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Nonlinear
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buckling
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may be
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evaluated
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in
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SAP2000 through nonlinear analysis with P-Delta and Large Displacement effect. The displacement of selected joints may be plotted against loading configuration to reveal softening behavior and the onset of structural buckling.
Modeling tips
- When analyzing symmetrical structures, users may need to introduce either a geometric or loading imperfection to initiate buckling.
- Request multiple output steps in the load case definition to improve convergence and better indicate buckling response.
- If a structure loses load-carrying capacity, use displacement control rather than load control. This refers to the load-case control definition, and not how the load is actually applied.
- Users may need to tighten convergence tolerance, possibly to 1e-6.
- Elements should be small enough to capture nonlinear geometric effect. Four to eight frame or shell elements are typically necessary per span.
- When buckling-case instability is severe, nonlinear static analysis should be converted to direct-integration time-history analysis.
Difference between buckling analysis and nonlinear static analysis to evaluate buckling
During linear buckling analysis, perturbations are applied to the undeformed configuration of a structure. A specified set of loads are observed for which deflections could induce instability under P-Delta effect. Linear buckling analysis produces a set of buckling factors and corresponding mode shapes. Multiplication of loading by these buckling factors indicates the scaled loading conditions which would induce buckling. Similarly, the mode shapes are normalized displacements of the buckled structure, indicating the configuration within which the structure would buckle.
During nonlinear static analysis, the total load is applied incrementally. Stiffness and response are evaluated at each increment. Between each displacement step, stiffness may change due to the following effects:
- P-Delta, which involves large tensile or compressive stresses on transverse bending and shear behavior
- Large displacement, where deformed configuration is considered when assembling the equilibrium equations
- Nonlinear material behavior, where structural performance considers inelastic element response. SAP2000 implements material nonlinearity through frame hinges and nonlinear layered-shell elements.
Because nonlinear static analysis considers material nonlinearity in generating buckling response, results are often more realistic than linear buckling analysis. The results of nonlinear static analysis are indicated by a plot of deformed configuration against load application. This plot displays the softening behavior which indicates the onset of buckling.
The CSI Analysis Reference Manual is an excellent resource for information on buckling. Users are recommended to review the following chapters:
- Load Cases > Linear Buckling Analysis
- Geometric Nonlinearity > Overview
- Geometric Nonlinearity > P-Delta Effect