollow tube beam. Let's say the beam we are talking about in this example is a trailer tongue. Any of you that pays attention, knows that rectangular sections are used much more frequently than square for a trailer.

I had always assumed that the rectangular section was used, because as with a bridge, that tongue needed to be strong in bending in response to the load of the boat or whatever is being carried by the trailer. The weak section is oriented the other way, because you don't intend that tongue to see a direct load, from the side, correct? Yes, I understand that there is still dynamic side loading of the tongue, but let's keep this simple.

One way that trailer tongues do see a significant side load though, is when they are jackknifed!! It makes sense that you would not want to jackknife, but still, it happens, particular in rental trailers...

So, what is the advantage of the 4x4 square over the 5x3 rectangle? I'd say this:

It's nearly as strong in the load direction as the rectangular section, but it is almost twice as strong from the side were the trailer to be jackknifed.

OK, please check my statements above, and then evaluate the statement above.

Thanks, more to come

CM

 

[ColonelMonk]

Brad

I have seen that as well, I'm talking about fully jackknifing to contact, and then not caring at all, just stomp on the gas and then blame the manufacturer when this significant piece of steel breaks.

The reason that it's more plausible than it sounds, is because like I said, there is only so far the rear trailer can go before the tongue makes contact with the front trailer. 45 degrees... So it's not hitting their trucks, it's hitting the rear of the front trailer. So you get both trailers all stacked up behind you. Imagine it - the rear trailer is at 45 deg to the front trailer, which is also at some angle 45 or less to the truck. The sets of tires front and rear both trying to roll in opposite directions. Once you have it locked up, you can hammer down and it kinda goes straight, skidding both sets of tires as it goes... Sounds ridiculous, but a big 10 yard semi-dumptruck can make it do this.

Now, I want to say again, that I'm not trying to design to this "undue" load. I think it's ridiculous. But the current tongue seems to be holding up to that abuse, either that or they have finally figured out how to drive.

So in comparison to the old tongue in this weak axis, my new 4 x 4 tongue has roughly the same properties of cross-section for the jackknifed load. I realize that's not all there is to it....

I do need to take it a few steps further and come up with some stress calcs for the load and steel we're using and make sure that I'm still OK for the load we're hauling. I "KNOW" that it is, I just don't know that it is.

Attached is a sketch. Like I said before, the tongue is removable. It's inserted about 20" into the receiver/backbone of the trailer frame itself, and secured with a 3/4" bolt. The steel of course, does not have a perfect fit, so there are thin strips of bar welded to the outside of the tubing to tighten it up some. I think the clearance around the tube is like .05-.06 around.

The load, well the whole trailer is 4000#. I've shown you in the pic, the loads are kind of scattered around. It's not even close to exact, the lift for example might be bolted to the trailer on the front portion of the trailer, but stowed it hangs over the whole trailer to the rear. Can't forget about the load of the frame itself and axle....

So not sure if a simple load scheme considering all of this rigid and fixed is OK, or whether it needs to be turned into something more complex. I'd like to know what you think. Rather than figuring the it exactly, I think it's better to pick a worst case and if it passes that, you're good to go.

 

[Brad805]

I have seen the type of case you describe. I spun out on a hill going sledding and went in reverse all the way down the hill with the trailer jack knifed against my truck.

Has your boss defined the goal? All of us that are involved in this discussion have codes to work to. I don't know what the automotive standard is for your state, but in general the section sizes do not seem unreasonable for a 1 ton trailer. The trailer GVW actually seems heavy. From what you have described, my guess is the hitch was bent in the horizontal plane before retrofitting. I bet the renter had a trailer wheel pinned against something and kept backing up when it was already jack knifed against the bumper. That is an unreasonable force to design for unless that is what your boss wants. I would be inclined to pick a percentage of the rated cargo load for the horizontal force. If your boss prefers to design for the full bumper force you could estimate the load that would have caused a permanent bend in the old pipe section.

That is a difficult hitch detail for longevity. I suppose this is the type of trailer that gets stationed at a site for a period of time and you don't want it stolen.

 

[ColonelMonk]

Howdy Brad, and all

Exactly. It's being abused.

GVW seems heavy, but the frame is about 700#, the tongue is 250#, footprint is about 9 x 9', there is a lead acid battery bank, a large hydraulic mast/boom, Solar, etc... So it's every bit of 4000#.

Small company. Boss has not defined a goal per se - I have a list of "wants" for this new design, and many of them are around making the brutal heavy tongue something that customers and workers can manage. When you look at the trailer you can see how out of place it is. At the time they had the problems, it was easier to make it heavier than it was to lose the offending customer, but then you make a bad decision and have to live with it forever. In accommodating the "wants" the massiveness has got to go. Everyone that was here is "nervous" but they aren't engineers either.

We have some of our competitor's trailers (we rent them out) and they are a little lighter, and use a 3 x 3 x .25 tongue. The tongue is also removable, and easy to handle because it's not overbuilt. Haven't had a single problem with any of them, had them in the fleet for a decade.

There aren't any real standards that I can find that specifically govern trailer frames, but as I referred to earlier, commercially available tongue products specifying the use of 5 x 3 x .188" tubing for use up to 9000#. The "tongue weight" at the hitch, using a 10% min standard would be 900#. That's a MUCH larger load than we are dealing with. Our load is less than half, but like I said, when tandem towing there is a tensile load of two trailers or 8000# rolling, and a 400# tongue weight. Also, I'm not using the 5 x 3, but instead 4 x 4 x .25 and it has similar "strong axis" properties, better "weak axis" properties, and the same weight per foot as the 5 x 3. It's more than strong enough.

We do intend to have a PE look this over, being a safety product we simply can't afford not to. Might just have them do the bending calculations from the trailer load perspective, and the fact that there's a bolted joint and all but I think designing it to hold up against jackknife is ridiculous. If somebody wants a "heavy duty tongue" we can offer it with 4 x 4 x .375 Tubing, and weld it on....

Regarding the receiver, I hear you, but like you said correctly, these sit more than they are on the road. You start a bridge reconstruction and they might be there for 3 months before being moved again. The receiver is 3/8 wall. Obviously, you're not concerned about receiver, you're concerned about the tongue and the wall/point loading. They haven't had an issue with breakage since they went to the larger 6 x 3 x .375 tubing with thicker wall.

Thanks for your help so far.

 

[Brad805]

If you are building multiple models you should look into some of the software options to model the units accurately. The advantage you have when you are dealing with something you re-produce time and time again is you can spend a lot of time studying different aspects. This is especially true when it is a relatively simple assembly. Look at the solidworks or inventor forums to see what other mechanical guys are doing. This software allows you to examine many different load cases that many PE's will not do unless you indicate them to be a concern. One needs to have seen how they get used to know what to look for.

I understand the trailer weight better now. This is an job site trailer with permanent accessories.

The boss needs to decide on what is reasonable. In reality, the cost differential using the bigger section is chump change. If trailer rental is like temporary bridge rentals the payback time for the build cost is short. Minimizing long term repair can be profitable. If you are not getting any complaints about the weight of the hitch I might leave it alone or simply improve upon the design. The reckless in the rental world will always one up you regardless of your design. This is true even moreso when you are sending your product to a site without roads. Good luck.

 

[IRstuff]

Tough to make things idiot-proof; idiots are ingenious.

TTFN
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[XR250]

FWIW, it may be easier to find a coupler for the 3" wide member than the 4" wide.