# Consideration of P-Delta Effects (Second-Order Analysis) in the Response Spectrum Analysis According to ASCE 7-16

### Technical Article

RFEM offers the option to perform a response spectrum analysis according to ASCE 7-16. This standard describes the determination of seismic loads for the American market. It might happen that the P-Delta effect has to be considered due to the stiffness of the entire structure in order to calculate the internal forces and carry out the design.

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:

$\mathrm{\Theta}=\frac{{\mathrm{P}}_{\mathrm{x}}\xb7\mathrm{\Delta}\xb7{\mathrm{I}}_{\mathrm{e}}}{{\mathrm{V}}_{\mathrm{x}}\xb7{\mathrm{h}}_{\mathrm{sx}}\xb7{\mathrm{C}}_{\mathrm{d}}}$

Θ |
Stability coefficient |

P_{x} |
Maximum design vertical load on and above story x |

Δ |
Design deformation of the story defined in Chapter 12.8.6 |

l_{e} |
Importance factor according to 11.5.1 |

V_{x} |
Horizontal shear between floors x and x - 1 |

h_{sx} |
Story height below the considered story x |

C_{d} |
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:

${\mathrm{\Theta}}_{\mathrm{max}}=\frac{0.5}{\mathrm{\beta}\xb7{\mathrm{C}}_{\mathrm{d}}}\le 0.25$

Θ_{max} |
Maximum value of stability coefficient |

C_{d} |
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:

$\mathrm{Value}\mathrm{a}\mathrm{c}\mathrm{c}\mathrm{.}\mathrm{to}\mathrm{s}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{d}\mathrm{-}\mathrm{o}\mathrm{r}\mathrm{d}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{a}\mathrm{l}\mathrm{y}\mathrm{s}\mathrm{.}=\mathrm{Value}\mathrm{a}\mathrm{c}\mathrm{c}\mathrm{.}\mathrm{to}\mathrm{linear}\mathrm{static}\mathrm{a}\mathrm{n}\mathrm{a}\mathrm{l}\mathrm{y}\mathrm{s}\mathrm{.}\xb7\left(\frac{1}{1-\mathrm{\Theta}}\right)$

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.

#### Keywords

ASCE 7 ASCE 7-16 Seismic Earthquake P-Delta Stability

#### Reference

#### Links

Write Comment...

Write Comment...

Contact Us

Do you have further questions or need advice? Contact us via phone, email, chat, or forum, or search the FAQ page, available 24/7.

New

AISC 341-22 Moment Frame Member Design in RFEM 6

The three types of moment frames (Ordinary, Intermediate, Special) are available in the Steel Design add-on of RFEM 6. The seismic design result according to AISC 341-22 is categorized into two sections: member requirements and connection requirements.

Associated Products