Adv,
I'm not making assumptions, & btw that's lower case "ntsqd".
I am looking at the sequence of power moving thru the system and analyzing how each is affected by re-gearing.
Something that I learned in designing racing disc brakes (those used by Mr. Yates and others): It does not matter how much torque can be produced at the wheel mounting flange, it only matters how much torque the tire can transfer to the ground. This is true whether it is propelling torque or retarding torque. The tire doesn't know the difference or care.
With a higher numeric axle ratio (on the Left Coast we call those "Shorter" gears, not taller; neither is a very good description) and no other change(s) at maximum effort the stress in the axle shaft increases because of the torque multiplication. At least until the traction isn't there to support any more torque. From the pinion U-Joint forward nothing has changed so there is no change in stress in those components.
If there are no other changes, then everything forward of the pinion U-Joint doesn't to work quite as hard to get the job done at less than max effort. Said differently, with no other changes the stress in the axle shaft is the same because the loading hasn't changed, but because of the greater torque multiplication the stress in everything forward of that pinion U-Joint is lower for any given level of effort that is less than max effort.
Add the taller tires. That increases the stress in the axle shaft. Which in turn increased the stress forward of the pinion U-Joint because it effectively reduced the torque multiplication meaning that the power-train has to produce more power to achieve the same level of effort, though not as much as it would have had to do by adding those taller tires without the ratio change.
Now add the camper. Again stress in the axle shaft was increased (both the torsional stress as well as the cyclic bending stress). So too has been the stress increased in all of the power-train from the pinion U-Joint forward, but also again this stress is lower than it would be without the ratio change to increase the torque multiplication at anything less than maximum effort.
Up to this point I've been careful to not examine the stress in the ring & pinion itself. True that a higher numeric ratio results in a pinion gear with fewer teeth and those teeth will be smaller than a lower numeric ratio gear-set. At max effort the same power produced by the power-train will be applied to smaller gear teeth and the stress will be higher as a result. At anything less than max effort the power-train will not have to produce as much power to achieve the same results as prior to the gear change due to the greater torque multiplication, so the torque applied by the power-train will be lower for any given effort level below max. It can not be assumed that the smaller teeth are always more highly stressed, only at max effort are they for sure more highly stressed. At less than max effort there too many variables to make any assumptions, an in-depth analysis needs to be done.
This all assumes that the driver continues to operate in exactly the same fashion. That may or may not be a good assumption. With more acceleration available it tends to get used more.
MTBF is a Fatigue Life calculation, In low carbon steels the fatigue life is set as infinite and the max stress per cycle is calculated from the part's geometry and the alloy's properties. the geometry is adjusted or the alloy changed until the part will basically never fail. Toyota's MTBF target stress value for truck axle shafts must be a very large number. Short of hanging with those who like to install 5.29's and 40" tires, and then go beat their truck against the rocks to find out what breaks this time I have not seen or read of Toyota 8" axle shaft failing. They have failed, of course, but not in this use type.
