Corwin C wrote:Now ... if the stacks are attached rigidly (i.e. welded) it creates a whole new monster that would require modifying the equation a little (I'm willing if anyone wants it, right now I feel lazy.) I believe, however, that the 1x2's stacked on top of each other and rigidly welded would be very slightly higher than the 2x2 (I'm guessing less than 102% of the 2x2), and the 1x2's stacked side by side would be essentially the same as they are without being welded because there is essentially no shear between the parts (122% of the 2x2).
The welded configurations are essentially a 2x2 with a web inside. The web is the size of the interior of the tubing x twice the thickness. Therefore the moment of inertia will be the moment of inertia of the 2x2 (0.3702 in^4) plus the moment of inertia of the web (I = 1/12[bh^3]) ... I'm also assuming that the weld is perfect and allows absolutely no movement (shear) between the parts.
2 - 1"x2" welded horizontal:
I = 1/12[1.8438*(0.0781*2)^3]+0.3702 = 0.3708 in^4
2 - 1"x2" welded vertical:
I = 1/12[(0.0781*2)*1.8438^3]+0.3702 = 0.4518 in^4
Here's my final, final comparison. (added decimals to show how close the horizontal configurations were)
2"x2" = 0.3702 in^4
1"x2" vertical = 0.2259 in^4 or 61.02% of the 2x2. Two stacked side by side would be 122.04% of the 2x2.
1"x2" horizontal = 0.0744 in^4 or 20.10% of the 2x2. Two stacked on top of each other would be 40.20% of the 2x2.
drumroll please...
2 - 1"x2" horizontal welded = 0.3708 in^4 or 100.16% of the 2x2.
2 - 1"x2" vertical welded = 0.4518 in^4 or 122.04% of the 2x2.
There you go Gus ... I actually over estimated the strength of the horizontal welded configuration.
