# An interpretation of the slope-deflection method (or displacement method)

I want to be sure that the way I like to think about the displacement method of analysis is correct.

Suppose that a beam as given by the figure below is to be solved.

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?

• Have you searched before posting? A similar question was answered recently - if you find it before me that’s fine... – Solar Mike Jan 2 '18 at 21:48
• Yes, I did. But I didn't find anything satisfying. – muimerp Jan 2 '18 at 21:56
• This seems relevant : engineering.stackexchange.com/q/13444/10902 – Solar Mike Jan 2 '18 at 22:05
• Thank you for the link, but it doesn't help me that much. But let me ask you: would you accept what I've written as acceptable? – muimerp Jan 2 '18 at 22:36
• How did you get PL/8? – Jem Eripol Jan 3 '18 at 0:12