## Deflections Determined by Three-Moment Equation

**Summary of key points**

- The three-moment equation can be applied at any three points in any beam. It will determine the relation among the moments at these points.
- The terms $6A\bar{a}/L$ and $6A\bar{b}/L$ refer to the moment diagram by parts resulting from the simply supported loads between any two adjacent points described in (1).
- The heights h
_{1}and h_{3}from the equation

$M_1L_1 + 2M_2(L_1 + L_2) + M_3L_2 + \dfrac{6A_1\bar{a}_1}{L_1} + \dfrac{6A_2\bar{b}_2}{L_2} = 6EI \left( \dfrac{h_1}{L_1} + \dfrac{h_3}{L_2} \right)$

refer to the respective vertical distance of points 1 and 3 from point 2. The height h is positive if above point 2 and negative if below it.