dana 60 strength?

what would be the biggest tire a dana 60 could handle without having to worry about breaking?  

That depend on vehicle size and weight, whether it is locked or not and axle shaft size as D60's usually have about a 1.34 inch axle shaft and some have a 1.5 inch one.  

a 3/4 ton chevy with a part time locker and a lead foot. what would the 1.34 handle and what would the 1.5 handle?  

id say your safe with up to 40s....maybe some will say its too much but i wheeled in a 3500 chevy crew cab longbed....it was a huge truck with some 38 inc tires and a MEAN!!!! big block 502 and of course a lead foot and niether the rear 14 bolt or front dana 60 complained.....  
Solid axle chevys can't be beat!
My dream truck: 73-91 chevy 3500 crew cab srw with dana 60/14bolt, 6 inc long travel lift with KING shocks, 37 inc tires and a 24v cummins diesel, nv5600 and np205

heavymetalk20:
a 3/4 ton chevy with a part time locker and a lead foot. what would the 1.34 handle and what would the 1.5 handle?

Smaller axles handle less torque. I would say up to maybe 38's with a locker (locker reduces capacity because of added strain on axles) Sure some do more but I am talking fairly bullet proof here not gray area operation.  

I can't say what the limit is but I can tell you that I was running 42x15x16.5 with 5.38 gears and a full spool with a Dana 60 with 30 spline 1.34 inch axels and they didn't hold up at all I would snap them like toothpicks every time I encountered any moderately hard obstacle. I run a full size bronco. My Dana 60 front seems to be holding up well but it has 35 spline axles and they are much thicker than the rear. I swapped in a 14 bolt and have had much better luck.  
Can't beat an old Ford