HI,

you can do it by using flac 2d modeling software. flac recording any spectral response as a history for example velocity ; displacement and acceleration in any point you need ander your acceleration history you can also use a local damping or rayleigh damping to present your 5% dampening .you can also plot all records history in xls graphs.

good luck

@Zakaria Bouraoui

Hi

Although other software can do this procedure, I want to know the formula and numerical solutions ...

Thanks

Dear Ardalan,

Try using the method described in the article:

"Determination of Standard Response Spectra and Effective Peak Ground Accelerations for Seismic Design and Evaluation" (by Enrique E. Matheu, Don E. Yule, and Raju V. Kala)

Article attached.

Regards.

Erioni

The method in the paper recommended by Erion gives a nice, generic, approximate spectrum.  If you want the actual response spectrum for an actual time history of ground motion, then the Earthquake Engineering Research Institute published at very nice monograph on the topic.  The title is "Dynamics of Structures: A Primer."  The author is Anil K. Chopra. 1981 1st Edition and 2005 2nd Edition.  All the equations are in this book.