Question on Finite Element Analysis:

For the structure shown below, the beams have a length of $800$ mm $,$ made of construction steel and their crosssection is shown. Nodes $1$ and $3$ are fixed to the wall and the four beam elements are welded together at node $2.$ Nodes $4$ and $5$ can slide horizontally. Determine:

a$)$ The element stiffness matrix for all four elements, $(10$ points$),$

b$)$ Write the connectivity table for the system, $(5$ points$)$

c$)$ Determine the system $($overall$)$ equations $($assembly$),(30$ points$)$

d$)$ Determine the proper boundary conditions and the force vector, $(10$ points$)$

e$)$ Apply the boundary condition and find the final equations in matrix form, $(15$ points$)$

f$)$ Solve the equations and determine the nodal displacements, $(15$ points$)$

g$)$ Determine the reaction forces, $(15$ points$).$

$E=210$GPa

$F=5000N$

$q=4000\frac{N}{m}$

Cross$-$section of the beams