$3.(20$ points$)$ A beam $120$ inches long is fixed at both ends. There is constant $\backslash ($ E$=30\backslash$times $10^\{6\}\backslash )$ psi and $\backslash ($ I$=50\backslash )$ in$.\backslash (\{\}^\{4\}\backslash )$ There is a constant downward force $60$ pounds per inch on the first $40$ inches of the beam, and no other applied forces. Calculate the displacement and rotation at $40$ inches $($hint: use two elements, one of $40$ inches and one of $80$ inches$).$