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]

Here's the text of this discussion, in quotes and italic:

"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.

 

[rb1957]

"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.

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

 

[PAstructural08]

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.

 

[Brad805]

Strength aside, many times the choice of a section for an assembly such as a trailer is a practical one. It is easy to cut fit a square section.

 

[ColonelMonk]

OK, so here's the deal. But please, do answer the questions in my original post, that is the more important issue.

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

 

[ColonelMonk]

rb1957 (Aerospace)
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.

 

[jayrod12]

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.

 

[ColonelMonk]

PAstructural08 (Structural)
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.

 

[CELinOttawa]

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...

 

[jayrod12]

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.

 

[ColonelMonk]

jayrod12 (Structural)
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.

 

[ColonelMonk]

jayrod12 (Structural)
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.

 

[PAstructural08]

Correct, if you were only worried of jackknifing (horizontal forces) than you would increase the width of the tongue.

 

[ColonelMonk]

CELinOttawa (Structural)
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....

 

[ColonelMonk]

PAstructural08 (Structural)
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

 

[Brad805]

I had circular sections on the brain earlier. oops.

Is the attached sketch generally the case? When you say jack knife, do you mean bumper into the hitch?

 

[ColonelMonk]

Brad805

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.

 

[Brad805]

The reason I asked is truckers with truck/pup combinations will jack knife the pup all day long when dumping the front trailer, and that does not cause problems, but rarely will you ever see a real trucker's pup impact his truck. I get the intent of your original question, but I bet there is a local stress concentration when the unit has been jack knifed improperly.

 

[BAretired]

If you are concerned about strength, you should be using the plastic moduli Zx and Zy, not the elastic moduli Sx and Sy.

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 = th[sup]2[/sup]Fy/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. th[sup]2[/sup]Fy/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