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h1. Eigenvalue analysis

Please note that Buckling is the [load-case|kb:Load case] type for *eigenvalue analysis*.

Eigenvalue buckling analysis predicts the theoretical buckling strength of a structure idealized as elastic. In the classic Eigenvalue method, structural eigenvalues are computed from the loading and constraint conditions of a given system. Tabulated solutions provide buckling loads for basic structural configurations. Each load has an associated buckled mode shape which represents the shape a structure assumes when buckled. For real structures, imperfections and nonlinear behavior keep systems from achieving this theoretical buckling strength. Since eigenvalue analysis over-predicts buckling load, nonlinear buckling analysis is recommended.


h1. Nonlinear buckling analysis

Please note that Static, Nonlinear with P-Delta and Large Displacement is the load-case type for *nonlinear buckling analysis*.

Nonlinear buckling analysis is a more accurate method which incrementally increases applied loading until a structure becomes unstable. This condition of instability is indicated by a small increase in load level causing a very large change in deflection. Nonlinear buckling analysis is a static method which accounts for material and geometric nonlinearities (P-Δ and P-δ), load perturbations, geometric imperfections, and gaps. Either a small destabilizing load or an initial imperfection is necessary to initiate the desired buckling mode.


h1. Important considerations

* The primary output from linear buckling analysis is a set of buckling factors. Applied loading is multiplied by these factors to scale the loading such that it causes buckling in a given structure. Please refer to the [_CSI Analysis Reference Manual_|doc:Analysis Reference Manual] (Load Cases > Linear Buckling Analysis) for additional information.

* Since the deflections, forces, and reactions of linear buckling analysis correspond to the normalized buckled shape of a structure, users must run nonlinear buckling analysis to obtain the actual displacements, forces, and reactions. Figure 1 illustrates the nonlinear buckling-analysis output of a column subjected to an initial imperfection where lateral load induces displacement equal to 0.6% of column height. Softening behavior indicates the onset of buckling.

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!Evaluate_buckling_by_nonlinear_analysis.png|align=center,border=0!

{center-text}Figure 1 - Nonlinear buckling analysis of a column{center-text}

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Users may download the analytical model for this system through the [P-Delta effect for fixed cantilever column|tp:P-Delta effect for fixed cantilever column] test problem.


h1. See Also

* [kb:Nonlinear buckling]