ABS rule - Sum of absolute values
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The absolute values are added together algebraically. |
SRSS rule - Square Root of Sum of Squares (Pythagorean addition)
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Combination as square root of the sum of squares. |
DSC rule - Double Sum Combination
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Combination with accounting for correlation between the modes (Newmark, Rosenblueth 1969, 1971). Rmax = Sqrt (DoubleSum of Ri*Rj*rhoij). For sign adjustment modified to Rmax = Sqrt (DoubleSum of abs(Ri*Rj)*rhoij). Rmin=-Rmax. rhoij are the correlation factors depending on the specified damping ratio and the duration of the seismic event. See CQC for sign adjustment justification.
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CQC rule - Complete Quadratic Combination
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Combination with accounting for correlation between the modes (Der Kiureghian, 1979, 1980). Rmax = Sqrt (DoubleSum of Ri*Rj*rhoij). For sign adjustment modified to R = Sqrt (DoubleSum of abs(Ri*Rj)*rhoij). rhoij are the correlation factors depending on the specified damping ratio and the duration of the seismic event.
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CQCX - Variant of CQC (without sign adjustment)
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Variant of the CQC rule. CQCX is the original CQC as described in literature (without sign adjustment). Sign adjustment corresponds to limiting phase shift considerations to 180° whereas the original CQC essentially considers phase shifting constraints over 360°. Using this approach effects in fully considering any mass damper effects, i.e. the result values can drop down below SRSS results. Note: Due to scientific discussions in 2012 we came to the conclusion that CQCX is the correct approach and the CQC solution with sign adjustment is too conservative.
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