Lightweight structural materials selection involves both material properties and geometric properties. In pure tension, a solid straight rod and a hollow tube of the same metallic cross sectional area (meaning same weight per unit length) made of the same material will yield (stretch) at the same load. [In axial (or lengthwise) compression, however, the hollow tube will generally way outperform the solid rod in resistance to buckling failure.]
In bending, buckling or torsion, however, this equality of behavior in axial tension is not true. The engineering calculations for yielding for both rod or beam bending and buckling involve the moment of inertia of the rod/beam shape. "Formulas for Stress and Strain" Raymond J Roark. an engineering classic reference.
For torsion, the appropriate geometric parameter of the rod/beam cross section is the polar moment of inertia.
These geometric factors end up making the performance of a solid rod in axial compression (buckling failure), bending or torsion much worse than a hollow tube of the same cross section area (same weight per unit length) [of the same material] would be.
Put simply, the fact that the most common frame geometry of the older exterior frame backpacks was a hollow metal tube was no accident.
If you take into consideration putting the reinforcement metal into a confining cloth tube or slot, the buckling conditions are radically modified by the lateral support. While this may be difficult to calculate, there can be substantial increases in the buckling load and the original aluminum flat (shaped) bars in the early internal frame backpacks can perform quite well.
There are internal frame backpacks which use small diameter hollow metal tubing placed inside confining cloth tubes which perform quite well. Some of the Osprey packs come to mind.
If you are going to use solid rods in a backpack frame, it would likely be a good idea to give them lateral support (anti-buckling) by confining them into well fitted cloth tubes attached firmly to the pack walls. This appears to be well known to manufacturers.