Square tubing torsion calculations????

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The Artist formerly known as Turbo84
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I'm spending a boat load of time welding and grinding on the frame lately, and my mind starts to wander occasionally. I'm trying to do some comparison between the stock squarish sections of the frame, and the equivalent if made with round tubing. Anybody seen any formulas for calculating torsion of a square tube?

thanks,
Mike
 
A calculation for square tubing will not bring you anything, as the stock frame is 2 u channels welded tgether, and not even all the way through. if you weld it up completely, then you will sort of have a square tubing frame...but still not exactly.

What do you want with torsion? You're not talking about a driveshaft, considering the whole, yes there's torsion but what you want to look at is just stiffness in a single direction.

For a same diameter and wall thickness a square tube will be stiffer than round, however the round will have a significantly less cross sectional area (and weight), if you even out the cross section (larger diameter round tube) the difference will be less.

If weight is no issue and size isn't either, a square and round section, same weight, same wall thickness...the round will be stiffer.


D = OD, d = ID
____________
Area of round tube = PI/4 (D^2 - d^2)
Area of square tube = (D^2 -d^2)
Moment of inertia, round tube = (PI/64)*(D^4 - d^4)
Moment of inertia, square tube = (1/12)*(D^4 - d^4)
 
Torsional calculations assume that the torsional moment will be applied at the axial center of the shape. The problem with evaluating frame cross-sections is that the applied torsional moment may not follow the centroid of the structure and may also be combined with bending or other forces.

You remember this from a while back:

Sectiontext.jpg
 
A calculation for square tubing will not bring you anything, as the stock frame is 2 u channels welded tgether, and not even all the way through. if you weld it up completely, then you will sort of have a square tubing frame...but still not exactly. Gotta disagree. All frames, whether fully welded or spot welded, have a certain torsional strength value, just "somes better than others". My frame is welded throughout the length of the wheelbase. So I ought to be able to make some comparisons for different segments of the frame.
What do you want with torsion? You're not talking about a driveshaft, considering the whole, yes there's torsion but what you want to look at is just stiffness in a single direction. Gotta disagree again. Pure stiffness is fine for when you're running over speed bumps in a parking lot, but torsional stiffness is what you want during cornering as there are different mass and c/g moment arms, along with different f/r spring rates trying to twist the frame into a spiral.
For a same diameter and wall thickness a square tube will be stiffer than round, however the round will have a significantly less cross sectional area (and weight), if you even out the cross section (larger diameter round tube) the difference will be less.

If weight is no issue and size isn't either, a square and round section, same weight, same wall thickness...the round will be stiffer.


D = OD, d = ID
____________
Area of round tube = PI/4 (D^2 - d^2)
Area of square tube = (D^2 -d^2)
Moment of inertia, round tube = (PI/64)*(D^4 - d^4)
Moment of inertia, square tube = (1/12)*(D^4 - d^4)

I'm just trying to do some rough calculations of the basic squarish frame shape along with the tubing I've embedded in the frame. My plans are to do an actual torsion measurement of the frame, and as I can't actually do a before/after comparison, I'd just like to have a rough idea of the contribution of each material.
 
Torsional calculations assume that the torsional moment will be applied at the axial center of the shape. The problem with evaluating frame cross-sections is that the applied torsional moment may not follow the centroid of the structure and may also be combined with bending or other forces.

You remember this from a while back:

Sectiontext.jpg


UMMMM....

Ok, if you say so....:thumbs::surrender::eek:
 
I'm just trying to do some rough calculations of the basic squarish frame shape along with the tubing I've embedded in the frame. My plans are to do an actual torsion measurement of the frame, and as I can't actually do a before/after comparison, I'd just like to have a rough idea of the contribution of each material.

I think you are missing my point. I'm not argueing that a frame has torsional stiffness, of course it deos. I even went sofar as to test mine with a long beam, adding bars and checking the result. i did it for the front and the rear (after the kickup area)

What I'm trying to say is, if you position your members in critical areas and use triangles or "height"for stiffness in a certain direction you can build a torsionally stiffer frame. I thought you wanted to look at individual sections, not the frame as a whole.

As for the welding, sure the frames have a torsional stuffness, but comparing a spot welded overlapping u channel frame to a square section of tubing, what does that bring you? The square tubing results will most likely be way off from the actual frame.
 
I'm just trying to do some rough calculations of the basic squarish frame shape along with the tubing I've embedded in the frame. My plans are to do an actual torsion measurement of the frame, and as I can't actually do a before/after comparison, I'd just like to have a rough idea of the contribution of each material.

I think you are missing my point. I'm not argueing that a frame has torsional stiffness, of course it deos. I even went sofar as to test mine with a long beam, adding bars and checking the result. i did it for the front and the rear (after the kickup area) I would have liked to have tested mine prior to each modification, but this project has dragged on a lot longer than I had planned (bunch of family stuff got in the way, plus this double E's incredible inefficiency at doing mechanical fabrication, LOL), so I just haven't had the discipline to stop at each modification iteration to anchor & measure the frame.

