Q$2.$ A continuous beam structure as shown in Figure Q$2$ subjected to uniform distributed load of $6k\frac{N}{m}$ and point load of $30kN.$ The beam is supported by a fixed support at A and roller supports at B and $C.$ Flexural rigidity, $EI$ of the beam is $25{10}^{9}kNm{m}^2.$ By using the flexibility method, determine

$($a$)$ the vertical reaction forces at supports B and C $($solution must consider reaction at supports B and $C$ as redundant$),$

$($b$)$ member end moments for the beam, and

$($c$)$ draw the shear force and bending moment diagrams for the beam.