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Dipl.-Ing. (FH) Stefan Frenzel
2021-07-28

CQC and SRSS Rules in Dynamic Analysis

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

Answer:

The Complete Quadratic Combination (CQC) rule must be applied if there are neighboring modal shapes with periods differing by less than 10% when analyzing spatial models with mixed torsional/translational eigenmodes. 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:

ECQC=∑i=1p∑j=1pEi·εij·Ej

εij

Correlation coefficient
Standard CQC Rule

with the correlation coefficient:

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)
Correlation Coefficient (CQC Rule)

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

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

D

Dämpfungswert

r

Quotient der Eigenkreisfrequenzen (ωj/ ωi)
Correlation Coefficient (CQC Rule, Simplified: Di = Dj)

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:

ECQC = ∑i = 1p fi · Ei     where     fi = ∑j=1pεij·Ej∑i=1p∑j=1pEi·εij·Ej
Modified CQC Rule – Equivalent Linear Combination

Dialog Box for Superposition Rule
Dialog Box for Superposition Rule
Author

Mr. Frenzel is responsible for developing products for dynamic analysis. He also provides technical support for customers of Dlubal Software.

References
  1. Meskouris, K. (1999). Baudynamik, Modelle, Methoden, Praxisbeispiele. Ernst & Sohn.
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