CQC mode superposition is the rule with the usual Complete Quadratic Combination. It is defined in different scientific textbooks with the formula given below for a certain result component Rk is:

Rk,tot = √(ΣΣ(Rk,i*ρij*Rk,j)).

The matrix [ρij] is known as the correlation matrix describing the correlation between the different natural modes.

The question, how to consider in this context the signs of Rk,i and Rk,j has been controversially disputed in the past. There are hints in the textbooks that signs have to be adjusted, but no clear prescription. Therefore we offer in RM Bridge CONNECT Edition the two alternatives: CQC with adjusting the signs of the individual modal contributions and CQCX without adjustment.

At the time of doing first programming work the procedure with sign adjustment was strongly meant as the correct solution and the resulting values are in fact on the conservative side. Therefore this procedure was implemented as CQC rule in the program. The following formulas are used in this procedure:

Rk,tot,max = √(ΣΣ(Rk,i*sgn(Rk,i)*ρij*Rk,j*sgn(Rk,i))) and

Rk,tot,min = - √(ΣΣ(Rk,i*sgn(Rk,i)*ρij*Rk,j*sgn(Rk,i)))

with sgn(Rk,i) and sgn(Rk,i) denoting the sign of the respective value.

This corresponds to the assumption that the contributions of all modes have the same sign.

Hint: Later investigations and discussions with earthquake specialists, around 2012, showed that most likely a procedure without sign adjustment is actually to be considered in a more modern approach, the correct procedure. This procedure is offered in RM Bridge under the name CQCX. In this light, it is recommended to use always CQCX instead of CQC.

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