Problem $1$:

Use the matrix formulation of the displacement method of analysis to analyze the beam system and loading shown below. Consider two elements $($i$.$e$,$ elements AB$,$ and BC$)$ and determine:

a$)$ The vertical displacement under the load

b$)$ The reactions at the boundary conditions

c$)$ The bending moment and shear force diagrams for the beam.

Assume that all the flexural stiffness $($EI$)$ of the beam is constant and neglect axial deformations $($i$.$e$.,\backslash (\backslash$mathrm$\{$A$\}=\backslash$infty $\backslash )).$ Thus, you can degenerate the $\backslash (6\backslash$times $6\backslash )$ frame element stiffness matrix into a $4$ x $4$ element stiffness matrix for a beam element.