Response Spectrum - max acceleration

[Solar88]

Hey Guys,

I hope you can help me.

I have got a comprehension question about the development of a response spectrum. I have modeled a SDOF-System (with a natural frequency of 5 Hz) in sap2000 and stressed the system with a time-history-function.

The acceleration results of the single joint are less than die results in the response spectrum by 5 Hz. I have always thought that the maximum acceleration of the joint ist equal to the response spectrum acceleration by 5 Hz.


Please tell me when i made an error in reasoning. Thanks in advance

 

[stressed]

I don't follow your reasoning, and there's no way to know whether the time history function you used was in any way related to your response spectrum function and analysis.

 

[JoshPlumSE]

The response spectrum was developed from the same Time-History motion?

If so, then I would think they would match. What damping values are you using? Because the damping value assumed when creating the Response Spectra may not have matched what you set in your model.

Also, what Time-History motion are you using? And, are you SURE that this input record corresponds to the response spectra you used.

I ask because I recently ran into a similar issue and discovered that there are actually two slightly different El Centro N/S acceleration records floating out there! That threw me for a loop for awhile.

 

[Solar88]

thanks for your help,

my Time-History-Function is a user defined sine-function (period = 1) and my damping values are zero. My Load Case Type is FNA. After the analysis I looked at the max absolute joint acceleration and at the Response Spectrum Curves (by 5 Hz - natural frequency SDOF System). Both values were different.

 

[bkal]

You have not answered JushPlum's question fully. There are two key points in his email:
- the time history you used in your SDOF model has to be compatible with the spectrum you are using for comparison -is it?
- the spectrum values depend on the damping - you need to have the same damping valued in your SDOF model.

 

[Solar88]

that is the first time I use sap2000, so I don´t have much experience with the programm.

-what exactly do you mean with compatible? My time history function is a simple sine-function (T=1, Amplitude 1g)
-my damping values are zero (when I define the Load Case and when I display the response spectrum curve)

 

[bkal]

You said that you compared your SAP2000 results (acceleration) with the acceleration 'in the response spectrum'. What is this response spectrum, how did you get it?

In your case if you calculate a response spectrum from your input motion (sine function) it should be the same (similar) to the response spectrum from which you are reading acceleration for 5Hz.

I am guessing now (as I am not familiar with SAP2000) that the response spectrum from which you read at 5Hz, is actually a response spectrum calculated for the motion of the node (joint). If this is the case, you are not comparing likes with the likes. Peak acceleration of your joint should be compared to the response spectrum of the input motion (sine function) at its natural frequency, and not the response spectrum of the joint.

 

[Solar88]

thank you for your help bkal,

I get my response spectrum after the FNA. It is the response spectrum from the joint resulting from the input motion (sine function). I compare the value of this response spectrum at 5Hz with the value of the max absolute acceleration of the joint and they are not equal.

Is this comparison wrong?

 

[bkal]

If I understand it correctly, it is wrong. You should be comparing the peak acceleration of your joint with the response spectrum calculated from the input motion exciting you SDOF (i.e. your sine function).

 

[Solar88]

yeah, I am not quite sure about my response spectrum comparison and guess that you are right. Maybe it is a dumb question but how can I display the response spectrum from the input motion?

 

[bkal]

I am afraid that I do not know SAP2000 that well.

 

[JoshPlumSE]

There is a program (PRISM?) I used recently which converts a TH record into a response spectra. It took me awhile to find it, though it was pretty easy to use. I'll see if I can find a link for it...

http://sem.inha.ac.kr/prism/

Geared, of course, for converting a seismic record into a response spectra. But, if your input motion is a sine wave, then it should work convert that as well.