Exam $1-$ Part B$.$

$1.(35$ points$)\backslash ($ A $\backslash )$ force $\backslash ($ F $\backslash )($in the negative $\backslash ($ y $\backslash )-$direction$)$ are applied at the end of a cantilever steel pipe $\backslash ($ A B C D $\backslash )$ of outside diameter $($OD$)$ and thickness $(\backslash ($ t $\backslash ))$ as shown. The pipe ABCD has for dimensions $\backslash ($ A B$,$ B C $\backslash )$ and $\backslash ($ C D $\backslash ).$ Using the Castigliano method determine the following:

b$.$ The vertical deflection at point $\backslash ($ D $\backslash )$ in the $\backslash ($ y $\backslash )-$direction by each segment $\backslash ($ C D$,$ B C $\backslash )$ or $\backslash ($ A B $\backslash ).$

d$.$ The total deflection at the free$-$end in the $\backslash ($ y $\backslash )-$direction.

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

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

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

Solve for the values in section $060$ and an elastic modulus of $30000$ksi