The other thing to consider is how pipe, tube or box section is made. Most mild steel pipe is made out of sheet metal that is folded and welded. Box is generally made out of pipe that is drawn through a die and mandrel to form its shape. Some box is drawn through several dies. With each die that the box is drawn through, the crystal lattice of the steel is elongated, which increases its tensile strength. So box is generally stronger than pipe, box that is twice drawn can be as much as twice as strong (according to Australian standards at least). Some tube is actually drawn right from the start, and drawn many times before its final shape so it can also be very strong when compared to regular pipe, but also more expensive. I have some software on my work computer from Smorgan Steel (one of our local manufacturers) that has all the engineering data, so I will compare two standard profiles of pipe and box that have the same cross sectional area and see what the actual difference in strength from that. It won't be authoritative for non-Australian steel, but it will give you some idea at least.So, for the same weight of metal and same wall thickness, round will be stiffer than square by about 20%. For the same dimensional size, square will be stiffer than round by about 40% and about 20% heavier. What I found though, was that by using 1 1/4" x .049" square instead of 1" x .063" square, the bigger but thinner square tube was 60% stronger and 5% lighter. Those strength percentages apply to both bending and torsion.
The other thing about elongated crystal lattices in steel, is that when you weld them, often the heat effected are is somewhat normalized. So you have to be careful how you weld this stuff together, sometimes you need gussets etc., otherwise you welds become the weakest link in your frame.
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