Question $2$: $(30$ pts

The system described in the figure consists of a solid copper pipe $AB(600$ mm long and $20$ mm in diameter$),$ which is connected by means of a rigid board to an aluminum pipe $BD(800$ mm long, with an external diameter of $40$ mm and an internal diameter of $32$ mm $).$ the copper rod

Harnessed to a hard wall in Bank A$.$

$,$L Aluminum properties: Shear modulus: Gal$=24$ GPa, Young's modulus al$-69$ GP Copper properties: Shear modulus: G$=47$ GPa, Young's modulus E$-120$GP

In the first step: the aluminum tube is free at its end D$.$ Using a rigid plate in the center of the aluminum tube, bank $C,$ activate a twisting torque $1$ which should rotate the rigid plate at point $B$ at an angle of $2$

degrees

$(5$ points$)$ Calculate the torque T needed to obtain an angle of $2$ degrees $.$ at point B$.$ b$.(10$ pts$)$ Calculate the twist angle of the free end of the aluminum tube $($point D $).$

In the second step: after applying the torque from the previous sections, weld the end of the aluminum tube to a hard wall At point D $,$ after welding, stop applying the torque $T.$

third. $(10$ pts$)$ Calculate the maximum stress in the copper rod and the aluminum tube at this stage.

$(5$ pts$)$ Calculate the twist angle at point $C($relative to section $($A$).$