Question $1$

$($a$)$ Consider the truss linkage, made from steel with a Young's modulus of $200$ GPa, shown in Figure Q$1$a$.$ Global node numbers $(1),(2)$ and $(3)$ are indicated.

Determine local stiffness matrices for each element

Assemble the global stiffness matrix

State the boundary conditions and loads imposed on the relevant vectors

Show the boundary conditions applied to the entries of the main finite element equation $\{F\}=\{K\}\{U\}$

Determine the displacements of node $2.$

Determine all the reaction forces at node $3.$

$[25]$

Figure Q$1$a