MecMovies 4.0 : M6.6: Twisting of a Compound Torsion Member

Diagram shows a shaft with brass segment A B of length 1800 millimeters which is connected to aluminum segment B C of length 800 millimeter using a flange at B and a torque T of 50 Newton meter is applied on C. The x axis is taken along the axis of the cylinders and the y axis is taken along the rigid support at A and perpendicular to the x axis. A positive internal torque T subscript 2 acts on B C towards B.

Note: Assume a positive internal torque.

The maximum acceptable angle of twist for segment $(2)$ is $ϕ_{2} = 0.02873 rad$ . Rearrange the torque-twist relationship to solve for the minimum acceptable polar moment of inertia $J_{2}$ :

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

$∴ J_{2} = \frac{T_{2} L_{2}}{G_{2} ϕ_{2}} = \frac{(50 N - m) (800 mm) (1, 000 mm/m)}{(26, 000 {N/mm}^{2}) (0.02873 rad)} = 53, 549 {mm}^{4}$