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P-Delta effect, one type of geometric nonl= inearity, involves the equilibrium compatibility relationships of a structu= ral system loaded about its deflected configuration. Of particular concern = is the application of gravity load on laterally displaced multi-story build= ing structures. This condition magnifies story drift and certain mechanical= behaviors while reducing deformation capacity.
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/or Lar= ge-Deformation analyses may become necessary. The two sources of P-Delta ef= fect are illustrated in Figure 1, and described as follows:
P-=CE=B4 effect, or P-"s= mall-delta", is associated with local deformation relative to the element c= hord between end nodes. Small P-delta effects can affect overall structural= behavior by slightly reducing the buckling load, and can change the moment= within the member.
Typically, P-=CE=B4 only becomes signific= ant at larger displacement values or in especially slender columns. (Powell= 2006). Small P-delta effect is important for local buckling and for design= algorithms that expect member buckling to be accounted for by analysis.&nb= sp;This includes the AISC direct-analysis method.
Small P-delta is automatically included i= n frame elements to the extent that the deflected shape can be well represe= nted by a cubic curve. The frame small P-delta effect is very accurat= e for a single element with effective-length factor of 2 (cantilever), and = it is moderately accurate for an effective-length factor of 1 (pinned or sw= ay condition). When accurate small P-delta effects are important for = analysis or design of a member, it is generally recommended to auto-mesh fr= ame objects into 2 or more elements, especially for axial loads close to bu= ckling. 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-=CE=94 effect, or P-"b= ig-delta", is associated with displacements of the member ends. Large P-del= ta effect is important for overall structure behavior under significant axi= al load. As indicated intuitively by Figure 2, gravity loading <= em>will influence structural response under significant lateral displa= cement.
P-=CE=94 may contribute to loss of latera= l resistance, ratcheting of residual deformations, and dynamic instability = (Deierlein et al. 2010). As shown in Figure 3, effective lateral stiffness = decreases, reducing strength capacity in all phases of the force-deformatio= n relationship (PEER/ATC 2010). To consider P-=CE=94 effect directly, gravi= ty 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).
Large P-delta is included in all elements= =E2=80=93 frame, shell, solid, link.
The Types of P-Delta anal=
ysis article further explains the difference between P-=CE=B4 and P-=CE=
=94.
Note that P-delta effects increase lateral flexibility for members under= compression, but they can also increase the lateral stiffness for= members under tension. In some systems the two effects can cancel out, at = least for overall system behavior. For example, lateral wind loading on a b= uilding already under gravity load may increase the compression on one side= of the structure and decrease it on the other side, perhaps even going int= o tension. Locally, the members under greater compression are more likely t= o buckle than the members on the windward side, and small P-delta effects c= ould be important. However, the lateral stiffness of the overall building i= s little changed by the presence of the wind load as the increased flexibil= ity of columns on one side is counteracted by the smaller effect (or even t= ension stiffening) on the other side.
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