$20$ points $-$ The spring structure shown below is made of

five $(5)$ springs and supported by fixed nodes at $1,2,$ and $5$

$($the displacements of nodes $1,2,$ and $5$ are zero$).$ Consider

that $k_1=k_5=100\frac{N}{mm}$ while $k_3=k_4=k_2=300\frac{N}{mm}$

and the applied force in node $3,F_3=200N.$ Using finite

element method,

a$.$ Show the element stiffness matrix of all elements

b$.$ Construct the global stiffness matrix

c$.$ Show the reduced stiffness matrix $-$ this should be $2$ by $2$

d$.$ Compute the displacement of nodes $3$ and $4-$ you may use Matlab to do this

e$.$ Compute the support reaction forces of nodes $1,2,$ and $5$

f$.$ Compute the five $(5)$ element forces