Response Spectrum Analysis

Accelerograms of an earthquake

Main Features

What it is?

A Response Spectrum is a plot of the peak or steady-state response (displacement, velocity or acceleration) of a series of oscillators of varying natural frequency, that are forced into motion by the same base vibration or shock. The resulting plot can then be used to pick off the response of any linear system, given its natural frequency of oscillation. One such use is in assessing the peak response of buildings or piping systems to earthquakes.

In earthquakes, the accelerations in each axis recorded by the accelerometers are mathematically treated and converted into Acceleration Vs Frequency response spectra.

Response Spectrum analysis allows a complex system to be broken down into many simple systems that vibrate at a single frequency, its natural frequency. And apply the curve Acceleration Vs Frequency of the response spectrum to each one of them so that, when combining them, we find the global response.

In tall structures the Response Spectra in each direction are usually different.


AutoPIPE can apply up to 50 response spectra to a piping model.

The spectrum response analyses that can be performed with AutoPIPE are:

Multiple Response Spectra

For multiple spectra, groups of supports are defined and the spectra are applied to each group on each axis.

Selecting the supports for each group is simple as the Elevation Support Selection Tool can be used.

Normally the ground level has a base spectrum calculated according to the standard and the following levels must be calculated based on the structure and for each direction.

AutoPIPE will automatically create the equations for stresses according to the standard you are using.

Assignment of displacements for SAM analysis


In case the piping system is supported by two or more structures, an analysis with the movement of the supports (SAM) must be additionally performed and combined with the multiple spectrum analysis.

SAM is a static analysis based on the deformations caused by the movement of the supports. It is very important to do it whenever the pipes are supported since the structures will have different natural modes of vibration and therefore, they will move in a non-solidary way.

Multiple Spectral Analysis of a Combined Pipe and Pipe Rack System