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# Uncovering the Mystery of Response Spectrum Analysis - Part III

August 29, 2014 By: Nick Veikos

This is the third in a series of 3 posts discussing Response Spectrum Analysis. My first post discusses the overall approach and input curves, and in the second, I talk about computing the structure’s response using these curves. In this post, I will talk about some of the common errors and misconceptions related to using this method.

A major cause of error in response spectrum analyses is not using sufficient modes. Ideally, you want to compute all the modes that are contained in the frequency range of the spectrum. So, if your spectrum goes to 2,000 Hz, you want to obtain and combine all the modes up to 2,000 Hz. Sometimes this is not possible, so there are rules of thumb and other techniques (Missing Mass, Static ZPA) to help account for the modes not computed. Details of some of these methods can be found in Reference 1, below. If you ignore modes important to the overall response, you will be producing non-conservative results. If in doubt, use more modes and see if your answers change significantly.

Sometimes errors are introduced by a non-conservative choice of the mode combination method. Many are available and some work better than others in certain circumstances, e.g. – when you have closely spaced modes. If you get widely varying results using different combination methods, it may be wise to run a full transient analysis in order to better understand the system response.

A common misconception is that increasing the damping level of the finite element model will alter the response. This will happen if you are using multiple input response curves, developed using different damping levels. But if you are using only one curve, there will be no change – only one curve exists and it will be used to develop the scaling factor, no matter how much damping you include in the finite element model. To assess the effects of different damping levels, you must input response curves corresponding to those damping levels.

Another misunderstanding is that the response spectrum result at a given natural frequency should be identical to that from a harmonic response analysis which uses the response spectrum values as the base input. I’m not sure where this idea comes from, but based on the number of times I have heard people make this claim, it seems to be very prevalent in the engineering community. There is no logical reason for this thinking. The response curve is a response of a single DOF oscillator at a given frequency. Using this response as an input to a harmonic response analysis makes no sense.

What can be done, however, is to estimate the harmonic response to a base excitation at selected modes using the response spectrum calculations, but adjustments must be made. With this approach, the desired base motion for the harmonic response analysis should be scaled by 1/2ζ, where ζ is the damping ratio, and used to define the response spectrum input curve.

For example, suppose we wanted to approximate the harmonic response at the first few natural frequencies to a .001” base excitation for a system having a damping ratio of 2.5%. We could define a displacement response spectrum input curve with amplitude of .001”/2(.025)=.02” over the desired frequency range and perform a response spectrum analysis. For well-separated modes, the response spectrum scaled results for the individual modes would be fairly close to those from a harmonic response analysis with a .001” base excitation. At higher frequencies, where modes are likely more closely spaced, the correlation between the two methods will drop off. If you are using a response spectrum analysis for this purpose, no mode combinations are performed, of course.

Hopefully this series of blogs on the response spectrum method for finite element analysis helps to explain a little bit of what is going on “under the hood” and clears up some of common misconceptions about this approach. Please chime in with any comments or additional items to consider that I’m sure I overlooked.

1.  Combining Modal Responses and Spatial Components in Seismic Response Analysis, Regulatory Guide 1.92, Revision 2, Nuclear Regulatory Commission, Office of Nuclear Regulatory Research, July 2006.