Page Comparison

{table-plus:enableSorting=false|align=right|borderColor=white|title='Figure 1 - P-Delta effect'}


| !P-delta col, Figure 1.PNG|border=1,height=300px! |
{table-plus}

{table-plus:enableSorting=false|borderColor=white|align=right|width=10px|height=320px}


| |
{table-plus}

\\

*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).
\\
\\
{hidden-content}
The difference between P-δ and P-Δ is explained in the [Difference between P-Delta|kb:Difference between P-δ and P-∆] article. This article also strives to visually demonstrate the logic behind P-∆ emphasis over P-δ application during multi-story-building analysis and design.
\\
\\
P-Δ implementation is described in the [P-Δ implementation|kb:P-∆ implementation DRAFT] article.
{hidden-content}

\\

!Figure 2 and 3.png|align=center,border=0,height=300px!

{list-of-resources2:label=P-Delta|drafts-root=P-Delta drafts}


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.