$4.[$By Hand $-10$ points$]$ Solve the following beam problems $(($a$)$ and $($b$))$ below using the work$-$equivalence methods discussed in class for uniform distributed loading. You are expected to solve these problems analytically. Find the displacement at the center $($midspan$)$ of the beam, the reactions at the supports. Show the nodes, elements, elemental stiffness matrices, assembled global matrix, boundary conditions, and the nodal displacements$/$slopes$.$ Report your answers symbolically. Assume constant El throughout the beam.

$($a$)$

$($b$)$