Problem $4(15$ pts$)$

Use the slope$-$deflection method to FORMULATE a solution procedure for the following frame problem. All the beams and the columns have a length of h ; and El is a constant for all beams$/$columns

$(1)$ Recognize the number of DOFs $[5$ pts$].$

$(2)$ Write out all the necessary slope$-$deflection equations $($the moment functions$)$ and the necessary equilibrium equations coming from the free$-$body diagrams that can be used to solve the recognized DOFs. Solving the equation system is NOT necessary $($optional if you try to have bonus points$).[10$ pts$]$

$-$ Hints: At each story, the lateral displacement is constant for the beam$-$column joints.

$-$ Notation wise: suppose the first story's lateral drift is $\backslash (\backslash$Delta $1\backslash ),$ the second story's lateral drift is $\backslash (\backslash$Delta $2\backslash ).$

$-$ Then the relative story$-$drift for the second story is $\backslash (\backslash$Delta $2-\backslash$Delta $1\backslash ).$

$-$ If you make reasonable attempt to solve and obtain part of the DOFs, $+5$ bonus points.