Weak Form Solution for Fixed-Free and Fixed-Hinged Column — Lesson 2

This lesson covers the concept of Euler Buckling Load with different boundary conditions. It starts with a recap of the hinged-hinged and fixed-fixed columns, explaining how the second order differential equation was derived from the equilibrium equation in a bent configuration. The lesson then introduces two new sets of boundary conditions: fixed-free and fixed-hinged columns. The methodology for deriving the governing differential equation and finding the critical load is explained. The lesson also demonstrates how to solve these equations using displacement and slope conditions. The lesson concludes with a detailed explanation of how to determine the effective length of a column when one end is hinged and the other end is fixed.

Video Highlights

01:10 - Explanation of the Euler Buckling load
04:13 - Explanation of the boundary conditions for the fixed-free column
12:04 - Derivation of the solution for the fixed-hinged column
18:21 - Graphical solution of the transcendental equation

Key Takeaways

- The governing differential equation for columns is derived from the equilibrium equation in a bent configuration.
- The order of the governing differential equation is 2, and essential boundary conditions are used for solving it.
- The Euler Buckling Load can be determined for different boundary conditions: fixed-free and fixed-hinged columns.
- The effective length of a column when one end is hinged and the other end is fixed can be determined by comparing it with the Euler column.