EP 1110-2-12
30 Sep 95
Table 7-2
Combining Modal Responses: Complete Quadratic Combination Method (CQC) and Double Sum
Method (DSM)
Method 3: Complete Quadratic Combination (CQC)
8 εi εj (εi
rεj)r 3/2
Pij
1
2 2
2
4εi εj r 1
4 εi
εj r
2
r2
r2
where
εi = modal damping ratio for the ith mode
εj = modal damping ratio for the jth mode
ωj
r
ωi
This method is based on both modal frequency and modal damping. However, for design of gravity dams, there is no procedure
available to establish reasonable damping ratios for the higher modes. The effective viscous damping factor calculated according
to the recommended procedure in this EP is used for all modes.
Method 4: Double Sum Method (DSM)
1
2
(ωi
ωj )
1
Pij
(ε ω
εj ωj)
i i
where
ωi
ωi (1
εi )1/2
2
ωj
ωj (1
εj )1/2
2
2
εi
εi
tdωi
2
εj
εj
tdωj
td
10 seconds (earthquake duration)
This method is similar to CQC, but is slightly more conservative.
Note: Refer to Table 7-1 for the basic equation for obtaining the total modal response, and for definition of terms not provided on
this table.
7-10
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