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Thomas Eichner, MSc.
2023-12-22

Determination of Sensitivity Coefficient to Investigate Need for Second-Order Analysis in Dynamic Analyses

To evaluate whether it is also necessary to consider the second-order analysis in a dynamic calculation, the sensitivity coefficient of interstory drift θ is provided in EN 1998‑1, Sections 2.2.2 and 4.4.2.2. It can be calculated and analyzed using RFEM 6 and RSTAB 9.

Sensitivity Coefficient θ

The sensitivity coefficient θ is defined as follows [1]:

θ = Ptot*drVtot*h
θ Interstory drift sensitivity coefficient
Ptot Total gravity load at and above the story considered in the seismic design situation
dr Interstory drift, determined as the difference between the horizontal displacements ds at the top and bottom of the story under consideration; the displacements are determined using the linear design response spectrum with q = 1.0.
Vtot Total seismic story shear determined by using the linear design response spectrum
h Story height
Sensitivity Coefficient θ

In the following, the procedure for calculating the sensitivity coefficient is shown using the example of a reinforced concrete building with a main floor and six upper floors.

Building Overview (KB1866)
Building Overview

To calculate the sensitivity coefficient, additions are used:

After modeling the building, it is necessary to define the stories using the Building Model add-on.

Story Definition with Building Model Add-on (KB1866)
Story Definition with Building Model Add-on

Then, a calculation according to the response spectrum analysis is required.

Creating Response Spectrum Analysis (KB1866)
Creating Response Spectrum Analysis

If the input is complete, you can analyze the results after the calculation. The most important parameters for the dynamic analysis can be found in the result tables of the spectral analysis. In the Results by Story subcategory, you can also see the sensitivity coefficient of the individual stories.

Displaying Story Results and Sensitivity Coefficient (KB1866)
Displaying Story Results and Sensitivity Coefficient

After calculating the sensitivity coefficient of the interstory drift, a case distinction regarding the relevance of the second-order analysis is made according to EN 1998‑1, Sections 2.2.2 and 4.4.2.2 [1].

Case Distinction for Second-Order Analysis

1. Sensitivity Coefficient θ ≤ 0.1

The second-order analysis does not have to be considered.

2. Sensitivity Coefficient 0.1 < θ ≤ 0.2

The second-order analysis may be taken into account approximately by a factor equal to 1 / (1 − θ).

3. Sensitivity Coefficient 0.2 < θ ≤ 0.3

The second-order analysis must be considered directly. You can do this by adjusting the geometric stiffness matrix in RFEM 6 and RSTAB 9. Find more information in this Knowledge Base article: KB | Considering Second-Order Analysis in Dynamic Analyses in RFEM 6 and RSTAB 9

4. Sensitivity Coefficient 0.3 < θ

The design of the structure is invalid and requires revision.

Author

Mr. Eichner is responsible for the development of products for dynamic analysis and provides technical support for our customers.

Links
References
  1. EN 1998‑1. (2013). Eurocode 8: Design of Structures for Earthquake Resistance – Part 1: General Rules, Seismic Actions and Rules for Buildings; EN 1998‑1:2004/A1:2013.
  2. CEN. (2002). Eurocode 0: Basis of Structural Design; DIN EN 1990:2002. Berlin: Beuth Verlag GmbH.
  3. Werkle, H. (2008). Finite Elemente in der Baustatik, (3rd ed.). Wiesbaden: Vieweg & Sohn.
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