Bending Resistance - Hollow tube vs. Solid Rod
The second moment of area, also known as the area moment of inertia is a property of a cross section that can be used to predict the resistance of beams to bending. The deflection of a beam under load depends not only on the load, but also on the geometry of the beam's cross-section. This is why beams with higher area moments of inertia, such as I-beams are so often seen in building construction as opposed to other beams with the same cross sectional area. The higher the area moment of inertia, the greater the resistance to bending.
The formulas for area moment of inertia for solid and hollow round beams are;
Solid round beam (rod):

Hollow round beam (tube):

Where = outer diameter and = inner diameter

Assuming the two beams are made of the same material, the beam with the higher area moment of inertia will be more resistant to bending.
Case 1.
Two round beams each of which has the same weight (quantity of material and cross sectional area). If we choose a solid round rod of 1 in. diameter and a round tube of 1.5 in. outer diameter, the inner diameter of the round tube would be 1.118 in. resulting in a wall thickness of the 0.191 in. or a little more than 3/16 in. wall thickness to give the same cross-sectional area (the same amount of material thus the same weight).
Solid Rod:

Area moment of inertia: d=1 Hollow Tube:

Area moment of inertia:

di = 1.118

So comparing area moment of inertia for the hollow vs. the solid beam:

d = 1.5

The hollow tube area moment of inertia is approximately 3.5 times that of a solid rod of the same cross sectional area (weight).

Case 2.
Two round beams each of which has the same outer diameter. The hollow tube will weigh less (smaller quantity of material) and have a smaller cross sectional area than the solid rod. If we choose a solid round rod of 1 in. diameter and a hollow tube with the same wall thickness as Case 1 (0.191 in.).
Solid Rod:

Area moment of inertia: d=1 Hollow Tube: di = 0.618

Area moment of inertia: d = 1.0

So comparing area moment of inertia for the hollow vs. the solid beam:

But the cross sectional area (weight) of the hollow vs. the solid beam:

So in this case, the hollow tube area moment of inertia is approximately 85% the solid rod of the same diameter but the cross sectional area (weight) of the hollow tube is only 62% of the solid rod.

Case 3.
Selection of the right cross section material can result in improvements in both bending strength and weight. Again consider two round beams; one solid, the other hollow. If we choose a solid round rod of
1 in. diameter and a hollow tube with a 1.125 in. outer diameter and 0.75 inner diameter resulting in a wall thickness of 0.1875 (3/16) in. the results will be:
Solid Rod:

Area moment of inertia: d=1 Hollow Tube:

Area moment of inertia:

di = 0.881

d = 1.125

So comparing area moment of inertia for the hollow vs. the solid beam:

And the cross sectional area (weight) of the hollow vs. the solid beam:

So in this case, the hollow tube area moment of inertia is 128% of the solid rod but the cross sectional area (weight) of the hollow tube is only 70% of the solid rod.