In Gurps, how powerful do you need to fight a tank?

[Anaraxes]

You'll want GURPS Supers, p. 123 ("Man versus Machine").

Originally Posted by Bathawk

bending cannon barrels

All else being equal, a hollow tube is stronger against bending than a solid bar of the same mass. It's also weaker than a solid bar of the same diameter. Here's a calculator if you really want to do the math.

Looking at a picture of an M1 Abrams 120mm gun bore, it looks like the wall thickness is around 15% of the outside diameter of the gun. Risking a bit of math this late at night, looks like a force of about 400,000 pounds to bend steel with your hands 36" apart. That's ST 500, or 400 with vanilla Extra Effort, or a mere +14 ST (Super-Effort) if you're using those rules.

tearing turrets off

A modern tank turret weighs somewhere in the neighborhood of 1/3 the weight of the entire tank. Typically nothing significant attaches the turret to the hull other than the turret's own weight. If you're strong enough to lift that ~20 ton weight, there's no additional "tearing" necessary. Grab it and fly away.