Boundary Conditions for Column with General Case of Elastically Supported Ends — Lesson 1

This lesson covers the concept of critical load for columns with elastically supported ends. It explains why columns in most structural configurations are supported by other elements providing elastic type of restraint. The lesson delves into the use of the fourth order differential equation to find the critical load and discusses the boundary conditions for columns with both rotational and extensional restraints. It also provides an example of a simply supported column with one end rotationally restrained. The lesson further explains how to solve the governing differential equation and find the constants using boundary conditions. It concludes with a discussion on the critical load for a hinged-hinged column.

Video Highlights

00:30 - Explanation of why columns are usually supported by other structural elements
06:46 - Simplification of the boundary conditions
13:17 - Explanation of the rotational restraint provided by the member B C
29:56 - Solution of the equation to find the root and calculation of the P value

Key Takeaways

- The fourth order differential equation is used to find the critical load.
- Boundary conditions for columns include both rotational and extensional restraints.
- The governing differential equation can be solved and constants can be found using boundary conditions.
- The critical load for a hinged-hinged column can be calculated using the derived equations.