Re: Tire /Rim Size
The 31x10.5's will mount on stock rims, but those rims really are too narrow for the tires.
My spare tire is a 33x9.50 BFG M/T mounted on a stock rim, and despite the tall sidewalls and narrow width, the tread is very "rounded" because the sidewalls are really pulled in. The shorter, wider 31x10.50's you have will really wear unevenly in the center if you mount them on stock rims.
A general rule of thumb is to mount the tires on rims that are 0-2 inches narrower than the tread's actual width. Obviously, larger tires have more room for variation than smaller tires.
Most 33x12.50's have about a 9-to-10-inch-wide tread. The narrowest wheel you'd really want to mount them on is a 7-inch-wide rim. I had my 33x12.50's on 15x8's and that was (in my opinion) the ideal size. My current 33x14.50's have a 12.5-inch-wide tread and are mounted on 15x10's which are almost too narrow. Their height (as tall as some 35's) helps make up for that. At street pressure, only the center 9 inches of tread actually touches the ground because of how narrow (for the tire's width) the wheels are. But this helps reduce the rolling resistance from so much rubber rolling on the pavement, and it helps protect the edge of the rim and holds the bead better when aired down.
Most 31x10.50's have around an 8-inch-wide tread. A 6-inch-wide wheel would really be pushing the limits of width differentiation, and the stock 15x5.5 would be too narrow. If it was me, I'd go with a 15x7 wheel for the 31x10.50's.
-- Geoff Beasley