[MechEng83]

Originally Posted by Nate Laverdure

Polar moments of inertia:

AndyMark 1/2" churro tube .00535 in^4  [Solidworks]
1/2" hex bar              .00752 in^4  [Wikipedia]
1/2" round bar            .00614 in^4  [Shigley 8th ed. Table A-18]
VexPro 1/2" round tube    .00570 in^4  [Shigley 8th ed. Table A-18]

*WARNING* Summary of Graduate-Level Mechanics of Materials concept ahead

The polar moment of area is only useful in terms of torsional rigidity. The torsion constant requires a much more complex formulation (the Prandtl membrane analogy). It is only identical to polar moment of area for circles.

Then, you have to use the modulus of rigidity (G) of the material and the distance from the central axis to the outer-most point to determine the shear stress. and compare this to the maximum allowable shear stress of the material.

The dimpled sides of the churro profile actually make it incredibly weak in torsion compared to a solid section or even a full hexagon with a hole in the middle. The membrane or "soap bubble" analogy lets you have a bit of understanding as to how rigid something is in torsion. If you imagine a membrane or soap bubble is attached to the outside edges and the membrane is inflated the volume is analogous to the torsion constant of the section. If there are open sections that are completely contained, the membrane is "flat" in that area. This is why a thin walled tube is very strong in torsion compared to a 359 degree non-closed section.

tl;dr - science says churros are weak in torsion.