Bending of Beam-Column by End Couples — Lesson 2

This lesson covers the concept of beam-column bending, focusing on the effects of lateral loads and continuous lateral load on a compressed beam. It explores the bending of beam-columns by couples, the deflection caused by moments, and the conversion of point loads into moments. The lesson also discusses the equation of the elastic curve, the concept of antisymmetric bending, and the calculation of slope. It provides a detailed explanation of how to derive the expressions for elastic curve, deflection, and slope. For instance, when a beam-column undergoes antisymmetric buckling, the rotational restraint offered by the beam is 6EI by L.

Video Highlights

00:41 - Discussion on bending of beam-column by couples
08:15 - Derivation of the expression for theta A and theta B when a moment is acting
15:10 - Derivation of the expression for the elastic curve when two equal couples act together
23:19 - Explanation of the effect of two equal couples producing a single curvature
31:58 - Derivation of the expression for the elastic curve when two equal couples produce antisymmetric bending

Key Takeaways

- Beam-column bending is influenced by lateral loads and continuous lateral load.
- The bending of beam-columns by couples can produce antisymmetric and symmetric bending.
- Moments acting at the end of a beam-column can cause deflection.
- Point loads can be converted into moments for calculation purposes.
- The equation of the elastic curve can be derived when there is a point load acting.
- Antisymmetric bending results in double curvature in the beam-column.
- The slope or theta value can be calculated by differentiating the y value with respect to x.