The beam shown below has constant $E(100$GPa$)$ and $I(8{10}^{-5}{m}^4)$ along the length of the beam. Assume axial rigidity and do not add any extra nodes $($remember that extra nodes complicate the problem$).$ Using the direct stiffness method,

a$.$ Determine all joint displacements. $[9$ points$]$

b$.$ Determine all support reactions. $[9$ points$]$

c$.$ Find the element forces for element $3$ and draw the shear and moment diagrams for element $3$ using these forces. $[9$ points$]$

d$.$ Use MASTAN$2$ to model the beam and verify your answers. Note that you may need to add additional nodes$/$elements to model the beam correctly on MASTAN$2.$ Attach a screenshot of your model, the moment diagram and the deflected shape calculated by MASTAN$2[3$ points$]$