Problem $2(35$ points$)$

Consider the two$-$story frame with an overhanging bay shown below. Use the systematic methodology presented in class $($last example in lecture notes Chapter $6$: Plastic Analysis$)$ to determine the plastic collapse load and plastic collapse mechanism. Use the sign convention shown in the figure.

a$)$ Determine the potential plastic hinge locations

b$)$ Identify all basic plastic mechanisms

c$)$ Create a systematic direct combination of mechanisms table

d$)$ From the basic collapse mechanisms and combined mechanisms identify the critical collapse load and plot the collapse mechanism