Reasonable rotating shaft deflection?

I'm designing a rotating shaft that carries a wheel. The load is assumed to be 1/2 the hub load placed on the shaft at each end of the rigid hub (20,000 each end). The deflected angle at the bearings is well within tolerance for the bearings chosen. The shaft is 31 inches long and I'm calculating a deflection in the center of 0.052 inches. My calcs for stresses and fatigue are all very good.
I'm not able to find any references to reasonable deflection of a shaft. I'm finding that I need huge increases in diameter to change the max deflection.
I would appreciate some feedback on commonly accepted shaft deflection such as acceptable radial deflection per foot of length or whatever.
Thanks in advance!

This document might be helpful...

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Thanks Kelly, yes, I've seen that document. It's good, but it only gives recommendations for shaft deflections for the benefit of gears. I don't have any gears, so I'm not concerned with gear misalignment. I'm just supporting a wheel, so I'm wondering about simple deflection in the center of the shaft. What's reasonable? is 0.050" in 31" reasonable for this? I'm looking for a guideline like for floors, the common deflection allowed for floors is 1 in 400. Is there a similar rule of thumb for shafts?

Floors are "usually" non-dynamic items. (Trouble if they aren't!) Shafts are definitely dynamic animals. The factors causing and affected by shaft deflections are so widely variable that across the board standards would be impossible. Consider this: loading and support arrangements, speed, accelerations, imbalanced loads, attachment geometry, stress concentrators (like keyways or shoulders), mechanical requirements, fatigue, etc.

You would be best advised to analyze your situation, look for the causes and effects of deflections under all operating conditions, determine for yourself what deflection is acceptable, apply a factor of safety, and design it.

Adding to jboggs post (above), floors are well understood engineered applications. Applying a rule-of-thumb to floor design is safe.

I think that since your design shows good deflections at most loading points, I would focus on deflection effects at the wheels. After you understand what is required at the wheels (or other critical application points) back-design the supporting components to meet the deflection/stress requirement.

Check the deflections at all critical locations and then let the deflections be what they want to be at the rest of assembly.