$1.(10$ marks$)$ Fig. $1-1$ shows a statically indeterminate truss under a horizontal force of $1000$ kN at node D and support settlement of $30$ mm at node C$.$ The structure stiffness matrix $\backslash (\backslash$mathbf$\{$K$\}\backslash )($unit: $\backslash (\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}\backslash ))$ is given below. Take $\backslash ($ E A$=12000\backslash$mathrm$\{$kN$\}\backslash )$ for all members. Solve this problem using Stiffness Method. The code numbers and member's orientations are defined in the same figure.

a$)$ Use the given structural stiffness matrix $\backslash (\backslash$mathbf$\{$K$\}\backslash )$ to determine the unknown nodal displacements at node D$.$

$(6$ marks$)$

b$)$ Compute the reactions at node C $.$

$(2$ marks$)$

c$)$ Compute the member axial force for member $1.$

$(2$ marks$)$