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FAQ 003413 EN

5 August 2019

# What does superposition mean according to the SRSS rule in the dynamic analysis??

In the Settings, you can define how results from different mode shapes of the structure are combined. The modal combination is the first step of the dynamic combinations. The modal responses can be combined with the Square Root of the Sum of Squares (SRSS) or the Complete Quadratic Combination (CQC). Both of these quadratic combinations can be applied in the standard form or modified as an equivalent linear combination. The standard form of the SRSS rule combines maximum results and the algebraic signs are lost; the combination expression is as follows:

${\mathrm E}_{\mathrm{SRSS}}\;=\;\sqrt{\mathrm E2\;1\;+\;\mathrm E2\;2\;+\;\dots\;+\;\mathrm E\;2}$

In the RFEM add-on module RF-DYNAM Pro, a modified form of the SRSS rule is available to determine the corresponding results, such as the corresponding internal forces. In relation to the standard form of the SRSS rule, the corresponding internal forces are usually much smaller. Furthermore, the corresponding signs are correct in relation to the governing internal force. The SRSS rule is used as an equivalent linear combination:

${\mathrm E}_{\mathrm{SRSS}}\;=\overset{\mathrm p}{\underset{\mathrm i=1}{\sum{\mathrm f}_{\mathrm i}}}{\mathrm E}_{\mathrm i}$

with:

$f_i=\frac{E_i}{\sqrt{{\displaystyle\sum_{i=1}^p}E_j^2}}$

If this formula is applied, the results are consistent.