$20$ points $-$ A simple plane truss is made of two identical bars $($with

$E=1e6Pa,A=0\mathrm{.}0001m^2,$ and $L=2m),$ and loaded as shown in the

figure on the right. Assume that each bar is a simple $2$D bar

element. The load P is $10$ KN $.$ Using finite element method,

compute:

A$.$ The displacement of node $2$

B$.$ Stresses of elements $1$ and $2$

C$.$ Support reactions on nodes $1$ and $3$

Show the following steps to get the answers.

The local stiffness matrix of each element.

Transformation of the local stiffness matrix to global CS$.$

Assembly of the global stiffness matrix.

Application of the boundary conditions and reduction of the global stiffness matrix.

Unknown displacements of node $2.$

Support reactions and verification of the results using force balance law.

Stresses in bars $1$ and $2.$