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Buckling refers to a sudden change in shape of a structural element when it is subjected to a critical load. This phenomenon is most commonly observed in columns or beams that are under compression. Instead of simply compressing uniformly, the element bends or deforms laterally when the applied compressive force exceeds a certain threshold. This critical load is known as the buckling load.

The buckling of a structural member is an instability phenomenon. It occurs because the member loses its ability to resist the applied compressive force in its original straight configuration. Once buckling begins, the lateral deflection can become very large, even with a slight increase in the load. This can lead to catastrophic failure of the structure.

Several factors influence the buckling load. The material properties of the element, such as its Young's modulus, play a significant role. The geometry of the element, including its length, cross-sectional shape, and moment of inertia, is also crucial. The way the ends of the element are supported, known as boundary conditions, also affects its buckling behavior. For instance, a column with both ends fixed will have a higher buckling load than a column with both ends pinned.

Euler's critical buckling load formula, developed by Leonhard Euler, is a fundamental equation used to calculate the buckling load for an ideal column with pinned ends. While this formula is a simplification, it provides a good understanding of the underlying principles of buckling. In real-world engineering applications, more complex analyses are often required to account for imperfections and other real-world conditions. Buckling is a critical consideration in the design of bridges, buildings, aircraft, and many other structures where compression is a primary force.