On 10/30/11 7:59 PM, Grant Saviers wrote:
> Like your logic, but squares have more steel "further out" from the
> neutral axis so they win (or at least moment calculators say so)
>
> see http://www.engineersedge.com/section_properties_menu.shtml
>
> Compare a 4" od x 3" id pipe with a 4" sq od x 3.5" id sq tube. Many
> shapes are there to play with.
>
> About the same moments and the pipe is much heavier. 5.5 sq in cross
> section of steel for the pipe and 3.75 sq in for sq tube, a 50% increase
> in weight per foot for tube.
>
> And there is a diagonal moment calculator for squares (squares win in
> all cases).
>
> What am I missing? (of course there is a lot more to structures than
> this one number)
>
You're comparing a 1/2" wall round tube with a 1/4" wall square tube.
Since the moment is Router^4Rinner^4 the added wall thickness adds
weight without much strength (tube is better than rod, as it were).
If you make the weight/ft (cross sectional area) the same (I did it by
making the tube bigger), you see the expected advantage for round.
Try 4" square tube, 3" inside (1/2" walls)
area (weight per length) = 7
moment = 14.6
Compare to
5" ID round tube, 4.01" id (1/2" walls)
area = 7.01
moment = 18.0
If your constraint were "what's the strongest that will fit in a 4x4"
square, then square tube will win, since even a solid 4" diameter round
bar won't be as strong in bending: that r^4 term out to the corners.
Large diameter thin walls is the strongest in bending and torsion, etc. BUT
the practical problem is that as it gets thinner, small defects become a
bigger problem. If you column load it, it's even worse (the standing on
an empty aluminum can thing).. a tiny asymmetry in loading or the metal
will lead to buckling.
Yes, if you know the direction of the load, and it's always the same,
then some other shape will be better (a long thin sheet, for instance)
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