How Do I Calculate the Shaft Diameter Based on Gear Forces and Moments?

[TyErd]

Homework Statement

Already calculated:
Tangential Forces :

Pinion A=2850 N
Gear B=2850 N
Pinion C= 8550 N
Gear D= 8550 N

Radial Forces:

Pinion A= 1000 N
Gear B= 1000 N
Pinion C= 9100 N
Gear D= 9100 N

Diameters:

Pinion A= 60mm
Gear B= 180mm
Pinion C= 60mm
Gear D= 200mm

The distances between Gear B and Pinion C for the moment can be said to be X(mm). and the distance between the gears and bearings can be said to be Y(mm).

Homework Equations

Moment = F*d

The Attempt at a Solution

I've attached a picture of how the gears/shaft/bearings are arranged.
My question is how do i calculate the shaft diameter(s)

using the moment formula i know that i can calculate torque for each gear. It would just be the tangential force*the radius of the gear. I have no clue what to do with the radial loads or if I need to calculate any other forces.

any help?

 

[TyErd]

just worked out the torque for each gear:

Pinion A: 85.5 Nm
Gear B: 256.5 Nm
Pinion C: 256.5 Nm
Gear D: 855 Nm

not sure what to do with these...

 

[CWatters]

Not my subject but perhaps..

http://www.engineeringtoolbox.com/torsion-shafts-d_947.html

Tmax = (π/16) σ_max D³

where
σ_max = maximum shear stress (MPa, psi)