Critical Load of Euler Column: Large Deflection Theory — Lesson 1

This lesson covers the concept of small deflection theory and large deflection theory in the context of Euler columns. It explains how to derive the critical load of an Euler column by considering both theories. The lesson also discusses the linear governing differential equation and how it is obtained using the expression of curvature. It further elaborates on the concept of curvature and how it is expressed in terms of slope and deflection. The lesson also provides a detailed explanation of how to develop the governing differential equation and how to differentiate it to obtain the expression for large deformation theory. The lesson concludes with a comparison of the load deflection curve for large deflection and small deflection theory.

Video Highlights

00:37 - Explanation of curvature expression and assumptions made
06:20 - Explanation of the concept of radius of curvature
13:41 - Explanation of the concept of cos 2 theta and its significance
23:00 - Derivation of the expression for the critical load of the column
31:06 - Derivation of the expression for the mid height deflection

Key Takeaways

- Small deflection theory results in a linear governing differential equation.
- The expression of curvature is obtained by assuming the slope dy/dx = 0 due to small angle of deflection.
- The critical load of an Euler column can be derived by considering large deflection theory.
- The governing differential equation for large deformation theory is obtained by differentiating the expression of curvature.
- The load deflection curve for large deflection theory shows a slight increase in load with increasing deflection during the early stage of bending and a more pronounced increase in load after considerable deformation.