This lesson covers the concept of Euler buckling load and the method of solving column problems using a 4th order differential equation. It discusses four different boundary conditions: hinged-hinged, fixed-fixed, fixed-free, and fixed-hinged. The lesson also explains the derivation of the 4th order governing differential equation and its application to columns with different boundary conditions, including those with elastic support. The lesson further elaborates on the process of deriving the governing differential equation for columns with unspecified boundary conditions and finding the critical load. It concludes with the explanation of the Eigen value problem in the context of buckling load and mode shape.

- The Euler buckling load can be determined using a 4th order differential equation.
- This equation can be applied to columns with any type of boundary conditions.
- The governing differential equation for columns with unspecified boundary conditions can be derived and used to find the critical load.
- The Eigen value problem is relevant in the context of buckling load and mode shape. The Eigen value represents the buckling load, and the Eigen vector represents the mode shape.

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