This lesson covers the analysis of mechanical stability models, focusing on the elastic buckling of columns under different boundary conditions. It delves into the equilibrium approach, energy approach, dynamic approach, and imperfection approach. The lesson explains the use of large and small deflection theory to find critical load and characteristics of equilibrium. It also discusses the Euler column and its different conditions of idealization. The lesson further elaborates on the process of deriving the second order differential equation by writing the equilibrium equation in bent configuration. The lesson concludes with an example of a column with fixed ends, demonstrating how to find the critical load.

- The governing differential equation for columns can be derived using equilibrium equations in bent configurations.
- The Euler Buckling load can be determined for different boundary conditions using the governing differential equation.
- The critical load for a fixed-free column can be calculated, and its deflected shape can be derived.
- For a fixed-hinged column, the transcendental equation can be solved graphically to find the smallest root.
- The effective lengths of columns with different boundary conditions can be compared.

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