Square Tube or Rectangular Cross Section, and practical application
Square Tube or Rectangular Cross Section, and practical application
(OP)
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
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






RE: Square Tube or Rectangular Cross Section, and practical application
"Let's say you have a simple beam, with a sawhorse at each end, and a dead weight hanging from the middle. Let's further say, the beam is 2x4x1/4 rectangular box tubing, on edge.
The appropriate I value is (2x4x4x4/12) - (1.5x3.5x3.5x3.5/12) = 5.31in^4
Now, the load in the center of the span is enough to either fail the beam or cause it to deflect more than we want. We need to beef up the beam.
I say, plate the top and bottom with 2x1/4 strip. You say, plate the sides with 4x1/4 strip. Who's right?
My I = ( 2x4.5x4.5x4.5/12) - (1.5x3.5x3.5x3.5/12) = 9.82in^4
Your I = (2.5x4x4x4/12) - (1.5x3.5x3.5x3.5/12) = 7.97in^4
So...my way used half as much steel and gained more strength than yours."
So yeah, that was counter to what "field intuition" would seem - though the calculations seemed to back it up. It confused me, and I started second guessing myself. Maybe I need to drink a rockstar or something...
Next, I'll try to sum this up.
RE: Square Tube or Rectangular Cross Section, and practical application
pick your poison ...
square tube has better "weak axis" allowable than reactangular;
rectangular has better strong axis.
another day in paradise, or is paradise one day closer ?
RE: Square Tube or Rectangular Cross Section, and practical application
For square tube S=8.83/2= 4.41in^3.
4.41 > 3.84 so square tube is stronger.
RE: Square Tube or Rectangular Cross Section, and practical application
RE: Square Tube or Rectangular Cross Section, and practical application
I'm redesigning a trailer. This trailer currently has a MASSIVE tongue, and when I started working here, I had to ask why was this thing so big in relation to the load of the trailer.
Apparently, they had problems with some broken tongues which seemed to be limited to one particular customer. Without going into specifics, there were originally some issues that were traced back to poor design and also a fabrication sub-contractor taking shortcuts. But still, being able to break an overbuilt tongue of this size is a symptom of some real abuse that no trailer tongue was ever designed for.
At the time this problem happened, the customer was brand new, and it was the beginning of a long contract, so right or wrong we allowed them to dictate what should be done, and the result was this 250# monster that does need to be removed (this is a piece of equipment, not just a trailer for carrying things) and basically, it's really made that a chore that sometimes requires heavy equipment or dangerous lifting by workers to complete.
I'm coming back at this from the other side, which is we don't need it to be overbuilt to 10X safety factor because some customer thinks it should be OK to jackknife it.
But I do still want the tongue to be reasonably strong and resistant to minor jackknife mishaps.
I have reduced the crosssection of the tongue from 3 x 6 x .375 Rectangular section to a 4 x 4 x .25 square.
Let's compute I for the 3 x 6 tongue (thanks engineer's edge)
Loaded from top along 6" leg: I = 26.87 in^4
Loaded from side along 3" leg" I = 8.52 in^4
Whoever made this changes, who was trying to combat the tongue breaking when being extremely jackknifed, did it wrong, didn't they? If my assumptions from my first post are correct, then they strengthened the tongue in the wrong direction. They made it brutally strong to support a super heavy trailer load (like a 40,000lb trailer) and only marginally strengthened against the jackknife load.
If you compare the 3 x 6 side load scenario where I = 8.52, my 4 x 4 square tongue with I = 8.82 is slightly stronger, but I have shed about half the weight from the part of the beam that I don't need.
Am I on the right track here?
Sorry, it took me writing this thread to dust off the part of my brain where this stuff used to reside.
Thanks for reading,
CM
RE: Square Tube or Rectangular Cross Section, and practical application
16 Dec 14 18:52
"Each have the same weight per foot" ... do they ? i'd've thought that the 1/4" wall would be heavier than the 3/16" (since they have pretty much the same perimeter).
pick your poison ...
square tube has better "weak axis" allowable than reactangular;
rectangular has better strong axis.
Yeah, they do, according to my stocklist here from some supplier.... I didn't plan it that way. That was for the sake of argument, because I have gotten some comments "why aren't you using a rectangular section"
The truth is, with my redesign of the trailer frame, it's a packaging issue, the 4" "depth" from the trailer deck is more desireable than 5"... But it framed my conversation.
So yes, not only was I doing this for packaging reasons, but the 4 inch in the direction of jackknife made sense, since that the original worry all along.
