What is the difference between SRSS, CQC, and Rose mode combination methods in Response Spectrum analyses?

Let's say we just have 2 modes to combine in a Response Spectrum analysis.
If you see the equations in Section 17.7.6 of the Theory Reference, we really end up with an equation like the following:
R^2 = R1^2 + 2*epsilon*R1*R2 + R2^2
Now, one extreme is where epsilon=1. This is basically just summing up the modal response:
R^2 = R1^2 + 2*R1*R2 + R2^2
R = R1 + R2
R = |R1| + |R2| (in practice)
We don't offer this approach (called the absolute sum method) in ANSYS because no one really uses it - it is too conservative.
(You can get this result, though, with some simple APDL manipulation since the solution is a straightforward one.)

Now, consider epsilon=0. Then we have the following:
R^2 = R1^2 + R2^2
R = SRSS(R1, R2)
This is the SRSS method. Basically, another way to think of it is that we don't account for modal interaction (interaction of modes 1 and 2) since we neglect the R1*R2 term and just take the SRSS.

The CQC and Rosenblueth methods, on the other hand, use 0 < epsilon < 1 to calculate the total response, so we get somewhere in-between.
In other words, CQC and Rosenblueth account for some interaction of modes when the modes are closely spaced. The reasoning is that closely-spaced modes may interact with each other (be in-phase), so we should treat closely-spaced modes like the algebraic method (without the absolute values) while we should treat modes spaced far apart like SRSS.

However, because CQC and Rosenblueth consider the sign, do not think of these methods as always more conservative than SRSS. That is not the case - depending on the sign, CQC & Rosenblueth can be more or less conservative. Let's say R2 was a negative value while R1 was positive. Then, SRSS will be larger than CQC or Rosenblueth. However, if R2 and R1 had the same sign, CQC or Rosenblueth could have a larger result than SRSS.

Rosenblueth and CQC are similar - they both utilize random vibration theory to represent the seismic loading as white noise, although Rosenblueth assumes finite duration whereas CQC assumes infinite duration. If you plug in some numbers, you can see how the coefficients may compare between the two, although I think that they are generally similar.
The choice tends to be driven by the specification.

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Simple and clear description. Excellent.
Hasan, Fri May 26, 2017
Excellent description!
very easily understtod. Well done.
alex, Thu Apr 17, 2014