Following Silva's earlier example I filled in the as documented actual figure for the HollowTech 2 spindles diameter:
https://amesweb.info/Torsion/torsion-of-shaft-calculator.aspx
Selected "Hollow shaft"
Filled again in some rough bicycle alike values.
HollowTech axle diameter is documented as 24 mm.
Torque [T] 500
Rotation speed [ω] 60 rpm
Shaft outer radius [c2] 12 mm
Shaft inner radius [c1] 11 mm
Shaft length [L] 100
Modulus of rigidity [G] 300 GPa
=
1 mm wall thickness
RESULTS:
Maximum shear stress [τmax] 626.697 MPa
Angle of twist [θ] 0.997°
Torque [T] 500
Rotation speed [ω] 60 rpm
Shaft outer radius [c2] 12 mm
Shaft inner radius [c1] 10.5 mm
Shaft length [L] 100
Modulus of rigidity [G] 300 GPa
=
1.5 mm wall thickness
RESULTS:
Maximum shear stress [τmax] 445.14 MPa
Angle of twist [θ] 0.708°
Maximum shear stress difference is 626.697-445.14 = 181.557
That's 29% less stress in the material.
29% more reserve to avoid a snap, by a 1.5 mm instead of 1 mm thick wall.
The weight "penalty" is:
https://www.profilebendingmachine.com/steel-pipe-tube-hss-weight-calculator/
24 mm outer diameter, wall thickness 1 mm
Result: 60 gram
24 mm outer diameter, wall thickness 1.5 mm
Result: 80 gram
So, for the HollowTech 2 spindle (outer)diameter specification of 24 mm,
Increasing a wall thickness case of 1 mm to 1.5 mm (=+50% thickness)
- gains 29% more resistance to torsion-snapping (=
Good For Safety)
- gains 33% more weight (=Bad For Cheating in Races - the "extra" is 20 gram.
Yes, this Spindle Snap Safety +29% increase is Priced as 20 gram, but at the Counter they Complain to the Cashier because the lesser cheating might cost them 3 sec on 3 km and come in second...
... just to illustrate the rather big difference in priority between a cheat-racer and a commuter/shopper that happily wants to trade that 3 sec for no spindle snap.