P-Delta Effect on Structures

P-Delta Analysis is a Non-linear second-order analysis which exhibits a considerable increase in the base moment when a structure is subjected to large lateral displacement due to wind or seismic forces.

Before moving further, there are two terms that need additional clarification to understand the behavior on the whole. They are "Non-linear" & "Second-order". 

What is Non-linear Analysis?

To put it in a simple statement, "Stress-Strain relationship is not linear as in the case of linear analysis". Non-linearity may be classified as follows.

1. Geometric Non-linearity
2. Material Non-linearity
3. Boundary condition Non-linearity

P-Delta effect falls under the Geometric Non-linearity category. This particular non-linearity is due to the excessive deformation or deflection of the material or structure, even though they are in the elastic limit. 

Why P-Delta analysis is called "Second-Order" Analysis?

For easy understanding, when a structure is loaded, it will deflect or deform to relieve the stress. This deflection is said to be the first-order effect. Without any additional loading, if any stresses or adverse effects induced in a structure due to the first-order deflection, it is called a second-order effect.

P-Delta analysis is called a second-order analysis because it depends on the initial deflection of the structure. If the initial first-order deflection is more, then obviously the P-Delta effect will be more in the structure.

P-Delta Analysis

Usually, we used to analyze a structure in a static position with loads being applied to it and determine their responses. P-Delta analysis is nothing but analyzing a structure by applying loads on the deflected form of a structure. A deflected structure may encounter significant moments because the ends of the members have changed their position.

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