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

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.

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

The stress in shaft $(2)$ controls the capacity of the composite shaft. Accordingly, set $τ_{2} = - 50 MPa$ .

Note: The negative value is used here to be consistent with the direction of the external torque applied to flange $B$ as shown in the sketch.

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

$τ_{1} = - (\frac{c_{1}}{c_{2}}) (\frac{G_{1}}{G_{2}}) (\frac{L_{2}}{L_{1}}) τ_{2} = - (\frac{40 mm}{40 mm}) (\frac{76 GPa}{38 GPa}) (\frac{3, 000 mm}{4, 000 mm}) (- 50 MPa) = 75 MPa$