MecMovies 4.0 : M5.3: Deformation of a Compound Axial Member

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he figure shows a compound axial member consisting of a larger cylindrical segment A B which is marked 1 having a length of 1800 millimeters flanged to another cylindrical segment B C which is marked 2 having a length of 800 millimeters. Segment 1 is fixed to a wall at the point A. The x axis is taken along the common axis of the two cylindrical members and the y axis is taken perpendicular to the x axis along the wall. The tension load at the free end of segment 2 is P which equals 50 kilo newtons oriented in the positive x direction.

A load of $P = 50 kN$ is applied to a compound axial member. Segment $(1)$ is a $20 - mm$ -diameter solid brass $(E = 100 GPa)$ rod. Segment $(2)$ is a solid aluminum $(E = 70 GPa)$ rod.

Determine the minimum diameter of the aluminum segment if the axial displacement of $C$ relative to support $A$ must not exceed $5 mm$ .