MecMovies 4.0 : M6.21: Maximum Torque for Composite Shaft

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Diagram shows an aluminum shaft A B marked 1 and a brass shaft B C marked 2 with a flange in between at B. Both the shafts are centered on the central axis x. The shaft is supported at A and C. A torque T is applied at B. The radial and longitudinal lines are shown on the shaft. The deformation of the shaft is shown with a counterclockwise segment at B of angle phi subscript B, angle of twist. A caption to the bottom left of the shaft 1 reads: phi subscript 1 = phi subscript B. A caption to the bottom left of the shaft 2 reads: phi subscript 2 = negative phi subscript B.

The relationship between internal torque $T$ in a shaft and its angle of twist $ϕ$ is given by:

$ϕ = \frac{TL}{JG}$

Therefore, the torque-twist relationships for shafts $(1)$ and $(2)$ can be expressed as:

$ϕ_{1} = \frac{T_{1} L_{1}}{J_{1} G_{1}} and ϕ_{2} = \frac{T_{2} L_{2}}{J_{2} G_{2}}$