Shaft Torque Rating

Here is a YouTube vid explaining [1]

Allowable shear stress on a shaft is [2].

Here is a shaft size calculator. [3]

Here you can calculate the angular twist of a shaft based on its dimensions and torque. Note that their 'moment' means torque applied to the shaft. See [[4]]

So, for example a 3" steel shaft 2' long will deflect about 1 degree when subjected to ~10x geardown of our 6k in lb hydraulic motor. 2x more torque - and it will deflect about 2 deg, which is a reasonable limit where you can start to see the shaft twist.