Problem $3$:

Consider the statically indeterminate system shown below. The bar is subjected to a pair of concentrated axial loads at locations B and C$.$ Determine the deformation at location B due to this load and the distribution of internal forces along the system. Discretize the structure into nodes and bar$/$truss elements and use the matrix formulation of the displacement method of analysis $($i$.$e$.,$ Direct Stiffness Method$)$ to determine the displacement at location B$,$ the axial force distribution along the bar, and the reaction forces at locations A and D$.$