Round vs. Square Tubing

Determine the section modulus of each profile and use their ratio to determine the difference. Easy peasy.

I didn't mention I'm a non-engineer type. But I've heard of section modulus and I expect it'll be easy enough to find that info. Thanks

My apologies...Wiki has an entry on section modulus and formulas for calculation. It is based on the geometry of the profile. The greater the value, the stiffer the profile, the less the deflection under any given loading condition. By developing a ratio of the two profile's section mods, you'll have a relative difference in deflection for each loading condition. Good luck...let me know if you have additional questions.

Deflection is dependent on Second Moment of Inertia, "I". Stress is dependent on load and Section Modulus, "S". Relationship between Section Modulus and Second Moment of Inertia is dependent on distance from centroid to outermost portion of the section. For symetrical beams this is the distance from the middle of the beam to the outside (radius for round pipe, half the height for square tubing). Hence, the Second Moment will not be linearly proportional to the Section Modulus. To be accurate you should use the ratio of Second Moments to determine deflections.

As a suggestion, go to your local library and request a copy of "Manual of Steel Construction" by AISC (American Institute of Steel Constructors). Blue book or Red book is best, but all you may find is the Green (or later) LRFD books. In there you will find tables with the properties for round and square tubing/pipe for sizes you can find commercially. You should also find the formulas used to determine the deflection, stress, etc. that your program now determines.

For bending the modulus of a tube with D=ext dia and d= int dia is

Jsrd= Pi/32*(D^4-d^4)

For a square tube with ext side =D and internal side =d the modulus is

Jsq= pi/12*(D^4-d^4) Thus the ratio is Jrd/Jsq= 12/32= 3/8.

Hope it helps.

The product term "pi" will not occur in the value for a square cross-section.

For equal wall thickness, the ratio (square-deflection/round-deflection) should be pi*3/16, or about 0.589.

N.B. for deflections below the elastic limit, the orientation of the square section makes little difference to the deflection - but (if this is relevant be warned) it will affect the strength.