Problem $1[30$ points$]$

a$)[20$ points$]$ Determine the bending moment diagram for the frame shown below using the slope$-$deflection method. Neglect axial deformations. The bending stiffness, $EI,$ is constant and equal in all members.

b$)[10$ points$]$ Solve a$)$ using the stiffness method. No need to repeat calculations that are identical to portions of your answer to a$),$ but please compare the equilibrium equations to those you obtained in a$).$ Should they always be the same?