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Modal Combination Rules

What are the Modal Combination Rules in order to determine the peak value of the total response?

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Modal Combination Rules:

Rules to combine the peak modal responses rno (n = 1, 2, …, N) in order to determine the peak value of the total response (ro).

1. Absolute Sum (ABSSUM)

2065_modal rules1.jpg

- gives upper bound value which is usually too conservative
- not popular in structural design applications

2. Square-Root-of-Sum-of-Squares (SRSS)

1937_modal rules2.jpg

- the squared modal peaks are summed, and then find the square root of the sum
- provides excellent response estimates for structures with well-separated natural frequencies

3. Complete Quadratic Combination (CQC)

- applicable to a wider class of structures as it overcomes the limitations of the SRSS rule
- Each of the N2 terms on the right hand side of the equation is the product of the peak responses in the ith and nth modes and the correlation coefficient ρin (0 to 1) for these two modes.

1757_modal rules3.jpg

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