Response spectrum

A response spectrum is a plot of the peak response of single-degree-of-freedom oscillators, each with a different natural period but the same damping, to a given ground motion. Read at a building's period, it tells you the peak acceleration the building would experience if it behaved like that oscillator. It turns a complicated time history into one curve that designers can use directly.

Spectra from real records are jagged. Design spectra are smoothed envelopes of many records, normalised by peak ground acceleration and adjusted for site soil. They have a characteristic shape: a rise from the ground acceleration at zero period to a flat plateau at short periods, typically about 2.5 times the ground acceleration, then a decline roughly inversely with period. Soft soils extend the plateau to longer periods, because they amplify longer-period shaking.

The spectrum shows why tall, flexible buildings attract smaller accelerations than stiff, low ones, but larger displacements: spectral displacement equals spectral acceleration divided by the square of the circular frequency. Stiffening a building shortens its period, which can raise or lower its force depending on where it sits on the curve.

IS 1893 (Part 1) gives normalised design spectra for rock or hard soil, medium soil and soft soil at 5 percent damping, with factors for other damping values. The same spectrum serves the equivalent static method, at the fundamental period, and response spectrum analysis, at each modal period.