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The nuclear industry and the NRC have made response spectrum their preferred method for analyzing earthquake loading for over 40 years. They provide very clear guidelines for its input and how to combine the modal results, but the intricacies of how to use the combined results in a particular finite element program is by necessity the responsibility of the analyst.
That’s one reason why response spectrum is so loved by the tech. support engineer. It is so tricky it is almost impossible for users to avoid some type of mistake without tech. support assistance. For example, infrequent users can confuse it with random vibration or a harmonic sweep (sometimes called a harmonic response spectrum.) It's easy to do because the response spectrum curve looks very similar to the psd input curve and a harmonic specification of acceleration vs frequency. These users have called tech. support over the years when they noticed damping doesn't reduce the magnitude of the results as it does with other mode-sup methods. It doesn't though because a response spectrum is the solution to a load, not the load itself. The tech. support engineer who has studied response spectrum can be of invaluable assistance in making sure the user avoids any such common mistakes and look like a hero in the eyes of the customer. That's what us tech. support engineers live for!
A major shortcoming of response spectrum in my mind is that the SRSS type mode combination produces results without sign. That makes most of the usual linear postprocessing operations invalid. Even knowing that, the implication isn't clear unless you know what results are actually on the results file and which are computed "on the fly" at the time they are requested.
The basic quantities on the results file are the nodal displacements and reaction forces in the nodal coordinate system and the unaveraged element component stresses in the element coordinate system. A user has no easy way of knowing that, however. What is there is based in part on the need to keep the results file as small as possible and is somewhat arbitrary. So any operation that attempts to transform results into another coordinate system, sum forces, average stresses or compute derived quantities like SEQV from the component values on the results file can be a source of error.
Having said that, there is a special case where a force summation is correct. Starting at 13.0 an enhancement was made to sum response spectrum nodal forces accurately with FSUM accounting for the sign of the forces in the modal results. Also there is a way for a user to obtain a reliable derived stresses like SEQV. The idea is to request that the derived stresses be computed before the SRSS combination. This is done with the command SUMTYPE,PRIN. When this command is issued before the combination, the derived stresses are computed first and then operated on directly. This is slightly conservative, but importantly is an upper bound. With this option the component stresses are zeroed out and will not be available after the combination. It's a simple matter to do the combination twice though with and without SUMTYPE,PRIN. Note that SUMTYPE,PRIN is not available in the WB Mechanical Response Spectrum.
Some General recommendations for postprocessing response spectrum results are:
· Use the solution coordinate system (RSYS,SOLU)
· Only use FSUM to sum nodal values, not the total provided by PRRSOL
· Use unaveraged element results
· Only use derived quantities like S1, S2, S3, SINT, and SEQV after issuing SUMTYPE,PRIN before the combination.
If you do tech. support long enough you will discover there are only 10 Questions. Oh, of course there are a myriad of small difficulties, irritations, limitations and complaints that customers call in about, but I'm not talking about those. I’m referring to questions which are almost philosophical in nature. In my area of linear dynamics, one of the ten is "Should I do a Response Spectrum Analysis?"
One might be tempted to answer that if you were supposed to do a response spectrum analysis you would know. Certainly in the Nuclear Industry that is the case. The NRC or the engineer that wrote the spec. you must satisfy would make that very clear. But it’s not a customer from the Nuclear Industry that asks this question. It’s an engineer analyzing a rear view mirror that has been given a mil spec or some shaker table results or wants to do an impact test. A “spectrum” plot of ground displacement/velocity/acceleration vs frequency looks exactly like a response spectrum. The difference is that a response spectrum is the solution to a certain ground motion (e.g., a strong earthquake), not the excitation itself. If you have a graph of ground acceleration vs. frequency you should do a harmonic sweep instead. If you have a graph of motion vs. time you should do a transient. In general, if you aren’t given a response spectrum, that is, an envelope of peak response vs. modal frequency you should be using another method. However, it is possible to create your own response spectrum from ground motion vs. time. I’ll talk about that option in Part II.
A response spectrum is created by performing a transient analysis of a certain ground motion time-history on a set of 1 degree of freedom oscillators of varying frequency. The peak response of each oscillator over the duration of the transient becomes a point on the response spectrum graph vs. the frequency or period of the oscillator that produced it. Usually the peak responses are enveloped by a set of straight lines. The peak responses can be in the form of displacement, velocity or acceleration. Sometime all three are plotted simultaneously on a single tripartite graph vs. period instead of frequency and using log-log scales with the apparent purpose of discouraging the uninitiated from attempting to use the method.
The graph has the same information in the three different forms since for a given frequency, displacement, velocity and acceleration differ by the ratio omega and omega^2.
It’s not always explicitly indicated on the response spectrum graph that it was obtained assuming a certain amount of damping. As a result, it is not uncommon for users to specify damping in conjunction with a spectrum analysis and expect that it will diminish the response to the response spectrum. It doesn’t, damping is already “in there.” Damping input is used, however, to interpolate between multiple spectrums of different damping values [SV,damping ratio]. When damping has been specified as a material property the interpolation is done on mode by mode based on the amount of strain energy per material a mode has. Damping is also used by some of the combination methods to combine closely spaced modes.
What makes a response spectrum so useful is that the peak response of a single mode of a multi-dof model to a transient excitation can be computed from the peak response of a single dof oscillator of the same frequency. I’ve never lost a sense of wonder at this beautiful property of structural modes and it still interests me to think about questions like - At what location in my mode shape will I find this peak response? Because of this property of modes, every supplier of equipment or structure on a job site can perform a dynamic evaluation by a simple mode combination all using the same response spectrum, whether they are analyzing a fire hydrant or a “sky scraper.”
To summarize, you should do a response spectrum if you or someone else has created one for you. If you have a specification for the ground motion itself, do a harmonic, random vibration or transient analysis. If your spectrum has units of g2/hz do a Random Vibration analysis, which although referred to as a spectrum method is more like a harmonic sweep than a response spectrum An excellent reference on this topic is the book, “Response spectrum method in seismic analysis and design of structures” by Ajay Gupta.