Please note that Buckling is the load =
case used for **Eigenvalue analysis**.

Eigenvalue analysis predicts the theoretical buckling strength of a stru= cture which is idealized as elastic. For a basic structural configuration, = structural eigenvalues are computed from constraints and loading conditions= . Buckling loads are then derived, each associated with a buckled mode shap= e which represents the shape a structure assumes under buckling. In a real = structure, imperfections and nonlinear behavior keep the system from achiev= ing this theoretical buckling strength, leading Eigenvalue analysis to over= -predict buckling load. Therefore, we recommend Nonlinear buckling analysis= .

Please note that Static, Nonlinear with P-Delta and Large Displacements =
is the load case for **Nonlinea=
r buckling analysis**.

Nonlinear buckling analysis provides greater accuracy than elastic formu= lation. Applied loading incrementally increases until a small change in loa= d level causes a large change in displacement. This condition indicates tha= t a structure has become unstable. Nonlinear buckling analysis is a static = method which accounts for mat= erial and geometric nonlineariti= es (P-=CE=94 and P-=CE=B4), load perturbations, geometric imperfections= , and gaps. Either a small destabilizing load or an initial imperfection is= necessary to initiate the solution of a desired buckling mode.

The primary output of linear buckling analysis is a set of buckling = factors. The applied loading condition is multiplied by these factors such = that loading is scaled to a point which induces buckling. Please refer to t= he CSI =

*Analysis Reference Manual*(Linear Buckling Analysis, page 315) for = additional information.

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

Figure 1 - Nonlinear buckling analysis of = a column

Users may download the analytical model for this system through the P-Delta effect= for fixed cantilever column test problem.

- Nonlinear buckling artic= le