Slope-Deflection Equations for Indeterminate Structures - Intro to Structural Analysis

In this video, we derive and apply the slope-deflection equations, which then can be used to find the end moment and end forces on any segment of beam given the rotations, displacements, and loading on that beam.

The slope-deflection method forms the basis for so-called "stiffness methods" of structural analysis, wherein the primary unknowns are the displacements and rotations rather than the forces. Using equilibrium, we solve for the unknown displacements and rotations, and then we compute the forces and moments using these deformations.

Two examples are conducted. The first example uses the base slope-deflection equations, whereas the second example illustrates what happens when there are locations of zero moment or cantilevers

Fixed-end moments, which represent the loading along the beam, are tabulated for many common load cases. I like this version by Prof. Erochko at Carleton University (CC BY-NC-SA 3.0):
https://learnaboutstructures.com/sites/default/files/images/15-Appendix/Fixed-End-Moment-Table.pdf