If I'm not mistaken you are calculating the bending stiffness, not the torsional stiffness.

@dmalicky did extensive analysis with various cases to optimise a gantry tube. Here's the thread for reference: https://www.cnczone.com/forums/diy-c...d-posts-4.html

I also did some basic FEA on a small mill I'm building. Overall stiffness improved by 40% just by adding some bracing inside the tube (a 1m 260x180x12.5mm steel tube).

(Following FEAs are with a 1000N force at the cutter, the only thing changed between the two is the added bracing.)
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