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P-Delta effect typically involves large external forces upon relatively small displacements. 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 are illustrated in Figure 1, and described as follows:
P-δ effect, or P-"small-delta", is associated with local deformation relative to the element chord between end nodes. Small P-delta effects can affect overall structural behavior by slightly reducing the
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buckling load.
Typically, P-δ only becomes significant at unreasonably large displacement values, or in especially slender columns. (Powell 2006). Small P-delta effect is important for local buckling, or for design algorithms that expect member buckling to be accounted for by analysis. This includes AISC direct-analysis method.
Small P-delta is included in frame elements, to the extent that it can be represented by a cubic curve. The frame small P-delta effect is very accurate for a single element with effective-length factor of 2 (cantilever), and moderately accurate for an effective-length factor of 1 (pinned or sway condition). When accurate small P-delta effects are important for analysis or design of a member, it is generally recommended to auto-mesh frame objects into 2 elements, especially for axial loads close to buckling. For most other purposes, small P-delta effects as they impact the overall structure are adequately considered with a single frame object between connections
P-Δ effect, or P-"big-delta", is associated with displacements relative to member ends. Large P-delta effect is important for overall structure behavior under significant axial load. As indicated intuitively by Figure 2, gravity loading will influence
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structural response under significant lateral displacement.
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