Problem $2$: Consider the structure shown below and the local$/$global numbering of degrees of freedom indicated on the figures. A vertical load $Q$ is prescribed at the joint where the three members are connected as shown in the figure. The roller support at that connection prevents horizontal translation $($in either direction$)$ but allows for vertical translation$/$displacement as well as for a rotation.

a$)$ State the connectivity vector for each element.

b$)$ List the free DOFs $U_f,$ the constrained DOFs $U_e,$ the applied loads $P_f,$ and the reactions $P_e.$

c$)$ Solve for $U_f$ and for the reaction $P_4.$