MecMovies 4.0 : M6.22: Maximum Torque Applied to Coaxial Shaft

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Draw a $FBD$ around end $B$ .

Assume positive internal torques $T_{1}$ and $T_{2}$ in shafts $(1)$ and $(2)$ .

The equilibrium equation obtained from this $FBD$ is:

$\sum_{} M_{x} = - T_{1} - T_{2} + T = 0 ∴ T_{1} + T_{2} = T$