Q$\mathrm{.}5($a$)$: Determine the stiffness matrix for the given four node rectangular element $($Element Dimension$)$ sbown Fig. $5$ by the Gauss Quadrature integration rule using one point formula assuming plane stress formulation. Consider, the thickness of element $-22$ cm $,$ modulus of elasticity of the material $E=2\mathrm{.}10{10}^{3}k\frac{N}{c}{m}^2$ and $=0.$

Fig. $5$