Critical Load of Euler Column with Initial Imperfection — Lesson 2

This lesson covers the derivation of Euler load, the assumptions made in Euler's theory, and the behavior of imperfect columns. It explains how minor imperfections of shapes and small eccentricities of loading are present in all real columns, and how these factors affect the behavior of the column. The lesson also discusses the derivation of the critical load for an initially bent column and an eccentrically loaded column. It concludes with the analysis of the load deflection curve for an eccentrically loaded column and the conclusions drawn from the study.

Video Highlights

00:43 - Discussion on the imperfections present in real columns and the need to investigate the behavior of an imperfect column.
06:58 - Explanation of the solution for the governing differential equation and the complementary and particular solutions.
15:10 - Evaluation of the constants from the boundary conditions.
21:55 - Explanation of the load deflection curve for eccentrically loaded column.

Key Takeaways

- Euler's theory, based on the concept of a perfect member, provides a satisfactory design criteria for real imperfect columns, provided the imperfections are relatively minor.
- The Euler load is a good approximation of the maximum load that a real imperfect column can support without bending excessively.
- The critical load is the load at which the deformation of a slightly imperfect system increases without bound.
- Either eccentricity of loading or initial imperfection, both of which cause bending, can be used to simulate the behavior of an imperfect system.