MecMovies 4.0 : M6.19: Shear Stresses in Coaxial Shafts

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Diagram shows a shaft A B with an aluminum segment of length 1,000 millimeters and a brass shaft in the inside. Both the shafts are centered on the central axis x. 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 of angle phi subscript 1 = phi subscript 2 = phi subscript B, angle of twist.

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:

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