Question $3$

The continuous beam shown in Figure Q$3$ is fixed at nodes $1$ and $3$ and has a roller at nod $2.$ The span $2-3($member $2)$ is subjected to a uniform distributed load $q=20k\frac{N}{m}.$ The beam has $EI=4000kN{m}^2.$

Figure Q$3$

$($a$)$ Using the elemental stiffness matrix given below, assemble the global stiffness matrix.

$K_e={10}^3\left[\begin{array}{cccc}0\mathrm{.}22& 0\mathrm{.}67& -0\mathrm{.}22& 0\mathrm{.}67\\ 0\mathrm{.}67& 2\mathrm{.}67& -0\mathrm{.}67& 1\mathrm{.}33\\ -0\mathrm{.}22& -0\mathrm{.}67& 0\mathrm{.}22& -0\mathrm{.}67\\ 0\mathrm{.}67& 1\mathrm{.}33& -0\mathrm{.}67& 2\mathrm{.}67\end{array}\right]$

$($b$)$ Compute the global load vector.

$($c$)$ If the rotation at node $2$ is $=-0\mathrm{.}0112$rad draw the bending moment diagram for element $2.$

$($d$)$ Sketch the influence lines of the bending moment at node $1$ and the shear force at node $2.$