Rigidity of aluminium profiles and rectangular tube sections....

[routercnc]

Glad someone is still finding the spreadsheet helpful !

Yes Ixx and Iyy values relate to relative bending performance in the up/down or fore/aft direction (independent of material, just relating to the geometry).

Whilst this is important for a gantry what will dominate the requirement is the torsional stiffness as you point out. My spreadsheet allows you to calculate this for simple shapes but for complex shapes like profiles you need to use FEA which is probably what that company used.

As you and others noted continuous shapes with material away from the centre are best, and many quote a circle as the stiffest shape for torsion but actually there is a stiffer shape. A 50mm diameter square box section will twist less than a 50mm round tube. The extra bits in the corners of the box which are further away from the centre resist the torsion even more so it wins out. This is good news for gantries which can be square or rectangular which are more practical and be better for torsion plus way better for bending than the tube.

Also popular is adding 2 rectangles into an L shape and getting more stiffness with a very practical shape.