How to stiffen 1/2" aluminum tube?

[sphelps]

This process doesn't need to be done with trial and error. Simple beam formulas exist that anyone could follow.

Max deflection of a cantilevered beam is dmax=P*L^3/(3*E*I)

P = Load or weight of fixture (/2 for 2 supports) (Newtons, kg*10)
L = beam length (meters)
E = Modulus (70e9 Pa for aluminium)
I = Moment of Inertia = pi*(d0^4-di^4)/64 for tube/pipe (m^4)

Simple stuff, easy to back calculate for I for a desired amount of displacement (ie 3mm) then determine the OD tube needed. Alternatively calculate the displacement a steal rod will create to get an idea if inserting a piece inside the tube will be worth while. I for a solid rod is = (pi*d^4)/64.

For example, aluminium tube 12.7mm x 8mm will displace 13.8mm with 2.5kg applied at the end of a 0.5m length of tube. A solid tube of steel with an OD of 7mm will displace 44mm with the same weight and length. You could conclude from this that the steel insert will not be very beneficial.