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

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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 single torque of $T = 50 N-m$ is applied to a compound torsion member. Segment $(1)$ is a $32 - mm$ diameter solid brass $(G = 37 GPa)$ rod. Segment $(2)$ is a solid aluminum $(G = 26 GPa)$ rod.

Determine the minimum diameter of the aluminum segment if the rotation angle at $C$ relative to support $A$ must not exceed $3^{°}$ .