Rayleigh-Ritz Method for Torsional Flexural Buckling of Column — Lesson 5

This lesson covers the concept of torsional flexural buckling, focusing on different cases of boundary conditions and methods to find the critical load. It discusses the equilibrium approach used to solve three cases of boundary conditions, including simply supported bars, bars with built-in ends, and columns with one axis of symmetry. The lesson also introduces the Rayleigh-Ritz method, an energy method for finding the critical load. It provides an in-depth explanation of the calculations involved in determining the critical load, including the strain energy stored, external work done, and total potential energy. The lesson concludes with the application of these concepts in practical scenarios.

Video Highlights

01:10 - Explanation of the fourth case of boundary conditions
06:35 - Explanation of the process to solve the coupled equations
15:12 - Calculation of the strain energy stored due to bending
21:11 - Explanation of the process to find the external work done
27:44 - Calculation of the end shortening
33:07 - Calculation of the total potential energy of the system

Key Takeaways

- Torsional flexural buckling involves different cases of boundary conditions.
- The equilibrium approach can be used to solve these cases and find the critical load.
- The Rayleigh-Ritz method, an energy method, can also be used to find the critical load.
- Calculations involved in determining the critical load include the strain energy stored, external work done, and total potential energy.
- The smallest value of the critical load is used in practical applications.