Originally Posted by
nulrich
If the design goal is really just to match the stiffness of the existing tube then it's easy. To first order, the stiffness in both bending and torsion is directly proportional to material stiffness multiplied by (OD^4 - ID^4).
For example, aluminum is about 1/3 as stiff as steel, so a 3.00 OD x .049 aluminum tube would be slightly stiffer (because (2.00^4 - 1.902^4) < (3.00^4 - 2.902^4)/3). And it would weigh about half as much since aluminum is also about 1/3 as dense as steel.
In practice, it's quite likely that the stresses at the attachment points for the load or supports will dictate the size of the tubing rather than the pure stiffness of the section.
If the constraint is maximum OD of 3.00, then the above mentioned aluminum tube would be the lightest metallic solution. Carbon fiber makes it look silly, but you'd have to worry about fiber orientation and the stiffness calculation is a lot more difficult.
Nathan