The beam, ABC, show in Figure $1,$ is $2m$ long and is simply supported at either ends and carries a

uniformly distributed load of $8\frac{KN}{m}$ over the span, $BC.$ The flexural rigidity of the beam $El,$ is

$4{10}^{4}N{m}^2.$ Using Castigliano's theorem determine:

$($a$)$ The deflexion at position B

$($b$)$ The slope at position B

Figure $1$