Putting aside the rulebook’s “diameter” implication that only round tubing is suitable for frame construction, it may be instructive to look at the section properties of the two tubing types and orientations. Calculating these and unitizing them based on the round tubing properties, and using the same sections (1.625 dia x .125 wall) as johnneilson did with his model in reply # 17, we get the following:
Area I (in^4) S (in^3) 1/S Sig max Sig/A Deflection
circular tube 1.00 1.00 1.00 1.00 1.00 1.00 1.00
square tube 1.273 1.698 1.698 .589 .589 .463 .589
diamond tube 1.273 1.698 1.200 .833 .833 .654 .589
Which tells us that the square tubing is somewhat heavier (area ratio) than the round per unit length, that the bending moduli of the square and diamond are superior to the round, that the stress levels of the square and diamond are less than the round for the same load (Sig max), that the stress per unit weight is also superior, and the bending deflection under the same load is less than the round. This improved performance is largely due to the fact that a good part of the square and diamond material is outside the diameter of the round, and the sections are in effect larger.
So, maybe, as Blue noted, it would be good to step back from time to time and look at things as they are, not as they have become familiar, before loosing off-the-wall criticism.
As an aside, it is unclear where the results reported by Reply 17 went wrong, but it appears that he has confused the “deflection scale” number with the actual deflection. Clearly, 4” deflections are unrealistic. The deflections of the situation that he modeled are actually more on the order of 0.9” circular and 0.54” square. And that is assuming an elastic solution. In fact, all of these sections under that modeled loading are well beyond their mild steel material yield strength.