Well, there are several issues:
- Because the bore is eccentric, the neutral axis will not be at the center. So the bending stress will not be uniform--the extreme fiber stresses will not be the same value. (Unless the eccentricity is extreme, this will not affect the torsional shear too much.)
- Because the shaft is rotating, the rotational speed will drive the load picture. If the eccentricity is uniform the distributed load from the rotation will be uniform. If the eccentricity is caused by (for example) a wandering drill bit then the load will vary as the bore wanders, and the load may not be coplanar.
- Rotating shafts (even concentric ones) have critical speeds. Finding the critical speed of an eccentric shaft may be a significant challenge.
Start by posting a sheet--you'll attract a lot more help!