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Here's basic issue I'm sure someone's run into before. I got a nice set of 32's put on, but of course, the spare is still the stock 31'' tire. I've seen some donuts that look like they should be on bicyles, but I think they are all as TALL as the other tires. So, will the truck be face major problems in the event I use the spare, or is it a minimal effect? While I'm on the subject, how much weight can the stock tire carrier support, and can you get a 32'' cover? Would it look better just showing the tire?
As far as the issue of using a 31" tire as a spare while all your other tires are 32", it depends which tire had the flat. If you used the spare on the front tires you wouldn't have a problem driving your truck forever with that spare, if you never put it into 4x4!
Now if one of your rear tires had the flay and you used the 31" spare in the rear you should drive the truck no more than 30 miles and also don't exceed 50 m.p.h. The reason you need to follow these rules is because, running a different size tire on each side of a working axle will cause damage due to the imbalance in the gears! HOPE THIS HELPS!
Driving with different sizes on the rear is no different from driving in a slow circle - it won't hurt the gears or anything else.
But having different sizes on the front will throw the alignment off, and make steering unpredictable.
However, most new temp spares are significantly smaller than the stock tires they're intended to replace, and a truck is less affected than a small car with struts & FWD, so it's no big deal.
I think the stock spare cover would stretch over a 32 without too much effort.
If your truck has a limited slip or locker style differential then running different size tires in the rear will burn up the differential. If it is an open diff it shouldn't matter. If you do have a LS or locker driving a very short distance shouldn't hurt anything. I hope this helps.
Oh, and 4x4 on an odd size tire is definately NOT recommended! Smaller tire sizes should work in a "get me home" situation only. But then isn't that why we carry the spare anyway?
Texasguy is correct. As long as you are in 2wd and have an open diff in the rear, it will not hurt anything. If you were in 4wd I am assuming you are in terrain that allows some wheel slippage anyway so you should still be ok because the tire will slip some before hurting anything. You don't want to run in 4wd on hard packed surfaces anyway because that can cause extreme wear. If you have a lsd in the rear I would use it for very short periods and at slower speeds only. This will keep from burning up the clutches in the lsd. If you have a rear locker, expect some problems as it will always think one wheel is slipping and will stay locked up like a spool. And the reason there are warnings on using the donut spares about speeds and distance is that tires build heat while rotating. The small donut spares build excessive heat due to there size and can faill if pushed to hard.
As far as weight is concerned, I have a 33x12.5 mounted to my spare tire carrier. Unfortunately the weight of this has caused my tailgate skins to begin to seperate. I had this annoying squeek that I finally traced to the right rear corner, and upon inspection, found that it was the metal seperation. As soon as I removed the oversize spare, the noise disappeared. Now I just need to rebuild the seams on my gate!