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Pound for pound, round tubing is the strongest crosssection available. People use rectangular 'cause it is so much more convenient to hang stuff on. Ever notice a total lack of square tubing in stressed areas on a race car chassis?



round
Round chromemoly is right near the top.
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You have to be careful, with this sort of question, that you're comparing apples with apples, so I'll try to be accurate. With tubing of the same composition and weight per linear foot and with the outer diameter of the round tubing being the same as the outer distance across the flats of the square tubing, the square tubing will, for the same maximum stress, support a pure bending load about a third larger than round when both square and round are loaded about an axis which passes through the centroid of the tube's crosssectional area and which, in the case of the square tubing, is parallel to an edge.
If the bending axis of the square tubing is rotated 45 degrees, the square tubing will support a bending load about 3 times greater than the round. Some assumptions: Square tube radii equal zero. Above is based on maximum stress encountered only, which might not be directly related to acceptable performance or to discernable component failure. 


i would think that square tubing would be stronger. but, like Billy says, you have to make sure you use the right perspective. if you look at a cross section of material, using a unit of 1 for size, round tubing will have a circumference of pi, 3.14, when a square of 1x1 will have a perimeter of 4, so there is more material there. also, with the square tubing you get good strength because of the parallel sides which resist flexing, when a round tube could bend because the force is applied to the rounded side of the tubing and there is less surface area to support the pressure. maybe everybody uses round tubing because it's easy to work with and lighter because of less material?
JB 


Strength
A square obviously has more surface area than a circle. A triangle is the strongest geometric configuration. The arch being second. Since a circle is basically two arches. I would have to say tubing is less likely to crush. I have no idea which would bend first.



I am not an engineer, but which is stronger depends on the type of forces. As far as the roll cages in race cars, I believe that part of the reason for the round tubing is for safety of the driver. If a body part hits the edge of a square tubing, it is more likely to be injured than hitting a round object. On the other hand if you strike the edge of a piece of square tubing with a hammer, it will take considerably more force to damage it than the flat side will take, and the edges are usually rounded. The flat sides are the weakest parts of the square tubing.
Basically, I think there are several factors to consider. 


Need to go back to your mechanics of materials course. See this little essay on moment of inertia and radius of gyration of various shapes. Key sentence in this dissertation is "All things being equal, a circular pipe is the most efficient column section to resist buckling." That is why round tubing is used exclusively in high stress applications. Pound for pound it is the strongest section possible.



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The area inertia of a round section, about an axis through its centroid, is #R^4/4, where "#" equals "PI." That for a square section is 4R^4/3 when "R" is half the length of one side. If the square and round tubing is to have the same weight per linear foot, the areas must be equal. #(R^2(Rt)^2) = 4(R^2(RT)^2) where "t" is the wall thickness of the round tubing and "T" is the wall thickness of the square tubing. If we solve for "T," we find T = R(4R^2#(2Rtt^2))^0.5)/2. If we then substitute this back into the inertia and area equations and solve for the radius of gyration, we find it to be, for a round tube, ((2Rtt^2)/4)^0.5 and (#(2Rtt^2)/12)^0.5 for a square tube. So, the radius of gyration of the square tube is some 2.3% larger than that for the round. I don't want to accuse the author of the lecture of making a mistake. Perhaps he had some other "equal" in mind. I looked at the "home" for the site and couldn't find a way to easily contact him, so I'll leave it at that. But, when it comes to a pure bending load, the square is definitely stronger, even when using the definitions provided by the lecture site. 


For some good background on this and related matters, I recommend reading "Engineer to Win" by Carroll Smith. He relates the mechanical properties of a variety of structures, steels, fasteners, etc. back to racecar application. Amazon has it, so does Summit.
I'd break it out to do some studying on this topic but it is on a shelf behind all the spare parts I have stripped off the Jeep...... 


Willys, is not COLUMN LOADING referred to a vertical piece of material supporting a load and is not subjected to side loading? In that case, there should be no argument. Also, the essay is about buckling and not bending. In this thread application, most of our minds are keyed to side loading/impact and bending.
Trees 


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