MecMovies 4.0 : M6.20: Shear Stresses in End-to-end Shafts

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Diagram shows a shaft A B with aluminum segment marked 1 of length 1,500 millimeters inside which is a brass shaft marked 2 of length 1,000 millimeters. Both the shafts are centered on the central axis x. The shaft is supported at A and C. A flange B is in between the shafts 1 and 2 on which a torque T is applied. An internal torque T subscript 1 is applied on the post towards A and an internal torque T subscript 2 is applied on the post towards C.

Draw a $FBD$ around flange $B$ .

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

The equilibrium equation obtained from this $FBD$ is:

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