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

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Diagram shows a shaft A B with aluminum segment marked 1 of length 400 millimeters inside which is a brass shaft marked 2. Both the shafts are centered on the central axis x. A torque T is applied at B.

$\frac{τ_{1} L_{1}}{c_{1} G_{1}} = \frac{τ_{2} L_{2}}{c_{2} G_{2}}$

The stress in shaft $(2)$ controls the capacity of the composite shaft. Accordingly, set $τ_{2} = 100 MPa$ .

Compute the shear stress in shaft $(1)$ :

$τ_{1} = (\frac{c_{1}}{c_{2}}) (\frac{G_{1}}{G_{2}}) (\frac{L_{2}}{L_{1}}) τ_{2} = (\frac{25 mm}{21 mm}) (\frac{26 GPa}{38 GPa}) {(\frac{400 mm}{400 mm})}^{1} (100 MPa) = 81.45 MPa$