Geometric nonlinearity DRAFT

Geometric nonlinearity is when gravity loads act on the displaced configuration of a structure, increasing the internal forces on elements and connections. Of particular concern are column bending stresses induced by secondary moments which increase with lateral displacement. This behavior is illustrated in the figure on the right.

Geometric nonlinearity is also known as P-delta effect. Two sources of P-delta effect exist, including the following types:

• P-δ - also known as Large-Displacement effect, is associated with local deformation. Equilibrium conditions are evaluated using displacement relative to 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.

• P-Δ - also known as Gravity Load-Deformation effect, is associated with story drift, and 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 the figures below, 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 the figure below (left). 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%.

References

• 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.