Consider the two$-$dimensional truss framework shown in Figure $3.$ The cross$-$sectional area of each truss is $0\mathrm{.}1m^2$ and the truss material has an elastic modulus of $100$ GPa $.$ You are required to make a finite element model of this framework. Certain points have been labelled N$1,$ N$2,$ etc and you are required to consider these points as nodes in your finite element model. Nodes, N$2,$ N$3$ and N$4$ are rigidly fixed in all directions while N$1$ is free to move in the horizontal and vertical directions.

Eigure $3$

Q$2($a$)$

Marks$]$

Reproduce the table shown below $($table $1)$ in your answer book and fill in the blank fields by calculating the direction cosines $1$ and $m.$

Table $1$

Q $2($b$)$

$[10$ Marks$]$

Hence, using the completed table, determine the element stiffness matrix for each of the three elements.