I want to be sure that the way I like to think about the displacement method of analysis is correct.
Under this conditions, the only unknown is the rotation of joint $B$, $\alpha_B$. As I see it, the steps taken to compute $\alpha_B$ are:
i) apply a moment $M_B^F$ at point $B$ of the beam such that no rotation of $B$ takes place. Such a moment is clockwise. Due to this, node $B$ is under the action of an equal and opposite moment of anticlockwise direction and, therefore, according to the standard conventions, of positive value $PL/8$, and, as such, not in equilibrium;
ii) for node B to be in equilibrium, as it effectively is in the original structure, apply at beam $B$ a moment whose value will depend on $\alpha$; Node $B$ will be subject to an equal and opposite moment $M(\alpha_B)$ such that $$M(\alpha_B)+ PL/8=0$$
Is this a correct interpretation of this method of analysis?