Tubing

Strength is a measure of the ability of the material to withstand failure and stiffness is a measure of the ability of the material to resist deformation. So to use an analogy an elastic band is high strength low stiffness .. The ability to resist bending forces is a function of the second moment of area of the material.

So for two round tubes of the same external diameter made of different carbon steels with different wall thickness the higher grade steel (thin walled material) will flex more. Which is what Chris Juden's is describing in the last paragraph.

If you increase the diameter of the tube you increase the second moment of area and increase it's resistance to bending. So the thin walled tube will now flex the same amount as the thick walled smaller diameter tube. But it will weigh less. That's all theoretical ..

Nothing Columbus currently produces comes anywhere near 953 in terms of tensile strength.

Spirit = 1050-1250 MPa (equivalent to 725)
Max (Nivacrom) = 950-1050 MPa (equivalent to 631)

Not in tensile strength .. but as I said above strength is a measure of the ability of the material to withstand failure not the ability to resist bending force ..

953 has a Ultimate tensile Strength of 1750 - 2050MPa and a stiffness of 207GPa *

Spirit has a UTS 1050-1250 MPa and a stiffness of 207GPa *

Take a perfectly round down tube (not a mega tube) ..
953 is commercially available with a 36.4 dia and 0.45 wall at max butt position .. so the second moment of area is roughly 0.82cm4
Spirit is commercially available with a 38 dia and a 0.38 wall at max butt position .. so the second moment of area is roughly 0.79cm4

If you consider for argument that the tube (650mm long) is a simple cantilever built in at one end with a 5kg load hanging off the other end then the deflection at the tube end would be : 953 = 2.64mm and Spirit = 2.73mm. So we see with commercially available tubing Spirit is almost as rigid as 953 for these two tubes. Admittedly, 953 will last longer before fracture.

This is all generalisation because I haven't allowed for the tube butting at the ends and the forces applied to a down tube will not behave as a simple cantilever. But it's an illustration for what it's worth to show rigidity.

• data taken online from Columbus and Reynolds tube chart
  

What effect would the shaping of the Max tube have, or is that impossible to calculate (with the available data)?

Max was designed 'rule of thumb' to resist sideways forces at the bottom bracket with it's orientated ellipse profile. The ellipse is 40.3 x 30 and the tube has a 0.5 wall at max butt position. Considering locally the bottom bracket end where the ellipse is orientated on the x axis then the second moment of area using the above numbers is roughly 0.99cm4 so more rigid then a round 953 tube at this point to a force in the x axis .. however the tube shape transitions along the length and the second moment of area changes along the length and also in practice I don't believe the forces experienced would be aligned with the x axis only .. so honestly I can not calculate which is overall more rigid, I'd suggest Max.