Exercise $1$

Figure below shows a plane frame with fixed supports at A and D$.$ The frame carries point loads with the magnitudes as stated in the figure. The plastic moment resistance for members $AB,BC$ and $CD$ are $3Mp,2Mp$ and $Mp$ respectively. The values for $Mp$ is $45kNm$ and $L$ is $3m.$

$($a$)$ Determine the number of collapse mechanisms for the frame.

$($b$)$ Analyze the frame by plastic method to determine the value of the collapse load, W$.$

$($c$)$ Draw bending moment diagram at collapse condition.

$($d$)$ Determine all values of support reactions at A and D$.$