Why a tube beats a rod of the same weight

Second moment of area, and why material far from the centre does the work.

A hollow tube resists bending far better than a solid rod of the same weight and length, because material sitting close to the centre of a bent shape carries almost none of the bending stress and contributes very little to resisting it, while material pushed outward toward the surface, as it is in a tube, sits exactly where the stress is highest and does most of the work.

The physics of bending stiffness

When something bends, one surface stretches and the opposite surface compresses, and the amount of stretching or compressing at any point depends on how far that point sits from an imaginary line running through the middle of the shape, the neutral axis, where the material is neither stretched nor compressed at all. Material right at the centre of a solid rod sits almost exactly on that neutral axis, barely deforming as the rod bends and therefore barely resisting the bend either, while material at the rod's outer surface sits as far from the neutral axis as it can, stretching or compressing the most and doing almost all of the real work of resisting the bend. A solid rod wastes a good portion of its material at the centre, where it contributes little, and a tube corrects this directly by removing exactly that under-worked material from the middle and, for the same total weight, using the material saved to make the outer wall thicker or the whole tube wider, pushing more material out to where it can actually resist the bending stress properly. The effect is strong because resistance to bending grows roughly with the square of how far material sits from the neutral axis, so pushing material outward even modestly increases its contribution by far more than the distance moved would suggest. This is the same reasoning, applied to a round cross-section, that decides why corrugated plastic sheet resists bending so well along its ridges and why a solid rod is such a comparatively inefficient way to use material against bending in the first place, since in both cases what matters is not how much material is present but how far from the centre it has been placed.

The paper-tube comparison

A single flat sheet of paper collapses instantly under the weight of even one book laid across it, offering no useful resistance to bending at all, because every part of that thin sheet sits close to its own neutral axis and none of it is positioned to resist a bend effectively. Roll the exact same sheet of paper into a tube, using no more material and no more weight than before, and it can support the weight of several books stacked on top of it without buckling, because rolling the sheet has done nothing except move that same material away from the centre and out to a larger radius, exactly the improvement a tube makes over a solid rod, demonstrated with nothing more than a sheet of paper and a stack of books.

One figure worth keeping in mind

Because resistance to bending grows with roughly the square of the distance material sits from the neutral axis, moving material from the centre of a solid rod out to the wall of a hollow tube of the same weight can multiply the structure's resistance to bending several times over, using exactly the same amount of material simply repositioned to where it is actually useful.

What this changes in practice

Structural rods, tubes and frames are built hollow wherever bending resistance matters more than raw material cost, since a tube achieves the same, or considerably better, stiffness and strength as a solid rod using noticeably less material and weight to do it. This advantage has a limit, since a wall pushed too thin relative to the tube's diameter becomes vulnerable to buckling, crumpling locally under load rather than bending smoothly, so the benefit of hollowing out a structure only holds up to the point where the remaining wall is still thick enough to resist collapsing in on itself before it ever reaches the load a solid section of the same weight could resist. Finding that point is why tube diameters and wall thicknesses in a well-designed structure are rarely chosen at random, since the best trade-off between saving weight and avoiding a wall thin enough to buckle depends closely on how the tube is being loaded and how long it is between the points supporting it.