The beam shown below is made from a material that has a modulus of elasticity $E=30,000$ ksi. Member $1$ has a moment of inertia $I_1=300$ in ${?}^4$ and Member $2$ has $I_2=450i{n}^4.$ The support at A settles downward by $\frac{3}{16}".$ 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 each member and draw the shear and moment diagrams 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$]$

$($A$)$

NOTE: SUPPORT A

SETTLES $3/16"$

DOWNWARD