RE: Square Tube or Rectangular Cross Section, and practical application
So I would say no, they did not do it wrong. And in fact, I would probably have done the same thing.
You would have an increased stiffness in the jackknifing direction (meaning less deflection) with the square tube but the actual stresses would be roughly equivalent.
RE: Square Tube or Rectangular Cross Section, and practical application
16 Dec 14 18:57
First, I would say that the I value is not directly related to the stress/strength of the tube. When calculating deflections you would use I but when calculating stress you would use S (section modulus). That would be I/ybar; from your example above I=9.61.....S=9.61/2.5, where 2.5 is half of the 5 (ybar). So S=3.84in^3.
For square tube S=8.83/2= 4.41in^3.
4.41 > 3.84 so square tube is stronger.
Thanks for that. I'm basically in remedial strength of materials here, I never was very good at remembering these things, and in my career so far I've done so much sheetmetal and machine design that didn't require structural analysis that in 20 years the cobwebs have taken over. Use it or lose it, as they say. I always was a better design engineer and closet fabricator....
I'll look at that in more detail, and you're leading me back to my next question.
Yes, I want to do some basic calculations for bending moment and max stress. I think worst case scenario is acceptable. If it's not too much trouble, help me plug this into these equations! I'll make another post with a diagram.
RE: Square Tube or Rectangular Cross Section, and practical application
RE: Square Tube or Rectangular Cross Section, and practical application
And remember, due to manufacturing tolerances, the actual section properties of the supplied steel may differ from theoretical ones based on geometry. it is likely you are getting tubes that meet ASTM A500 series. The published section properties (based on the worst case manufacturing tolerances) are as follows
4x4x1/4: Weight is 12.20 PLF
3x6x3/16: Weight is 10.76 PLF
So I would have to reverse my answer and agree with you that if they were intending on strengthening it in weak axis bending then yes they did it wrong.
RE: Square Tube or Rectangular Cross Section, and practical application
16 Dec 14 19:25
I is related to stiffness. That's what Pastructural was trying to tell you. S is related to strength. Your section modulus for the 3x6 in the weak direction is only 2.4% less. It is also much stiffer in the strong direction. So for the same mass (which generally equates to the same price) you are taking a slight reduction in jackknifing resistance (2.4%) for a large increase in trailer load resistance (44% increase).
So I would say no, they did not do it wrong. And in fact, I would probably have done the same thing.
You would have an increased stiffness in the jackknifing direction (meaning less deflection) with the square tube but the actual stresses would be roughly equivalent.
Let me rephrase it a little....
This trailer only weighs 4000#. So whatever the original size of the tongue was (I think 5 x 3), it was more than strong enough to support the load of the trailer, jackknifing notwithstanding.
I don't yet know the exact figure, but the "tongue weight" at the hitch is around 10-15% of the total weight of the trailer. I'm thinking it's closer to 10%, or 400lb.
So you're hauling 4000lb with wind resistance in tension, and transferring say, 400lb to the hitch of the truck.
If your major problem, was that you wanted the tongue to resist breakage in a jackknife situation, wouldn't you have increased the width of the tongue instead of the height?
I understand what you're saying, that no matter what direction they increased the dimensions of the cross-section, it made the tongue stiffer. But if you were ONLY trying to resist breakage from jackknifing, and weren't concerned about it's looks, aesthetics, and any other practical reason, wouldn't have have increased the width of tongue instead of height?
CM
As a data point, there are commercially available tongue couplers and swing away hinges for a 3 x 5 x .188W that are rated to 9000# tow weight. So, that original tongue (that broke) was already well oversized
So you look at the I for the 6x3x.375 at nearly 27 compared to the 3x5x.188 at 9.6, which was already more than strong enough..... I realize that we all would have instinctively done what these guys did, but don't the numbers say it was backwards?
Keep in mind, that I'm trying to sell some naysayers, as well as do my due diligence. thanks.
RE: Square Tube or Rectangular Cross Section, and practical application
16 Dec 14 19:44
Ah crap, I made a mistake in my previous post and used 3/16" wall thickness for the 4x4 as well. See below for updated numbers.
