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*Geometric nonlinearity* is caused by gravity loads acting on the displaced configuration of a structure. This increases the internal forces on elements and connections. Of particular concern are column bending stresses. Resultant secondary moments increase with additional lateral displacement, as shown in Figure 1.

Geometric nonlinearity is also known as *P-delta effect*. There are two sources of P-delta effect, which include the following:

* *P-δ*, also known as Large-Displacement effect, is associated with local deformation. Equilibrium conditions are evaluated through local displacement relative to the element chord. This behavior 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, 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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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.