I understand that for a given quantity of material a tube is stronger than a rod.
I have a 1.4m clear acrylic rod with 16mm diameter however it is too flexible for its intended purpose (imagine supporting the ends and hanging a weight from the center).
Is it possible to increase/maximise rigidity through either increasing the diameter (max 25mm) and/or making it hollow?
Length must remain constant, and lower weight is preferable but not hard requirement.
Is it possible to increase/maximise rigidity through either increasing the diameter (max 25mm) and/or making it hollow?
Yes, up to the point where the walls collapse. For a solid rod, stiffness will go up roughly as the radius raised to the fourth power -- but weight goes up as radius squared.
For constant-weight tube, stiffness will initially go up as radius to the fourth (when the hole is small), then settle out to going up as radius squared. Keep it up, and because the wall thickness has to go down with increasing radius to keep the weight down, the thing will get fragile and just plain break (squeeze a soda can for an idea of why).
I have ... acrylic ... too flexible.
Materials selection may be an issue. Unless you must choose acrylic because of its looks or other non-strength physical properties, you may want to use something that's just plain stronger. Assuming that glass is right out, you may want to investigate other plastics for this job (or ask if there's a glass that you could use -- I don't know if you could get tempered glass tubes in those dimensions).
Maintaining diameter but making it hollow does not increase rigidity. It actually reduces rigidity a little but greatly increases the rigidity you get per weight.
Consequently, that means that if you maintain the same volume of material, you can make it hollow so that you can obtain a larger diameter for the same weight and that would increase the rigidity for the same weight. At that point you will be limited by how thin the walls can get before buckling.
Another approach is to fill the hollow with some material of lower density that has good compressive strength for it's density to help resist inward buckling (i.e. foam). This would allow you to get even enlarge your diameter even more while maintaining more or less the same weight with even thinner walls. But there is also outward buckling.
I was playing with the idea of inserting a polycarbonate square tube inside the polycarb round bar I need to have higher rigidity, but that also takes up some of the internal space which is an issue with my particular project. It may not be with someone else's. This would probably make the tube stiffer, and would allow for liquids or gasses to flow inside anyway. Maybe a polycarb channel instead of a square tube would work also, you could get the channel piece sized such that the two open ends have to compress inward somewhat in order to fit into the round tube. This might help increase rigidity also.
