Steel tables for calculating axle diameter

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Ah yes, I forgot to convert to MPa.

I am familiar with deflection however not sure how to calculate it under these parameters, could you give me some pointers?
 
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Just to be clear on one point - Is there another extension and load at the other end of the axle ?
 
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No there isn't, my design has one axle per wheel, so the other wheel is supported by a mirror image of this axle.
 
After looking over my calculations, I've realized I had my bending moment slightly too high, therefore my bending stress is wrong. My bending stress is actually 63MPa.