Most efficient shape for column buckling 1

[E720]

I was trying to find the lightest shape for a column for a project I am working on. I thought that a round HSS would definitely be the lightest but it turned out that a square HSS is the lightest. Aren't round shapes supposed to be the most efficient for column buckling because they have the same radius of g. about any axis. Is the discrepancy just because square HSS has a higher Fy? Thanks.

 

[atrizzy]

Does the square tube buckle at a higher load than the round even at long lengths? If so, it's likely not a Fy issue.

Your premise is a little misleading however as you're comparing 'lightness' of a section. A square section with a large x-secitonal dimension and thin wall will buckle at a higher load than a round section that's just as light, but with a much thicker wall, smaller x-sectional dimension, etc.

I get the sense that either there's more to it or we're not comparing apples to apples...

 

[Retrograde]

I remember reading somewhere that the most efficient shape for buckling of a hollow section is a equilateral triangle.

 

[Hokie93]

With a round HSS or pipe section having its material more concentrated at the centroidal axes compared to a square HSS, it makes sense that a square HSS has greater axial load strength when comparing two shapes of the same or similar weight and the same maximum cross-section dimension. Having the material more concentrated around the centroidal axes results in a lower moment of inertia, which lowers the radius of gyration.

 

[Compositepro]

Tapering the diameter down from the center to the ends can save considerable weight, albeit at added fabrication cost.

 

[BAretired]

For a round HSS, I/A = (d[sup]2[/sup]+ d[sub]1[/sub][sup]2[/sup])/16

For a square HSS, neglecting corner radii, I/A = (d[sup]2[/sup] + d[sub]1[/sub][sup]2[/sup])/12

Draw your own conclusions.

BA

 

[E720]

I worked out the math and a round HSS is in fact more efficient than a square HSS if they have the same areas, wall thicknesses, and yield strengths, but it will always be slightly bigger than the square HSS. A good example is HSS6x6x3/8 and HSS7.500x0.375. They have similar areas and wall thicknesses but the round one has a slightly bigger radius of gyration and obviously has a bigger profile.

 

[cliff234]

Out of curiosity, what is the reason that you are striving for the lightest possible section? AISC has preached for years that “least weight does not always equal least cost”. Very light weight columns might present challenges in the connection design. For example, if you have an HSS truss, Section 13 of the 15th Edition AISC Manual specifically cautions against using the lightest possible chord member. Likewise, if you have moment connections going through an HSS column there may be reasons to use a heavier HSS section (depending on your moment connection detail). Even shear connections can be problematic if you are using single plate shear connections with heavy reactions connecting to a thin-walled HSS column. You should think about the connections when selecting column sizes - especially if you are striving for the absolute lightest possible section - which is sounds like what you are striving for.

 

[E720]

This was just curiosity on my part.

 

[Hokie93]

E720, if you compare two members of the same nominal size (say, an HSS6x6x3/8 and an HSS6x0.500 or perhaps an HSS6.625x0.432), I think you will find the HSS6x6 has greater axial load strength. I second cliff234's comments regarding least weight and least cost and the impact of wall thickness on connection design.

 

[atrizzy]

If the same outside dimension is kept, I agree with Hokie that each member being 'nominal', the square shape will contain more of the material at a distance from the neutral axis and hence have more capacity.

 

[BUGGAR]

Consider local buckling, too.
For efficient large tubes, check what Valmont does.