Problem $1$: Given the following $2$ rod elements :

The stiffness for each element is $k_i=A_i\frac{E_i}{L_{\text{I}}}$ whre $A$ is the cross$-$sectional area, $E$ is the

Young's modulus and L is the rod length. For the following values:

For left element : $A_1=0\mathrm{.}050m^2,E_1=70$GPa,$L_1=1m,$

For right element : $A_2=0\mathrm{.}050m^2,E_2=210$GPa,$L_2=0\mathrm{.}50m$

Find:

a$)u_2=$ displacement of node $2$ in x direction

b$)$ Stress in elements $1$&$2$

Hint: Set up K $($stiffness matrix$),$ solve for displacements in $Kd=F$