Q$4.$ A two$-$bay frame as shown in Figure $Q4$ is loaded with point load of $20kN$ at point $B$ and at

mid$-$span of member BC$.$ A distributed load of $10k\frac{N}{m}$ is acting along member CD$.$ The

frame is fixed supported at A and F$,$ and pinned supported at E$.$ Using conservation of work

method;

$($a$)$ Draw all the collapse mechanisms of the frame.

$($b$)$ By using virtual work method, determine the maximum plastic moment, $M_p,$ of the

frame for all mechanism.

$($c$)$ Determine the critical $M_p.$