Seems to vary from tyre manufacturer to tyre manufacturer but 31/10.5/15s will fit but you may need to remove the front mud flaps, any wider and they'll stick out of the arches and any larger diameter and you will run into clearance issues. That said and I have only got 30s on and found I had to remove the mud flaps.
Its worth making sure your truck sits level as most have settled at the front end and need the torsion bars winding up to sit level - this will of course help with clearance but mainly with on the road manners.
