Load Deflection Curve for Beam-Column: GDE Approach — Lesson 3

This lesson covers the analysis of beams subjected to both axial and transverse loads. It explains how the bending effect, which is the primary effect in this case, is influenced by the presence of axial compression. The lesson provides a detailed explanation of the equilibrium equation and how it can be used to derive the expression for deflection when the beam is subjected to both transverse and axial load. It also discusses how the bending moment is affected by axial compression. The lesson uses an example of a simply supported beam subjected to end moments along with axial loading to illustrate these concepts.

Video Highlights

00:50 - Discussion on the primary effects of bending in axially loaded columns
06:46 - Derivation of the constants A and B using boundary conditions
14:27 - Explanation of the power series expansion of tan u
19:18 - Discussion on the load deflection curve when the beam is subjected to both transverse and axial loading
29:11 - Explanation of how the bending moment is affected by axial compression

Key Takeaways

- The bending effect in a beam is influenced by the presence of axial compression.
- The equilibrium equation can be used to derive the expression for deflection when the beam is subjected to both transverse and axial load.
- The bending moment in a beam is affected by axial compression.
- The deflection and bending moment that exist in the absence of axial compression are amplified by the presence of axial load.
- The resistance of a member to lateral deformation vanishes as the axial load approaches the critical load.