Three Moment Equation for Continuous Beam-Column — Lesson 3

This lesson covers the concept of beam-column bending, focusing on the derivation of the three-moment equation for continuous beams with axial load. It revisits the bending of beam-column by couples, discussing symmetric and antisymmetric bending. The lesson then delves into the analysis of a two-span continuous beam with axial load, deriving the three-moment equation for supports not on the same level. It also explains how to calculate the slope and axial load. The lesson concludes with the analysis of a continuous beam with supports at different levels, deriving equations for each node to find unknown moments.

Video Highlights

00:30 - Discussion on symmetric and antisymmetric bending
07:14 - Explanation of the equation for the right part of the continuous beam
11:48 - Explanation of the 3 moment equation
19:46 - Explanation of the relative rotation at node B
28:40 - Solution of the equations to find the unknown moments

Key Takeaways

- Two equal couples can produce antisymmetric and symmetric bending in a beam-column.
- The three-moment equation can be derived for a continuous beam with axial load and for supports not on the same level.
- The influence of axial load is significant in the bending of a beam-column.
- The three-moment equation is crucial in analyzing a continuous beam subjected to axial load.
- The concept of relative rotation at node B is essential in understanding beam-column bending.