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*Geometric nonlinearity* occursinvolves whenthe axialequilibrium loadand is applied to the displaced configurationcompatibility relationships of a structural element.system Thisloaded effectabout influencesits internal forces and further affects displacementdeflected configuration. Of particular concern is when gravity-load loadsapplication act on the laterally-displaced configuration of a structuremulti-story-building structures. ColumnMechanical bendingbehaviors stresses and interstorystory driftsdrift aremay then be magnified while deformation capacity is reduced.

Geometric nonlinearity is also known as *P-Delta effect*. There areP-Delta effect concerns conditions where relatively small displacements are subject to large external forces. If deformations become sufficiently large as to break from linear compatibility relationships, then Large-Displacement and Large-Deformation analyses become necessary. The two sources of P-Delta effect, contributions of which are shown in Figure 1, and described as follows:

* *P-δ*, also known as *Large-Displacement effect*, or P-"small-delta", is associated with local deformation. Equilibrium conditions are evaluated about displaced-configuration relative to the element chord. Ofbetween particularend concern is when local behavior breaks from compatibility relationships. nodes. Typically, P-δ only becomes significant at unreasonably large displacement values, or in especially slender columns. So long as a structure adheres to the slenderness requirements pertinent to earthquake engineering, it is not advisable to model P-δ, since it may significantly increase computational time without providing the benefit of useful information. An easier way to capture Large-Displacementthis effectbehavior is to subdivide critical elements into multiple segments, which transferstransferring behavior into P-Δ effect (Powell 2006).

* *P-Δ*, also known as *Gravity Load-Deformation effect*, or P-"big-delta", is associated with storydisplacements drift. This behavior is measured between relative to member ends. Unlike P-δ, this type of P-Delta effect _is_ critical to nonlinear modeling and analysis. As indicated intuitively by Figure 2, gravity loading _will_ significantly influence structural response whenunder thesignificant global system displaces laterallylateral displacement. P-Δ may contribute to loss of lateral resistance, ratcheting of residual deformations, and dynamic instability (Deierlein et al. 2010). InAs thatshown laterally-displacedin gravity loading magnifies internal forcesFigure 3, effective lateral stiffness decreases, reducing strength capacity in all phases of the force-deformation relationship (PEER/ATC 2010). This effect is shown in Figure 3. To consider P-Δ effect directly, gravity load should be present during nonlinear analysis. Application will cause minimal increase to computational time, and will remain accurate for drift levels up to 10% (Powell 2006).
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The difference between P-δ and P-Δ is explained in the [Difference between P-Delta|kb:Difference between P-δ and P-∆Delta] article. This article also strives to visually demonstrate the logic behind P-∆ emphasis over P-δ application during multi-story-building analysis and design.
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P-Δ implementation is described in the [P-Δ implementation|kb:P-∆ implementation DRAFT] article.
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h1. References

* Powell, G. (2006). _Nonlinear Dynamic Analysis Capabilities and Limitations_, Computers and Structures, Inc., Berkeley, CA

* Deierlein, G. G., Reinhorn, A. M., and Willford, M. R. (2010). _Nonlinear Structural Analysis For Seismic Design_, NEHRP Seismic Design Technical Brief No. 4., NIST GCR 10-917-5, National Institute of Standards and Technology, Gaithersburg, MD.

* PEER/ATC (2010). _Modeling and acceptance criteria for seismic design and analysis of tall buildings_, PEER/ATC 72-1 Report, Applied Technology Council, Redwood City, CA, October 2010.