# FAQ 003414 EN

### What is the meaning of the superposition according to the CQC rule in a dynamic analysis??

The complete quadratic combination (CQC) rule must be applied when analyzing spatial models with combined torsional/translational eigenmodes that have adjacent modal shapes whose periods differ by less than 10%.

If this is not the case, the square root of the sum of the squares (SRSS rule) applies. In all other cases, the CQC rule must be applied. The CQC rule is defined as follows:

Standard CQC Rule

$$ECQC=∑i=1p∑j=1pEi·εij·Ej$$

 εij Correlation coefficient

with the correlation coefficient:

Correlation Coefficient (CQC Rule)

$$εij=8·Di·Dj·(Di+r·Dj)·r32(1-r2)2+4·Di·Dj·r·(1+r2)+4·(Di2+Dj2)·r2$$

 Di, Dj Damping values r Quotient of the natural angular frequencies (ωj/ ωi)

The correlation coefficient is simplified if the viscous damping value D is selected to be the same for all mode shapes:

Correlation Coefficient (CQC Rule, Simplified: Di = Dj)

$$εij=8·D2·(1+r)·r32(1-r2)2+4·D2·r·(1+r)2$$

 D Damping value r Quotient of the natural angular frequencies (ωj/ ωi)

By analogy to the SRSS rule, the CQC rule can also be performed as an equivalent linear combination. The formula of the modified CQC rule is as follows:

Modified CQC Rule - Equivalent Linear Combination

$$ECQC = ∑i = 1p fi · Ei where fi = ∑j=1pεij·Ej∑i=1p∑j=1pEi·εij·Ej$$

#### Reference

 [1] Meskouris, K. (1999). Baudynamik, Modelle, Methoden, Praxisbeispiele. Berlin: Ernst & Sohn.

Write Comment...

Write Comment...

• Views 1975x
• Updated 17 May 2022

Submit Individual Question

Eurocode 3 | Steel Structures According to DIN EN 1993-1-1

Online Training 2 March 2023 9:00 AM - 1:00 PM CET

Eurocode 5 | Timber Structures According to DIN EN 1995-1-1

Online Training 16 March 2023 9:00 AM - 1:00 PM CET

International Mass Timber Conference

Conference 27 March 2023 - 29 March 2023

RFEM 6 | Dynamic Analysis and Seismic Design According to EC 8

Online Training 30 March 2023 9:00 AM - 1:00 PM CEST

Stability and Warping Torsion Analyses in RFEM 6 and RSTAB 9

Webinar 26 January 2023 2:00 PM - 3:00 PM CET

Modeling and Design of CLT Panels in RFEM 6

Webinar 19 January 2023 2:00 PM - 3:00 PM CET

Revit, IFC, and DXF Integration in RFEM 6 (USA)

Webinar 15 December 2022 2:00 PM - 3:00 PM EDT

Eurocode 5 | Timber Structures According to DIN EN 1995-1-1

Online Training 8 December 2022 9:00 AM - 1:00 PM CET

RFEM 6 | Students | Introduction to Timber Design

Online Training 25 November 2022 4:00 PM - 5:00 PM CET

RFEM 6 | Dynamic Analysis and Seismic Design According to EC 8

Online Training 23 November 2022 9:00 AM - 1:00 PM CET

Eurocode 3 | Steel Structures According to DIN EN 1993-1-1

Online Training 17 November 2022 9:00 AM - 1:00 PM CET

Construction Stages Analysis in RFEM 6 (USA)

Webinar 19 October 2022 2:00 PM - 3:00 PM EDT

Seismic Design According to Eurocode 8 in RFEM 6 and RSTAB 9

Webinar 11 October 2022 2:00 PM - 3:00 PM CEST

Analysis of Steel Joints Using FE Model in RFEM 6

Webinar 29 September 2022 2:00 PM - 3:00 PM CEST

RFEM 6 | Dynamic Analysis and Seismic Design According to EC 8

Online Training 21 September 2022 9:00 AM - 1:00 PM CEST

Eurocode 5 | Timber Structures According to DIN EN 1995-1-1

Online Training 15 September 2022 9:00 AM - 1:00 PM CEST

Consider Construction Stages in RFEM 6

Webinar 8 September 2022 2:00 PM - 3:00 PM CEST

Eurocode 3 | Steel Structures According to DIN EN 1993-1-1

Online Training 8 September 2022 9:00 AM - 1:00 PM CEST

Form-Finding and Calculation of Membrane Structures in RFEM 6

Webinar 25 August 2022 2:00 PM - 3:00 PM CEST

Length 51:42 min

Length 1:15:59 min

Length 0:55 min

Length 1:02:25 min

Length 49:14 min

Length 49:16 min

Length 53:58 min

Length 0:58 min

Length 1:12:47 min