The P-Delta effect is also known colloquially as the calculation according to the second-order analysis with applying imperfection. According to ASCE 7-16 [1], a check must be made after calculating the equivalent seismic loads as to whether it is necessary to consider this P-Delta effect. The following formulas are given at Point 12.8-16 in the standard.
It is not necessary to consider P-Delta effects on floor shear and moments as well as floor deformations if the stability coefficient is smaller than 0.1. This coefficient can be determined with the following formula:
| Θ | Stability coefficient |
| Px | Maximum design vertical load on and above story x |
| Δ | Design deformation of the story defined in Chapter 12.8.6 |
| le | Importance factor according to 11.5.1 |
| Vx | Horizontal shear between floors x and x - 1 |
| hsx | Story height below the considered story x |
| Cd | Deformation amplification factor according to Table 12.2-1 |
The stability coefficient must not exceed 0.25 to perform a second-order analysis. If the coefficient is greater than the maximum value, we recommend revising the structure, because it has no stability according to the second-order analysis. The maximum value is calculated as follows:
| Θmax | Maximum value of stability coefficient |
| Cd | Deformation amplification factor according to Table 12.2-1 |
where β is the ratio between the shear capacity of the single levels x and x-1. The conservative approach is to apply 1.0 here.
If the stability coefficient is between 0.1 and 0.25, the calculation can be performed according to the P-Delta analysis. It is also possible to calculate the determined internal forces and the deformation according to the linear static analysis, then increase it with a factor. The following formula is used:
The P-Delta effect according to ASCE 7-10 of 2016 does not have to be used consistently, as shown with the formulas. Therefore, it is worthwile to check the formulas according to 12.8.6 to avoid extra work.