Consider the beam below with one end fixed $($i$.$e$.$ no rotation or displacement is allowed$),$ calculate the deflection and rotation at the loading point.

$(25$

points$)$

Note: the stiffness matrices of the beam can be expressed as

$k^e=\frac{EI}{l_e^3}\left[\begin{array}{cccc}12& 6t_e& -12& 6t_e\\ 6t_e& 4t_e^2& -6t_e& 2t_e^2\\ -12& -6t_e& 12& -6t_e\\ 6t_e& 2t_e^2& -6t_e& 4t_e^2\end{array}\right]$

$1$ m

Young's modulus $E=100$GPa Moment of inertia $I=4{10}^{-9}{m}^4$