Load Deflection Curve for Beam-Column: Energy Approach — Lesson 4

This lesson covers the stability analysis of a beam column, focusing on the energy method, specifically Raleigh's method. It explains how bending and axial compression occur simultaneously in a beam column, and how the energy of axial compression is omitted in the analysis, considering only bending energy. The lesson further discusses the concept of total potential energy and how it is minimized to achieve equilibrium configuration. It also introduces the Rayleigh Ritz method, which involves assuming a suitable shape function for the system's deformation. The lesson concludes with an explanation of how axial load affects the bending moment in a beam column.

Video Highlights

00:25 - Introduction to stability analysis of beam column
05:04 - Explanation of external work done
12:03 - Explanation of equilibrium system
18:31 - Explanation of maximum bending moment at the center of the beam

Key Takeaways

- Bending and axial compression occur simultaneously in a beam column.
- In the energy method of analysis, only bending energy is considered, omitting the energy of axial compression.
- The total potential energy of the system is minimized to achieve equilibrium configuration.
- The Rayleigh Ritz method involves assuming a suitable shape function for the deformation of the system.
- Axial load affects the bending moment in a beam column, and this effect is calculated using the amplification factor.