Euler's buckling theory is a mathematical model used to determine the maximum axial load a long, slender column can withstand before it loses stability and bends laterally. The theory shifts the focus from the material's compressive strength to the structural stability of its geometry. It posits that at a specific "critical load," a column reaches a state of unstable equilibrium where any minor lateral force or structural imperfection will cause it to bow or collapse suddenly. This failure is often catastrophic because it occurs at stress levels significantly lower than what would be required to actually crush the material itself.
The theory is fundamentally based on the relationship between the column's stiffness, its cross-sectional shape, and its length. According to Euler's derivation, the critical load is directly proportional to the material's modulus of elasticity and the area moment of inertia, while being inversely proportional to the square of the column's effective length. This means that doubling the length of a column reduces its buckling strength by a factor of four. The theory also incorporates an "effective length factor" to account for different boundary conditions, such as whether the ends of the column are pinned, fixed, or free to move. While Euler's theory is highly accurate for "long" columns, it assumes the material remains within its elastic limit and the load is perfectly centered, meaning it must be used in conjunction with other formulas for shorter, intermediate columns that may fail through a mix of buckling and yielding.
