Use two equal two$-$node Euler$-$Bernoulli beam finite elements to analyze the beam problem shown in the figure below:

For the shown distributed loading, the corresponding element force vector for a typical element is given in the textbook $($Example $5\mathrm{.}2\mathrm{.}1,$ p$.248)$:

$\{f^e\}=\frac{q_0{h}_e}{12}\{[6],[-h_e],[6],[h_e]\}+\frac{q_0{h}_e}{60L}\{[-(9h_e+30x_e)],[h_e(2h_e+5x_e)],[-(21h_e+30x_e)],[-h_e(3h_e+5x_e)]\}$

where $q_0$ is the starting value of the distributed loading at $x=0,h_e$ is the element size, L is the total length of the beam, $x_e($also called $x_A$ in our class$)$ is the left$-$end coordinate of the element.

Do the following:

$($a$)$ Determine the element equations

$($b$)$ Assemble the global equations.

$($c$)$ Apply BCs$/$constrains and point sources to the global equations.

$($d$)$ Determine the condensed equations for the unknown primary variable nodal values and solve the equations.

$($e$)$ Do postprocessing to determine the bending moment at $x=3m($note $x=0$ is at the left end of the beam$).$