And remember, due to manufacturing tolerances, the actual section properties of the supplied steel may differ from theoretical ones based on geometry. it is likely you are getting tubes that meet ASTM A500 series. The published section properties (based on the worst case manufacturing tolerances) are as follows
4x4x1/4: Weight is 12.20 PLF
I = 7.59 in^4
S = 3.8 in^3
3x6x3/16: Weight is 10.76 PLF
Ix = 13.12 in^4
therefore a 73% increase in stiffness
Sx = 4.37 in^3
a 15% increase in strength
Iy = 4.44 in^4
a 41% reduction in stiffness
Sy = 2.97 in^3
a 22% decrease in strength
So I would have to reverse my answer and agree with you that if they were intending on strengthening it in weak axis bending then yes they did it wrong.
Ah, crap. Did it wrong again!! The 6 x 3 had a .375 wall.
But you did get what I was getting at, with the proper terms. Yes, they were trying to strengthen it in the weak axis, and went way overboard in the direction that had little effect.
If I can get you all to agree with me there, I can sell the fact that by increasing the width I have actually slightly increased it's strength to jackknifing, while at the same time making it weigh half as much.
RE: Square Tube or Rectangular Cross Section, and practical application
RE: Square Tube or Rectangular Cross Section, and practical application
16 Dec 14 19:41
Also there are times that adding side plates to an existing beam is the right way to go, and results in significant strength increase. You have also provided a partial restraint to the putter flanges, thereby negating a failure mode that governs many beams...
Thanks. That makes sense.
I think what threw me off, and I'm still not sure (should have done a separate thread) is how adding a tiny amount of material to the top of a tube can make it stronger, when we're adding it to the "weak axis" side....
RE: Square Tube or Rectangular Cross Section, and practical application
16 Dec 14 20:10
Correct, if you were only worried of jackknifing (horizontal forces) than you would increase the width of the tongue.
Thanks. When you distill it down, that's what this thread was all about. I had my chicken scratches here on my desk, but needed to air them out to get it to make sense.
How this all got started, was my searching for some ammo to prove my point, and I came across that other post which wasn't really contrary to what I was doing, but having unequal wall thicknesses is just a different consideration. It got me thinking (dangerous) and embarked on relearning some stuff in order to prove to myself that I knew what I was talking about. I have some more to relearn to do some basic calculations.
Thanks for help
RE: Square Tube or Rectangular Cross Section, and practical application
Is the attached sketch generally the case? When you say jack knife, do you mean bumper into the hitch?
RE: Square Tube or Rectangular Cross Section, and practical application
Generally, yes.
The front of the trailer is square but I don't think that really matters.
Jackknife - yes, that's what I mean. It's slightly more complex than that - the trailers travel in pairs, with the rear trailer connected to the frame of the front trailer. They are, as you might imagine, tricky when you need to back them up. Yet, it can be done with practice. And patience. We suspect that they were jackknifing the rear trailer (it can't jackknife further than 45 degrees) and then instead of trying again, they just hammer down and skid the rear trailer into place. 4000# of trailer! Obvious misuse! I think, further exacerbated by the use of trucks bigger than a pickup, which hurts the driver's visibility and also gives them the power to really abuse it.
So yeah, I realize that in pure tension the load is 8000#, not 4000, but since it's the bending calculation of the beam that's significant I was trying to simplify it.
I was just getting ready to create a sketch of the scenario, as the tongue is removeable - slips into a receiver on the trailer which does complicate the assumptions, I'm guessing. There would be both some distributed load as well as a slight pivot load on the bolt, and possibly a point load where the tongue could contact the edge of the receiver. Stay tuned.
RE: Square Tube or Rectangular Cross Section, and practical application
RE: Square Tube or Rectangular Cross Section, and practical application
If you are concerned about deflection, you should be considering Ix and Iy.
In the earlier example of adding plates to strengthen a w*h rectangular hollow section where w is width and h is height:
1. Add w*t plate top and bottom
Increase in strength = wt.Fy(h+t)
2. Add h*t plate each side
Increase in strength = th2Fy/2
where Fy is the yield strength of the steel.
So when w=2; h = 4; t = 1/4
1. wt.Fy(h+t) = 2.125Fy
2. th2Fy/2 = 2.0Fy
Adding plates top and bottom improves bending strength slightly more than adding plates on the sides and uses only half the material. Note that welding at the corners of the hollow section may be problematic.
BA
RE: Square Tube or Rectangular Cross Section, and practical application
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.
RE: Square Tube or Rectangular Cross Section, and practical application
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.
RE: Square Tube or Rectangular Cross Section, and practical application
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.
RE: Square Tube or Rectangular Cross Section, and practical application
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.
RE: Square Tube or Rectangular Cross Section, and practical application
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RE: Square Tube or Rectangular Cross Section, and practical application