Question $1$: Plastic Analysis $(60\%)$

For the frame shown in Figure Q$1$:

a$)$ Sketch the $3$ possible collapse mechanisms ensuring that you clearly identify the locations of the plastic hinges.

b$)$ Determine the value of $P$ that will cause collapse by each mechanism.

c$)$ Clearly state which is the critical mechanism.

You may assume that all members have plastic moment capacity $M_p=20kN$

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