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*Nonlinear* structural behavior may be associated with either geometric or material response. These sources of nonlinearity are described as follows:

* *Geometric* nonlinearity concerns the [P-Delta|kb:P-Delta effect] effects which are associated with the application of external loading upon the displaced configuration of a structure.

* *Material* nonlinearity concerns [inelastic|kb:Material nonlinearity] structural response in which the behavior of a component, system, or connection deviates from the initial stiffness tangent characteristic of linear-elastic behavior.


h1. Linear vs. nonlinear analysis

*Nonlinear* analysis methods are best applied when either [geometric|kb:P-Delta effect] or [material|kb:Material nonlinearity] nonlinearity is considered during structural modeling and analysis. If only elastic material behavior is considered, linear analysis methods should suffice, though P-Delta formulation may still be applied. Linear and nonlinear methods may be static or dynamic. A few of the traditional analysis methods, and the relations between their attributes, are presented in Figure 1:

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!Analysis type.png|align=center,border=1!

{center-text}Figure 1 - Analysis methods{center-text}

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Each of these analysis methods has benefits and limitations. An overview of each method is as follows:

* *Strength-based* analysis is a static-linear procedure in which structural components are specified such that their elastic capacities exceed the demands of loading conditions. Strength-based demand-capacity (D-C) ratio indicate the adequacy of each component. Since only the elastic stiffness properties are applied to the analytical model, strength-based analysis is the most simplified and least time-consuming analysis method.

* *[Static-pushover|kb:Pushover]* analysis is a static-nonlinear procedure in which a structural system is subjected to a monotonic load which increases iteratively, through an ultimate condition, to indicate a range of elastic and inelastic performance. As a function of both strength and deformation, the resultant nonlinear force-deformation (F-D) relationship provides insight into ductility and limit-state behavior. Deformation parameters may be translational or rotational. Pushover is most suitable for systems in which the fundamental mode dominates behavior. When higher-order modes contribute, as with taller buildings, dynamic analysis is best.

* *[Response-spectrum|kb:Response-spectrum analysis]* analysis is a dynamic-linear method in which maximum structural response is plotted as a function of structural period for a given time-history record and level of [damping|kb:Damping]. For a set of structural [mode shapes|kb:Modal analysis] and corresponding natural frequencies, the linear superposition of SDOF systems represents response. Response measures may be in terms of peak [acceleration|kb:acceleration], velocity, or displacement relative to the ground or the structure. Structures must remain essentially elastic since response-spectrum analysis is dependent upon the superposition of gravity and lateral effects. Results may be enveloped to form a smooth design spectrum.

* *[Time-history|kb:Time-history analysis]* analysis is a dynamic-nonlinear technique which may involve either the [FNA|kb:Fast Nonlinear Analysis (FNA)] or the [direct-integration|kb:Direct-integration time-history analysis] method. FNA is a [modal|kb:Modal analysis] application, whereas with direct integration, the equations of motion are integrated at a series of time steps to characterize dynamic response and inelastic behavior. Loading is time-dependent, and therefore suitable for the application of a ground-motion record. Time-history analysis may account for both material nonlinearity and [P-Delta|P-Delta effect] effects.


h1. Analysis objective

Engineers may use any of these analysis methods to:

* Characterize and gain insight into structural behavior.

* Generate information useful to the design decision-making process.


h1. Capacity Design

Nonlinear modeling and analysis is fundamental to [Capacity Design|kb:Capacity Design].


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