Bending and torsional moment

[rmmechanical]

Hi Guys,

I'm working on determining the diameter of a shaft that goes through a pulley on a belt conveyor.
After reading a tonne of texts I believe Shigleys offers the best approach (based on von Misses) for determining this diameter for shafts undergoing torsion and bending.
My problem is that this relies upon determination of the bending and torsion moment induced by the belt around the pulley shell.
I've attached a PDF with a quick sketch of what the layout looks like. Note that the tension force acts upon the shaft through the pulley shell and discs. For this example I've simplified to a single shaft diameter (assuming this to be the minimum acceptable diameter).
Assuming the tension (T1) of the top belt is 200kN and the bottom belt tension (T2) is 70kN, the distances and diameters are labelled.

What is the best method for working out the bending and torsion moments?

Thanks in advance!