Torsional Rigidity

[killer_datsun]

what has more torsional rigidity a piece of 2x4 steel square tube or a piece of steel round tubing that has the same diameter and wall thickness of the 2x4?

[silver69camaro]

You didn't specify if that was a 2" tube or a 4" tube....

[vanzuuk1]

I dont know the answer but my bet is that round is stiffer.

[David Pozzi]

I've allways read that round is stronger for a given size and weight of tube.
Lots of chassis get built for IMSA type cars out of square tube because it's easier to rivet aluminum panels to and they have to meet a high weight limit anyway.

[killer_datsun]

the tubing would have a diameter of 4 inches

[nancejd]

Also, there is no such thing as a square 2x4 tube, it would be rectangular.

[RobM]

....a roll cage on top of that tube is what gives is the torsional strength, the rec. tube gives you the beam strength you need

[DeepBlue68]

I'm not sure which one you're talking about:
1. Which material has better torsion resistance when you're just looking at a simple fixed beam undergoing torsion, or
2. Which one will give you higher overall rigidity from your rollcage as a whole

If you're talking about which cross section resists torsion better (topic number 1), that can be found using the polar moment of inertia of each of their cross sections. The higher the polar moment of inertia, the more resistant it is to torsional stress.

You didn't say whether you were referring to 2" diameter of 4" diameter, so I calculated both. For the circular cross section, the polar moment of inertia is given by:

2" Diameter
J = 1/32 * pi * diam^4
= 1/32 * pi * (2 in)^4
J = 1.57 in^4

4" Diameter
J = 1/32 * pi * diam^4
= 1/32 * pi * (4 in)^4
J = 25.13 in^4

Since I wasn't sure which kind of cross section you were talking about, I did it for all 3. For the rectangular cross section:

2" x 4"
J = 1/12 * b * h * (b^2 + h^2)
= 1/12 * (2) * (4) * [ (2)^2 + (4)^2 ]
J = 13.33 in^4

2" x 2"
J = 1/12 * b * h * (b^2 + h^2)
= 1/12 * (2) * (2) * [ (2)^2 + (2)^2 ]
J = 2.67 in^4

4" x 4"
J = 1/12 * b * h * (b^2 + h^2)
= 1/12 * (4) * (4) * [ (4)^2 + (4)^2 ]
J = 42.67 in^4

As for which one will give you a higher overall rigidity of your rollcage as a whole (topic number 2), I know very little about rollcage design and have never done any of it myself. Having said that, my guess would be that it will depend more on the design of the rollcage than the type of material used to construct it. If I had to guess, I would say that most of the stress seen by the individual beams in a rollcage is going to be of either an axial (tension/compression) or bending nature rather than strict torsion. But again, I don't know that, that's just what my instinct would tell me. Anyways, I hope that helps. And someone please correct me if I screwed up those calcs somewhere...it's been a while since I was in Mechanics of Materials.

[killer_datsun]

well I was thinking figuring out what would be torsionally stronger, chassis wise. I don't think rectangular tubing would work to well as a rollcage though

[silver69camaro]

Deepblue68, your calculations are incorrect. You need to subtract the PMOI for the hollow sections, since we are talking about hollow tubes. You can compare round tubes in the manner which you did, but not round to non-circular.

The 4" tube will be more rigid for a given length. But for the manner in which you are talking about, it's all a wash. For a flat plane (chassis), I'd use rectangular tube for it's good torsional rigidity (4" tube isn't very practical) and great bending strength, something which it tough to get with round tube. The torsional stiffness of a flat chassis is very limited.

Now, if you triangulate the chassis (with a cage or similar), then it's a whole different ballgame.

[killer_datsun]

yeah I am going to put a cage on it as well

[DeepBlue68]

Deepblue68, your calculations are incorrect. You need to subtract the PMOI for the hollow sections, since we are talking about hollow tubes. You can compare round tubes in the manner which you did, but not round to non-circular.

Oh, wow, I guess that's what I get for trying to do those calculations during a 6 hour study binge for a Controls exam I had this morning. Geez, that's pretty said I forgot to subtract the hollow sections out. Anyway, thanks for the correction. Am I anywhere close in thinking that most of the stress seen by members of a rollcage is either axial or bending (vs. torsion)?

Also, you're saying you can't directly compare the polar moment of inertia of a rectangular cross-section to that of a circular cross-section?

[silver69camaro]

Wait, you're saying you can't compare the polar moment of inertia of a rectangular cross-section to that of a circular cross-section?

If you don't subtract the PMOI for the hollow sections, then no you can't. Once the hollow areas are accounted for, then the two numbers can be compared.

[silver69camaro]

Am I anywhere close in thinking that most of the stress seen by members of a rollcage is either axial or bending (vs. torsion)?

To update my post to your updated post...

When I design cages, I deal mostly with direct forces, and columnar bending with longer bars. There is some torsional issues that you can think about, but honestly, I let FEA do the work on that.

When you twist a roll cage, most of the forces are primarily axial like you mentioned. Very well designed cages exhibit the most direct tension and compression forces (obviously it's stiffer that way), instead of weird moments and bending forces at the joints.

[DeepBlue68]

Cool...what FEA program do you use? We've learned on NE Nastran here at school, and to be honest I'm not a huge fan of it. I've heard from more than one person that I've interviewed with that it's not the best or the easiest to master, and there's better FEA programs around. Your thoughts?

[killer_datsun]

well my question is pertaining using either 2x4 rectangular tubing or 4 inch diameter circular tubing for the chassis.

[redss86]

I am not an engineer by any means, but here is my opinion. How much of a cage are you going with? If you are going to put a full cage (8 or more points) I would go w/ 2x3x0.125 wall rect. for the frame material. Otherwise, I would go w/ 2x4 rect. over 4 round any day of the week. In my opinion, 2x4 would be easier to work w/ than 4 round, especially if you have to fit it between the rocker and floor pan. I used 2x4x0.125 wall on my frame, and am planning on putting around 550 hp through 6 spd and 9" w/o a cage.

Again, this is just my .02,
Joe

[killer_datsun]

well this is for a long term project where I am going to try and build almost everything myself. so I am not really starting with any car as a basis

[Matt@RFR]

Why are you stuck on 4" round tube?? I've never heard of that being done, and see no reason for it either. Look at the attached picture. Every single one-off chassis I've ever been around has been built using the same basic materials (meaning 1.375" - 1.75" round tube for everything), and with a few tweaks, would make an excellent road race chassis.

I'm not about to spend the time to do the math, but I'm willing to bet you'd end up lighter using round tube versus RECTANGULAR tube.

(2x2 would be square, 2x4 would be rectangular)

Me thinks you've got a long way to go before you're ready to start designing your own chassis.

[killer_datsun]

I am not stuck on 4 inch round tube it is just something I threw out there to compare to rectangular tubing of the same heigth