Problem $3$:

For the truss structure, loading, and discretization shown below, determine:

a$)$ The element stiffness matrices in their local and global coordinate systems

b$)$ The global system stiffness matrix

c$)$ The reduced global system stiffness matrix

d$)$ The global structural load vector

e$)$ Solve for the nodal displacements and determine the force in both bars.

The areas for members $1$ and $2$ are $\backslash (6000\backslash$mathrm$\{$~mm$\}^\{2\}\backslash )$ and $\backslash (8000\backslash$mathrm$\{$~mm$\}^\{2\}\backslash ),$ respectively. For both bars E $\backslash (=200\backslash )$ GPa.