$(35$ points$)$ A force $F($in the negative $y-$direction$)$ are applied at the end of a cantilever steel

pipe ABCD of outside diameter $($OD$)$ and thickness $($t$)$ as shown. The pipe ABCD has for

dimensions $AB,BC$ and $CD.$ Using the Castigliano method determine the following:

b$.$ The vertical deflection at point $D$ in the $y-$direction by each segment $CD,BC$ or $AB.$

d$.$ The total deflection at the free$-$end in the $y-$direction.

e$.$ The slope at the free$-$end in the yz$-$plane.

The material has an Elastic Modulus $=200$GPa; Poisson ratio $=0\mathrm{.}3$

Neglect the energy due to transverse shear. Use absolute values as your answer.