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*Geometric nonlinearity* isoccurs causedwhen byaxial gravityload loadsis actingapplied onto the displaced configuration of a structural structureelement. This behavioreffect increasesinfluences the internal forces onand elementsfurther andaffects connectionsdisplacement. Of particular concern are column bending stresses. Resultant secondary moments increase with additional lateral displacement, as shown in Figure 1 is when gravity loads act on the laterally-displaced configuration of a structure. Column bending stresses and interstory drifts are then magnified while deformation capacity is reduced.

Geometric nonlinearity is also known as *P-Delta effect*. There are two sources of P-Delta effect, contributions of which include the following are shown in Figure 1, and described as follows:

* *P-δ*, also known as *Large-Displacement effect*, which or P-"small-delta", is associated with local deformation. Equilibrium conditions are evaluated throughabout localdisplaced-configuration displacement relative to the element chord. This behavior  Of particular concern is when local behavior breaks from compatibility relationships. 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-Displacement effect is to subdivide critical elements into multiple segments, which transfers behavior into P-Δ effect (Powell 2006).

* *P-Δ*, also known as *Gravity Load-Deformation effect*, which or P-"big-delta", is associated with story drift. This behavior is measured between 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 when the global system displaces laterally. P-Δ may contribute to loss of lateral resistance, ratcheting of residual deformations, and dynamic instability (Deierlein et al. 2010). In that laterally-displaced gravity loading magnifies internal forces, 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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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.