Figure $2$ shows a three$-$span continuous beam under uniformly distributed load of $\backslash (30\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}\backslash )$ on the first span, a concentrated load of $200$ kN acting at the middle of the third span and a concentrated moment of $100$ kNm at node $3.$ Model the continuous beam using three beam elements with code numbers defined in Figure $2.$ Take $\backslash ($ E$=200\backslash$mathrm$\{$GPa$\}\backslash )$ and $\backslash ($ I$=200\backslash$left$(10^\{6\}\backslash$right$)\backslash$mathrm$\{$mm$\}^\{4\}\backslash ).$ Use Stiffness method to solve this problem.

$1)$ Determine the nodal displacements $($and rotations$)$ at nodes $2,3$ and $4.$

$2)$ Determine the reactions at supports.

$3)$ Plot the shear force and bending moment diagrams.

Figure $2$