Are you suggesting the load is imposed, more or less, in some concentrated way on a spot at some limited locations on shaft as it rotates?

Fatigue due to bending, as oposed to torsional fatigue is different. I thought your were referring orginally to the fatigue as the shaft was asked to accelerate and deaccelerate (i.e. as the "wrenching" of the section occured, as opposed to the simple "bending").

In this case, from inspection of Tom's picture, the extension of the shaft was effected by a large diameter piece. It would seem to me that would reduce the torsional fatigue issues -- and it may have an affect on the component of "bending" fatigue, depending on how the shaft extension was configured as it meets the engine.

I do agree that simply putting a 6" extension of the same diameter would raise some concerns, but what they did appears to have mitigated both the vibration issues (from loading and shaft deflection) and point loading at the exit from the engine (where the sheave would have been orginally) and the extended sheave position to allow the new alternator to be mounted and "turned".

Calculating fatigue issues is not something that I had to do in my "Strength of Materials" lab class at the U of Illinois. The structures work that we did was mostly for objects that were supposed to move very little -- or else.