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Uncovering the Mystery of Response Spectrum Analysis - Part I

Response Spectrum Analysis
July 3, 2014 By: Nick Veikos

In the course of over 30 years of working with clients in the field of structural dynamics, I have found Response Spectrum Analysis to be one of the most misunderstood types of dynamics analysis. I’m not sure why, but think it is because the input to this type of analysis (the response spectrum) is not a load in the traditional sense, but a response.

I like to think of a response spectrum analysis as a quick-and-dirty way to get a (hopefully) conservative estimate of the peak response of a system to a transient event without going to the trouble of doing a transient analysis. The advantages of the method are that it is quick and easy, but the drawback is accuracy. So, if you are looking for a conservative solution, to which you will subsequently apply a large factor of safety, it is a good approach. This is why it is commonly used in the design of large structures subject to earthquake loads. If you are looking for accuracy, a transient analysis is the best approach.

In this series of three posts, I want to help clear up some confusion about what is really going on behind the scenes and help sort out some common misconceptions. There are many nuances to be aware of that I won’t get into; my goal here is just to provide some fundamental understanding to those that don’t have much experience performing this type of engineering analysis.

Step 1 - Obtain the input response spectrum

1) You start with a transient loading. This is the loading your system is expected to experience and for which you want to estimate the peak response.

2) The response spectrum value at a given frequency, f, is computed by capturing the peak response of a single degree-of-freedom oscillator with natural frequency f during the course of the transient event. The response is typically displacement, velocity, or acceleration. (Figure 1)

Figure 1

3) The process is repeated for a series of single degree-of-freedom oscillators, with varying natural frequencies, but all with the same prescribed damping ratio and an envelope is placed on these responses to form the response spectrum curve. At this point, the transient loading in the time domain has been converted to a curve of amplitude in the frequency domain. No phase information is available using this approach. Only peak amplitude at each frequency is retained. Thus a response spectrum is an envelope of the maximum responses of a number of single DOF systems to a given excitation.

Figure 2

4) Steps 2 and 3 are sometimes repeated to obtain different curves at different damping levels. (Figure 3)

Figure 3

Most of the time, steps 1-4 are already performed for you by a regulatory authority or client, and all you see are the resulting response spectrum curves. Usually it is only one curve. If only one, you should be sure to ask what level of damping was used to compute it in order to make sure that the damping used to determine the curve is consistent with the damping level in your actual structure. If your system has more damping than was used to develop the curve, the true response of the system will be lower than what you compute using the curve, so this is conservative.

On the other hand, if the damping in your system is anticipated to be lower than that used to develop the curve, you either need to add more damping to the actual structure, or request a curve computed at a lower damping ratio. Scaling based on damping ratio is another possibility.

The important thing is to understand where the response spectrum curves came from and not to use the curves blindly.

In my next post, I will talk about obtaining the response to this input.  Stay tuned!