Geometric nonlinearity occurs when axial load is applied to the displaced configuration of a structural element. This effect influences internal forces and further affects displacement. Of particular concern 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 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 element chord. 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, 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 article.

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.