# How can I calculate the yield strength of steel tube?

There's a lot of information -- and even some debates -- on which has a stronger yield strength between square and round steel tube. The majority points to square when the dimensions are equal at the same gage (1"x1" square vs. 1" diameter round).

However, what about square vs. rectangle? Assuming same gage, is the yield strength of a 1" x 1 1/2" that much stronger than 1" x 1"? What about 1/2" x 1 1/2" vs. 1" x 1"? Do you have to be a physicist to be able to make this calculation on your own or is there a layman's method of determining this?

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I'm not a rocket surgeon, but...I believe the yield strength of a HORIZONTAL tube would be in the planes perpendicular to the ground. So as long as the long side of the rectangle is perpendicular to the ground, it will be stronger than a square one with shorter sides. (it's basically acting as a joist at this point, and the thicker the joist, the stiffer it will be). For a vertical support, I believe the maximum strength comes from the narrowest dimension (that being the weakest 'link') – DA01 May 2 '13 at 17:05
The yield strength of structural steel is always 250 MPa regardless of shape. – Chris Cudmore May 2 '13 at 18:31

Some physics. Assuming the same material, length and loading, the bending strength is limited by the Second Moment of Inertia (I) of the cross sectional area. The math is complex, and even given a calculator, it's a bit confusing.

Assuming a vertical loading, You can estimate the relative change in the I value by cubing the scale change. (This estimate is accurate only for solid rectangular beams) This suggests that multiplying the vertical dimension by 1.5 would give a resulting increase in strength of 3.375 times.

If you're increasing the horizontal thickness, then you simply multiply by the scale. So increasing thickness by 1.5 would result in a strength increase of 1.5

I ran some numbers in an I calculator, and assuming a 3mm thickness, I got a value 3 times higher for 1.5" than for 1" if loaded against the longer axis, which shows that the estimator is reasonable.

For a 3mm tube of one inch, I got values of .8 and 2.75 for 1.5".

All things being equal, a hollow square is better than a hollow circle, and a hollow rectangle is better than both -- if you load it in the right direction.

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