What is P-delta , P-Delta Effects and P-Delta Analysis Parameters

What is P-delta & P-Delta effects?

P-Delta effect, also known as geometric non-linearity, involves the equilibrium and compatibility relationships of a structural system loaded about its deflected configuration. Of particular concern is the application of gravity load on laterally displaced multi-story building 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 Large-Deformation analyses become necessary. The two sources of P-Delta effect are illustrated in Figure 1, and described as follows: P- effect, or P-“small-delta”, is associated with local deformation relative to the element chord between end nodes.

P-Delta analysis parameters in Etabs

Initial P-Delta analysis may be specified in ETABS via Define>P-Delta Options and using either of the following two methods:

1. Non-iterative Based on Mass, in which load is automatically computed from the mass at each level. This is an approximate method which does not require an iterative solution, providing for faster computation. P-Delta is considered by treating the structure as a simplified stick model, a process which is most effective with a single rigid diaphragm at each level. Local buckling is not captured as effectively.

The benefit of this non-iterative method is that P-Delta may be considered in load cases which do not specify gravity load. When gravity load is specified, we generally recommend the Iterative Based on Load Cases method.

2. Iterative Based on Load Cases, in which load is computed from a specified combination of static load cases, then known as the P-Delta load combination. This is an iterative method which considers P-Delta on an element-by-element basis. Local buckling is captured more effectively. An example application may be when load includes the dead load case and a fraction of a live load case.

When the iterative method is selected, two additional options become available :

• Convergence Tolerance (Relative), Iteration is used to make sure that equilibrium is achieved at each step of the analysis. Use this parameter to set the relative convergence tolerance that is used to compare the magnitude of force error with the magnitude of the force acting on the structure. Using a smaller value ensures better equilibrium, although the default value is usually adequate.
• P-Delta Load Combination, in which users may specify the single load combination for the initial P-Delta analysis.

For example, suppose that a building code requires the following load combinations:

(1) 1.4 dead load

(2) 1.2 dead load + 1.6 live load

(3) 1.2 dead load + 0.5 live load + 1.3 wind load

(4) 1.2 dead load + 0.5 live load - 1.3 wind load

(5) 0.9 dead load + 1.3 wind load

(6) 0.9 dead load - 1.3 wind load

A P-Delta load combination of 1.2 DL + 0.5 LL is typically conservative when considering P-Delta effect due to the overall sway of a structure.

Combinations (3) and (4) will accurately capture this effect, while (5) and (6) should be conservative. Combinations (1) and (2) have no lateral load,

therefore P-Delta effect should not be of concern. Please notice this is a non-linear static case and should be performed only after the model runs without

any numerical issues for simple linear cases and results of basic variables such as deformations are within realistic or expected values.

P- effect

ETABS may account for P- effect, which is associated with local deformation relative to the chord between member ends. We do not recommend implementing this method because it will significantly increase computational time without providing the benefit of useful information. Instead, P- may be captured through either of the following methods:

• Apply design factors, which ETABS post-processing assumes to be done. These factors are therefore included in design, when applicable.
• Divide members into segments (at least two per column), then run each load case separately with a different P-Delta load combination for each.