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

## Technical Article on the Topic Structural Analysis Using Dlubal Software

### 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:

Stability coefficient

$$Θ = Px · Δ · IeVx · hsx · Cd$$

 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:

Maximum stability coefficient

$$Θmax = 0.5β · Cd ≤ 0.25$$

 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:

Formula 3

$$Value acc. to second-order analys. = Value acc. to linear static analys. · 11 - Θ$$

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.

#### Reference

 [1] ASCE/SEI 7‑16, Minimum Design Loads and Associated Criteria for Buildings and Other Structures

Write Comment...

Write Comment...

• Views 11411x
• Updated 01/11/2023

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

RFEM 6 | Students | Introduction to Timber Design

Online Training 04/30/2024 4:00 PM - 5:00 PM CEST

RFEM 6 | Students | Introduction to Steel Design

Online Training 05/15/2024 4:00 PM - 5:00 PM CEST

Connections with Circular Hollow Sections in RFEM 6

Webinar 02/29/2024 2:00 PM - 3:00 PM CET

Timber Floor Calculations in RFEM 6

Webinar 02/08/2024 2:00 PM - 3:00 PM CET

Stress Analysis of Stair Models in RFEM 6

Webinar 12/21/2023 2:00 PM - 3:00 PM CET

Introduction to Time History Analysis in RFEM 6 (USA)

Webinar 12/07/2023 2:00 PM - 3:00 PM EDT

RFEM 6 | Students | Introduction to Timber Design

Online Training 11/29/2023 4:00 PM - 5:00 PM CET

RFEM 6 | Students | Introduction to Steel Design

Online Training 11/15/2023 4:00 PM - 5:00 PM CET

Design of Cold-Formed Sections in RFEM 6 / RSTAB 9

Webinar 10/26/2023 2:00 PM - 3:00 PM CEST

Length 55:27 min

Length 1:02:20 min

Length 0:37 min

Length 0:58 min

Length 1:05:28 min

Length 0:44 min

Length 0:37 min

Length 57:23 min

Length 1:10:03 min