What I'm trying to say is, if you position your members in critical areas and use triangles or "height"for stiffness in a certain direction you can build a torsionally stiffer frame. I thought you wanted to look at individual sections, not the frame as a whole. I'm just looking at individual sections, and guesstimating the sum of the improvements. It's a inexact science, but it's all I got. Regarding triangles or height, that wasn't an option. All the mods are limited to the frame itself. I didn't want to cut up any of the bodywork. In essence, the frame torsion mods and C4 suspension inclusion are intended to be a "bolt-in" change to the original body.

As for the welding, sure the frames have a torsional stuffness, but comparing a spot welded overlapping u channel frame to a square section of tubing, what does that bring you? The square tubing results will most likely be way off from the actual frame.

I'm aware that the spot welded sections are inferior compared to a fully seam welded section of square tubing, but I have to start somewhere. Correct me if I'm wrong, but I've never seen any documentation of the beam or torsional strengths of a stock C3 frame out in the public domain. I'll have final data on my frame, just nothing "concrete" about the starting point. My calculations are not going to make the car faster or slower, but it gives me a better feel for the chassis as a whole.
 
I'm aware that the spot welded sections are inferior compared to a fully seam welded section of square tubing, but I have to start somewhere. Correct me if I'm wrong, but I've never seen any documentation of the beam or torsional strengths of a stock C3 frame out in the public domain. I'll have final data on my frame, just nothing "concrete" about the starting point. My calculations are not going to make the car faster or slower, but it gives me a better feel for the chassis as a whole.

I have never seen this torsional stiffness number published either. I can tell you that a modern vehicle is designed with a torsional stiffness of goal of 10000Nm/degree. I expect that a C3 frame is a fraction of that number.
 
I'm aware that the spot welded sections are inferior compared to a fully seam welded section of square tubing, but I have to start somewhere. Correct me if I'm wrong, but I've never seen any documentation of the beam or torsional strengths of a stock C3 frame out in the public domain. I'll have final data on my frame, just nothing "concrete" about the starting point. My calculations are not going to make the car faster or slower, but it gives me a better feel for the chassis as a whole.

I have never seen this torsional stiffness number published either. I can tell you that a modern vehicle is designed with a torsional stiffness of goal of 10000Nm/degree. I expect that a C3 frame is a fraction of that number.

That number sounds like a reasonable target. Given what I've got to start with (a stock C3 frame), I'll certainly keep my expectations modest. LOL Thanks for the info!
 
I may have some generic ladder frame data somewhere, it would give an idea of the C3 frame, I'll have to dig though, I don't know where I read it.

So, you want to increase torsional stability without adding a cage or anything, tha'ts going to be a challenge.

So, the bodywork has to stay intact? What about the floor? If you could build a backbone type floor, like on a C5/C6 you can work with the floor and more importantly the tunnel, you can get a good bit of torsional stiffness with a tub style rame/floor combo. Think about it, a cardboard box is so much stronger with all it's sides in place than if you were to take out one side. The same holds for the frame. I've posted it before when the JPL race car was discussed (the blue greenwood tube car), they riveted sheet aluminium panels to the space frame, those panels actually add to the frame's stiffness.
 
I may have some generic ladder frame data somewhere, it would give an idea of the C3 frame, I'll have to dig though, I don't know where I read it. I appreciate your time and efforts to find it.
So, you want to increase torsional stability without adding a cage or anything, tha'ts going to be a challenge. Welcome to my world. LOL
So, the bodywork has to stay intact? What about the floor? Call me inflexible, but I just can't get interested in cutting the bodywork. Just the limitations I'm putting on myself, I guess. If you could build a backbone type floor, like on a C5/C6 you can work with the floor and more importantly the tunnel, you can get a good bit of torsional stiffness with a tub style rame/floor combo. Think about it, a cardboard box is so much stronger with all it's sides in place than if you were to take out one side. The same holds for the frame. I've posted it before when the JPL race car was discussed (the blue greenwood tube car), they riveted sheet aluminium panels to the space frame, those panels actually add to the frame's stiffness.

As shown in the old pictures below, I've managed to add torsional stiffness to the frame by adding the torsion bars behind the trans crossmember and the front suspension crossmember. Additionally, I put angled struts from the rear upper shock mounts down to the pinion crossmember. All these seemed to help substantially. The only length of the wheelbase not easily improved was the distance between the trans crossmember and the engine mounting horns crossmember. (The engine and trans are in the way, obviously). I thought about fabricating a "birdcage" torsion setup in the tunnel above the transmission to take care of some of this wheelbase area, but right now it looks like the 5 speed trans takes up too much of the tunnel volume to allow adding tubing in this area. The stock Muncie might have allowed this opportunity, but that's academic, I guess. So, that's why I'm going to all the trouble of embedding the extra tubing in the frame rails between the trans crossmember and the front crossmember. I'm counting on an incremental improvement in beam strength and torsional strength due to the addition of these members. The weight gain is moderate, and fortunately low on the car.
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