Modal Combination Control
Enter the method of mode combination and specify whether to restore the signs of response spectrum analysis results.
Modal Combination Type: Set the method of combining modes in the response spectrum analysis.
SRSS: Square Root of Sum of the Squares
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SRSS method, which is most commonly used, renders close approximations of design response for a structure exhibiting well-distributed natural frequencies. However, it tends to overestimate or underestimate the combination for a structural system with close natural frequencies, which can be found in a multi-span bridge with continuous short spans. Another drawback is that it looses signs in the process of combination.
CQC: Complete Quadratic Combination
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Where
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: the representative maximum value for a particular response
: the peak value of the particular response for the i-th mode
: the ratio of the natural frequency at the i-th mode to the natural frequency at the j-th mode
: damping ratio
CQC method considers the probabilistic correlation between modes for a structural system with close natural frequencies, which can be found in a multi-span bridge with continuous short spans. By applying the correlation factor in combination using close natural frequency ratios, the overestimating or underestimating problem can be resolved. As shown in the equation above, the correlation factor will become 1 irrespective of the damping ratio when i=j, and it will become identical to SRSS method when the damping ratio is 0.
ABS: ABsolute Sum
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ABS method renders the largest responses among different combination methods. The signs are neglected by the use of absolute values. It tends to overestimate the response results. When a specific ratio such as the 100:30 rule, etc. is applied after combining the analysis results in each direction considering the directionality of earthquake, the maximum response is obtained by summing the absolute results in three directions.
Linear: Linear Sum
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In linear method, the user chooses specific modes and enters the Mode Shape Factors directly, which are then linearly combined. The signs are preserved. It is used to check the effects of a specific mode or compare responses by modes.
Add signs(+,-) to the Results
Specify whether to restore the signs deleted during the mode combination and specify the restoration method
Along the Major Mode Direction: Restore the signs according to the signs (+, -) of the principal mode for every loading direction.
Along the Absolute Maximum Value: Restore the signs according to the signs of the absolute maximum values among all the modal results.
Note
In general, structural characteristics can be reflected properly by using the Along the Major Mode Direction option and using the sign of the major mode that greatly contributes to the structural behavior. However, when torsion is considerable due to the structural irregularity, or the modes are closely spaced and the major mode is not very distinctive, the Along the Major Mode Direction option can partially distort the structural behavior. In such a case, it is desirable to opt for Along the Absolute Maximum Value option.
Select Mode Shapes
Select modes for modal combination. Using the Select Mode Shapes option, linearly combine the modes while entering the Mode Shape Factors directly.
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