Designing arms against buckling

[Gasperini]

We're at it again... We couldn't get the right Aluminum alloy, and were trying
to decide if a vertical arm could withstand the load we were going to put on
it.

We have a vertical, ~5 foot section made from 2x2 Al tubing, 1/16" thick -
Flimsy but light. We were concerned going to a weaker Aluminum alloy might
cause failure given our loading conditions.

Worst case scenario, this vertical piece would have a 180-lb axial load (in line
with the beam) and a 1090 in-lb bending moment throughout, from a grabber
which sticks out from the beam top. This setup gives us a long member in
compression, loaded eccentrically. (Simply put, the load is away from the
center of the beam.)

When beams are compressed, they will buckle or crush. Crushing is like a can
getting smashed. The yield strength is passed, the metal gives way, and
the can crumples into a little disc. Buckling is different; it occurs when part
of the beam bends out of line. You can see this if you press down on a
vertical meterstick. The middle part of the stick will bow out to the side.

So we had this 5 foot vertical section that was raising some buckling flags.
It is long, has a thin shell, despite it's decent radius of gyration (all of the
material is far away from the center.) I looked at the beam with the other
advisors, and we found the design was adequate. I'm posting a cleaned up
version of the problem we ended up doing, so other teams may benefit.

Remember, buckling is something to consider. Watch out for:
- Long, slender beams.
- Heavy loads far away from the centerline of a beam.
- Beams with most of the material toward the center of the beam.
- Heavy loads on an unconstrained beam.
(Think antenna ball with a brick instead of a ball. Bad idea.)

Here's what we were working on:

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