I'm building a set of monkey bars for my kids and want to use aluminum tubing (6061 T6) for the rungs. The tubes will be 3 feet long and 1 inch outside diameter. Supported on both ends with a circular metal pipe bracket. I have a choice of various wall thicknesses, all the way up to a full solid round bar. How do I calculate the minimum wall thickness I need to safely support (without any permanent deformation) something like 200 pounds at the middle point of the rung?
We use this equation for a simply supported beam loaded at its center with 200lbs. M= P x L/4 =200 x 3 /4 = 150 lbs.ft
for calculating the tube stress we convert this to 150 x 12 = 1800 lbs.inch
For a hollow round tube we calculate section module which is
$Z = 0.78 (R_o^4 -R_i^4)/R_o$ assuming you have 16 gauge tube with 0.065 inch walls, Z=0.1838 .
Now we have $sigma = M/Z so 42000 (allowable aluminum stress) = M/Z $
$M = 42000 x 0,1838/4= 1929 lbs$
Usually in applications like this which is dynamic loading they use a safety factor of 3 so you can expect this tubing to be able to support approximately
$ 600 lbs$.
Then again there are many standards of aluminum. For this illustration I assume 2024-T3 which has hi strength, you need to find out what you have.
This answer is just an illustration and you should check with the manufacturer about their tests on strength and ductility. Also connections and wall construction has to be checked.