A response spectrum is a plot of the peak response (acceleration, velocity, or displacement) of a single-degree-of-freedom system as a function of its natural period, for a given ground motion and damping ratio. It is the fundamental tool for characterizing earthquake ground motion and forms the basis of most seismic design spectra in modern building codes.
A response spectrum is a graphical representation of the maximum response of a family of single-degree-of-freedom (SDOF) oscillators β each with a different natural period but the same damping ratio β when subjected to a specific ground motion. The spectrum is typically plotted as acceleration, velocity, or displacement against period (or frequency). Because any linear multi-degree-of-freedom structure can be decomposed into independent modal SDOF systems, the response spectrum provides a direct link between ground motion characteristics and structural response.
The concept was introduced by Maurice Biot in the 1930s and popularized by George Housner in the 1940s and 1950s. It became the foundation of seismic design practice after the 1971 San Fernando earthquake, when it was recognized that peak ground acceleration alone was insufficient to characterize ground motion. Modern building codes β including ASCE 7, Eurocode 8, and the Iranian Standard 2800 β define their design forces through design response spectra, which are smoothed and amplified versions of site-specific response spectra.
The response spectrum is a statistical envelope, not a physical time history. Multiple ground motions with similar PGA values can produce very different spectra, particularly in the long-period range. For this reason, modern performance-based earthquake engineering often supplements the response spectrum with nonlinear time-history analysis for critical structures. The response spectrum also cannot capture the effects of duration, cyclic degradation, or the sequence of peaks β limitations that matter for structures with significant strength or stiffness deterioration. Despite these constraints, it remains the most widely used tool in earthquake engineering, both for design and for the interpretation of recorded ground motions.