Say you're going to make a bridge. You can choose between a square tube or a rectangle tube for the frame. Using just arbitrary numbers for easy figuring, use a 12"x12" square, and a 8"x12" rectangle on edge. Same wall thickness.

 Both tubes have the same vertical measure, but the rectangle would have the vertical sides closer together than the square.

 Which would carry more net weight in the center of the bridge?

 Using the I beam designs, I feel the rectangle would carry more net. Am I right or wrong? What do I need to type into google to find more answers?

The distance between the top and bottom plates will gain you the most( by memory, I think the distance relationship is squared,whereas increases in area have no multiplier, 1 to 1), but since you are keeping that constant, and only increasing the width, you will still get more strength from the 12" wide. It will take 1.5 times more effort to stretch the bottom flange, and 1.5 times more effort to compress the top flange, due to the increased area over the 8". Which is exactly what Exit is referring to regarding mass moment of inertia.

Image is of an I beam, but the principle is the same( in the up and down direction), just have two webs instead of one.  The formula at the bottom, I subscript X, is the one you would use, since the webs (verticals)are constant, regardless of width, you don't even need to calculate that, if all you want to do is compare.  A bigger moment, means stronger in that direction.

(area_moment_of_inertia_I_beam_example.jpg)

area_moment_of_inertia_I_beam_example.jpg (70KB - 915 downloads)

Tubes and I beams act exactly the same.  The web, or walls are just there to connect the top and bottom plates, by the moment of inertia formula below, you will find that nearly all of the strength comes from the top and bottom plates, due to their mass being most distant from the center point due to the distance squared term in the formula.  I beam just connects the two plates in a more efficient manner.  If the tubing has walls half as thick as the single web in the I beam, the capacity would be identical in the vertical direction, not in the horizontal though.

 Wow, I did'nt expect that kind of effort. I hope you did'nt go to too aweful much trouble. But thanks for that.

 Here's an old thread that many helped educate me on. Gearld J. also brought in the moment of inertia which is way over my head.

 Thanks a bunch for taking the time to put this info up.

 I was following your theory Paul. That's exactly how I was looking at it. But the problem is, I dont do a very good job of explaining my questions. In a pure one direction loading, the I beam must be stronger as there is math to back it up. But you know how it is in the land of farming,......there is no perfect loading. I'm really trying to figure out whether to use square or rectangle tube for a hitch on the back of a chisel plow. Not as large as the size I put up, but there would be side loads and all that other unforseen stress that gets put on it in the field.

 Ya know what scares me most about what you just typed? I think I actually understand it somewhat. Your explanation is put in a way that it makes some sense. I see now that you wrote it out, how the wall thinckness can be calculated. I still dont know, and probably thats a good thing, what the moment of inertia is to a tube. But I dont really have a lot of use for knowing much about that so........

 But one part I dont get on 8x12, is that it seems like the formula is for the rectangle tube laying flat instead of 12" tall and 8" wide. ? Is that right?

 Thanks a bunch for that, and taking the time to explain it to me. That really does help a lot.

You proposed a very interesting question, and I have enjoyed reading the answers, as I also build quite a few things here around the farm. Sometimes these projects are necessity, and sometimes for the pure enjoyment of using something that "I" built.

Now, since you further expanded what you are wanting to do, or purpose of the project, most rear hitches I've ever built have used rectangular tube, and even for a front hitch, thinking of a trailer project I just finished. Standing the vertical tube up, to get the most vertical loading out of it, but also in this situation, a channel iron gusset/brace, will reinforce the horizontal, or side to side loading. To use strictly a rectangular tube, or even a square tube, what you would need to decide, is which way the most force will be exerted on the tubing. If you have equal forces, both directions, then it's simply figure the strength needed, and a square box tube. If the forces are unequal, then using a rectangular tube becomes more prevalent, with focusing it's direction of use based on the forces applied. Simple.......... no, cause with farm equipment, we sometimes get that third element, and that is what I'll just call twist or maybe better stated as rotation of the plains. With what we put it thru, the force we apply, doesn't always stay in a vertical/horizontal plain, to the actual structure itself........ if that makes sense??????

In a real life failure, I really don't know, you may be right, but by the book, if the flanges are the same thickness, and the total beb thickness is the same, they carry the same load.  But that is all in static equilibrium, make it a dynamic load, and adds some stresses in other directions, including twisting, and the calculations don't fit onto nice neat diagrams like posted.

Yes, Crowbar, thank you for pointing out that some strength comes from the web itself, especially when you consider the h cubed terms contribution, just trying to simplify things, since the original question was keeping the vertical distance constant, and just increasing the width.  With structural steel, with thick webs, there is a significant contibution due to the web, but in many other materials or combinations, where weight savings is a concern, the webs are made as thin or light as possible letting the flanges take most of the load.  I'm picturing an engineered floor truss with 1.5 inch thick flanges and 3/8 thick discontinuous web.

Yup! there are many things in everyday life that show this...... trusses, steel joist, lattice boom cranes, even my old Link-Belt squirt boom had cutouts in the sides of the boom. A lot of flat bed semi trailers have the web cutouts to reduce weight.

 Ok, now that you have put this in layman terms, I think I can see the light at the end of the tunnel. This brings back many  things I have heard (should have learned, but......) over the years. Even now recall the science class in high school with the bridge building. Balsa wood, stirng and glue.

 But I can now see a little bit of why attention to the flanges are so much more important than the web. Though the web is the connection between the tension and compression, and is important in what it does, it does not take all that much to be just a connection. Whereas the flanges, top and bottom, have to resist compression and tension. It's the resistance to compression on the top flange and the resistance to stretch (or tensile strength?) of the bottom flange that do the main work. The web just allows them to do the work they need to do?

 Or...........................?

 Always drill and fasten to the web, never the flanges. And, make sure all un-used holes are filled with the proper size bolt, even if it means drilling a larger hole to use the proper fitting bolt. 

 So if you would have taken a 10x12 or so and carved the I that met the same dimensions as your 2x6 I, you'd be ok?

If you provide the physics accurately and avoid drawing conclusions I do not understand how there would be a liability problem. 

And I think it would be very useful.