Dave, if you just need to know the load on a single piece of the tubing before it permanently bends, that's pretty simple. Just increase the load in the calculator until you reach the yield stress of the material you are using (which you'll need to look up for the grade of steel you are using).
The following link will be of help:
http://www.engineersedge.com/beam_bending/beam_bending2e.htmThat is for a beam simply supported on the ends, not with ends locked as if they would resist rotation at the end (which at certain points in a throwing arm would in fact be the case). There are other scenarios at this link, which may be of help too:
http://www.engineersedge.com/beam_calc_menu.shtmlYou will need to calculate the area moment of inertia for these calculators, which for a box beam is relatively simple. For a solid rectangle
where b=base, h=height. You have a hollow rectangle (square actually), so you subtract the area moment of inertia of the "missing" part. So,
, where b1 and h1 are the outer base and height, and
and
are the inner base and height. Since you are using a square tube, b and h are the same, so
. Using your 25x25x1.6mm box tube (I assumed those were metric dimensions, so a roughly 1"x1"x1/16" tube),
. Watch your units and make sure you use common ones (m vs mm, etc).
Hope that helps!