A two-dimensional frame truss structure is composed of three truss elements. The nodes are numbered from 1 to 3 and the elements are numbered from (1) to (3) with element length of the third member is 1 m, as shown in Figure 2. The frame is loaded with a force F = 10 kN at node 2 at an angle 45 degrees as shown in the figure. The Young's Modulus of elements (1) to (3) is 200GPa, and the cross-sectional area of all elements is 5cm².

a)Write down the definition of a degree of freedom and state the total number of degrees of freedom for the truss structure in Figure 2. b)Write down the properties of a truss stiffness matrix. c)Using appropriate diagrams and boundary conditions. Include known and unknown values and ensure you justify your boundary conditions and statethe unit, write down: (i) the vector of nodal forces, f (ii) the vector of nodal displacements, u. d)Using appropriate diagram and formulae calculate the stiffness matrices for each element. Please ensure you include all your diagrams, working out and units. Using your answer to part (d), find the global stiffness matrix, K, of the frame. You must show how you obtained your solution and include thecorrect units. K^{e}=\frac{E^{e} A^{e}}{L^{e}}\left[\begin{array}{cccc}

c^{2} & s C & -c^{2} & -s c \\

s C & s^{2} & -S C & -s^{2} \\

-c^{2} & -S C & c^{2} & s C \\

-s c & -s^{2} & s c & s^{2}

\end{array}\right]