The L$-$shaped frame is made from two segments, each of length $L$ and flexural rigidity El$.$ If the frame

is subjected to a uniform distributed load $($as shown below$),$ determine the vertical displacement of

Point B$.$

$($a$)$ Sketch the bending moment diagrams for each segment of the frame due to the distributed

load, $W.$ You should determine a suitable coordinate system and equations to describe the

bending moment in each segment. Clearly state your expression for the internal moment in

each segment of the frame and the limits for $x_i($your limits of integration$).$

$($b$)$ Place a virtual force $($unit load$)$ that acts vertically at Point B and sketch the bending moment

diagrams in each segment of the frame. You should determine a suitable coordinate system and

equations to describe the bending moment in each segment. Clearly state your expression for

the internal moment in each segment of the frame and the limits for $x_i($your limits of

integration$).$ These should be consistent with those developed in $($a$)$

$($c$)$ Solve the vertical deflection at Point B$.$ You only need to consider the strain energy due to

bending.