Response Spectrum Terminology
Key terms used in response spectrum analysis: spectral acceleration, spectral velocity, spectral displacement, ZPA, amplified region, rigid region and spectrum ordinates.
Core terms
- Spectral acceleration (Sa): the peak acceleration of a single-degree-of-freedom oscillator with a given natural frequency and damping subjected to the ground motion
- Spectral velocity (Sv): the peak velocity of the same oscillator; pseudo-velocity is Sv_approx = Sa / omega
- Spectral displacement (Sd): the peak displacement of the same oscillator; pseudo-displacement is Sd = Sa / omega^2
- Zero-period acceleration (ZPA): the spectral acceleration at very high frequencies, equal to the peak ground acceleration; the rigid response plateau
- Amplified region: the frequency band where the spectral acceleration exceeds the ZPA due to dynamic amplification
- Rigid region: the high-frequency region where the spectral acceleration equals the ZPA and the structure moves with the ground
Spectrum types
- Ground response spectrum (GRS): spectrum at the ground level, used for building analysis
- Floor response spectrum (FRS): spectrum at a floor elevation, used for equipment qualification; includes building amplification
- Design response spectrum: a smoothed, codified spectrum representing seismic hazard for a site; not tied to a specific earthquake
- Required response spectrum (RRS): the spectrum that must be enveloped during shake-table qualification
- Test response spectrum (TRS): the spectrum actually achieved by the shake-table input motion; must envelop the RRS
Spectrum shape
A typical response spectrum has three regions: at low frequencies (long periods), spectral displacement governs and acceleration increases with frequency; at intermediate frequencies, spectral acceleration reaches a peak (the amplified region); at high frequencies (short periods), spectral acceleration asymptotes to the ZPA (the rigid region). The shape depends on the seismic hazard, site conditions and damping.