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

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Diagram shows an aluminum shaft A B with a support at A, marked 1 of length 4,000 millimeters and a brass shaft B C with a support at C, marked 2 of length 3,000 millimeters with a flange in between at B. The shafts are centered on the x axis. A torque T is applied at B.

Substitute the torque-twist relationships...

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

...into the geometry of deformation relationship...

$ϕ_{1} + ϕ_{2} = 0$

...to obtain the compatibility equation:

$\frac{T_{1} L_{1}}{J_{1} G_{1}} + \frac{T_{2} L_{2}}{J_{2} G_{2}} = 0$

This equation is based upon the deformations that will occur in the composite shaft, expressed in terms of the unknown internal torques $T_{1}$ and $T_{2}$ .