I understand the fact that a solid rod is stronger than a hollow rod given the same diameter. My question is whether this fact takes into account the weight of the rod itself. Imagine two 20 foot long 1/2" diameter steel rods- one is solid and the other is hollow. Support these two rods at either end. Which rod deflects more under its own weight? Which rod deflects more with a 10 lb load hanging from its center? My instinct is that the additional weight of the solid rod overcomes it's inherently greater rigidity. The hollow rod should deflect less than the solid rod in this scenario. Any thoughts? I don't know the formulas or software to calculate this, it's just something that I was pondering as I fell asleep last night. Thanks!