Due to the recent questions about complete quadratic combination (CQC) vs Dynamic Response force summations, below it's presented a little explanation to help illustrate/explain what our various reports mean.

Both of the following reports list the vertical load for the CQC of the seismic response for Direction X (Load Case 1):

Clearly, 36.5 kips, does not match 1676.115 kips, but what do these mean, and is there a bug? The short answer is that we are calculating the CQC of the responses differently in Dynamic Response and Combine CQC, “technically” this is not a bug, although the argument could be made that this is confusing and misleading.

When Dynamic Response combines the responses, it calculates the CQC of the modal reactions which are detailed in the Dynpac listing file. These modal reactions are calculated by summing the joint reactions calculated from the normalized mode shape displacement (i.e. F = K*X where X is known).

For example, the combination for the vertical load reported by dynamic response would then be:

Note: In SACS, mode shapes are always normalized to 1 in, so in metric analyses, you will need to consider units when calculating the modal response factor from the Modal Displacement

However, the combine calculates the CQC for each individual joint reaction FIRST and then sums them like so:

 

Where:

n is the iterator for joints

Fzni and Fzni are the vertical modal reactions in each joint, n, for modes i and j

 

The individual joint reactions can be obtained from a fixed joint reaction report from the Postvue database of the Dynpac analysis:

These are not equivalent! In fact, you can rewrite the Dynamic Response combination using Fzni and Fznj to illustrate the difference:

So what does it all mean? Well, when calculating CQC of a response, you should always perform linear combinations of the modal responses before doing CQC. This means that the force summations reported by Combine are technically wrong as they are the summation of the CQC response of the individual joint reactions. However, if checking individual elements or in this case joint reactions, the results in the common solution file are correct. We use the individual element results to design our structures, not global response, so there should be no issue with post-processing these results. At the end of the day, we should always treat these types of combinations as a statistical representation of maxima for individual elements and not a realistic load case that occurs at any given moment in time.