In the case of a static calculation of a structural model, one can verify the model by checking the applied and reacting forces to be equal zero.

I would like to adapt the same principle for a structural model with a response spectrum as an input.

Is it correct to do the following: 1) perform a frequency extraction procedure to obtain 90% of the eigenmodes contributing to the mass and rotational inertia. 2) calculate the mass of structure being excited and multiply it by the peak acceleration amplitude given in the response spectrum, eg 20g. 3) its not clear what this step should be... is there something I can do with the modal participation factors to help me calculate the total reaction load?

Any suggestions will be welcome.

Best Regards

  • $\begingroup$ Are you trying to find bugs in the code, or mistakes in your model? $\endgroup$
    – alephzero
    Commented Jul 1, 2019 at 11:53
  • $\begingroup$ @alephzero no. I would just like to know what the resulting dynamic loads are relative to the input loads. $\endgroup$ Commented Jul 1, 2019 at 12:03
  • $\begingroup$ I have performed a Modal Transient analysis. Its just a question of how to somehow verify the reaction via the Mode contributions $\endgroup$ Commented Jul 1, 2019 at 12:05

1 Answer 1


In response spectrum analysis of MDOF structures, the most common methods of modal combination are:

  • absolute sum (assume the peak response of all modes occurs simultaneously)
  • SRSS (square root of the sum of the squares)
  • CQC (complete quadratic combination)

If what you're aiming for is a pencil-and-paper check of the software output, the first two methods are most appropriate, and the absolute sum method should be conservative (sometimes overly conservative). CQC is more rigorous, and can give better solutions for structures with closely spaced modes, but it's best suited to a computer. It's worth noting that many off-the-shelf analysis packages will allow the user to choose a modal combination method when setting up the response spectrum analysis.

So, if eigenanalysis has supplied the frequency and mass participation for each mode, we can pull the peak acceleration for each mode from the acceleration response spectrum curve. Then, mass * acceleration gives the the base shear for each mode, and we find total base shear with our chosen modal combination method.

As for how many modes to consider, the standard of practice I'm familiar with (United States - bridges) is to include sufficient modes to capture at least 90% mass participation (not 90% of the modes).

Note that for seismic design purposes, you may need to take one final step and consider some combination of the longitudinal and transverse responses. The pertinent design code should specify.

  • $\begingroup$ You may also need to take into account the approximately static response of all the high frequency modes omitted from your modal dynamic model. This can include load paths that are completely missed by the low frequency dynamics. (Including "90% of the modes" is not a realistic option for a large FE model with say 100,000 DOF!) This may be a standard option in the software called something like "mode acceleration." A summary of the theory is here: vibrationdata.com/tutorials2/MA_method.pdf. $\endgroup$
    – alephzero
    Commented Jul 1, 2019 at 14:31
  • $\begingroup$ Thanks for pointing that out @alephzero - Yes, even for a fairly ordinary structure, capturing 90% of the modes would become silly. I had misinterpreted OP's statement as meaning capturing at least 90% mass participation (which is the standard of practice in my area). I edited my answer to reflect this tidbit. I don't have practical experience with the high-frequency modes consideration so I won't attempt to speak to that. $\endgroup$
    – CableStay
    Commented Jul 1, 2019 at 14:49
  • $\begingroup$ Hi guys,thanks for the replies. yes, it was a typo. I meant 90% of mass not modes! $\endgroup$ Commented Jul 2, 2019 at 8:17

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