Question 1

What is a seismic response spectrum?

Accepted Answer

A seismic response spectrum plots the maximum response (acceleration Sa, velocity Sv, or displacement Sd) of single-degree-of-freedom (SDOF) oscillators with varying natural periods subjected to the same ground motion. Structural engineers read the Sa value at their building's natural period T and calculate the equivalent static force F = Sa × m for seismic design. It is the foundational tool in earthquake engineering per ASCE/SEI 7 and ISO 3010.

Question 2

How does damping ratio affect the response spectrum?

Accepted Answer

Higher damping reduces spectral values. Using the damping correction factor η = √(10/(5+ζ×100)), a structure with ζ=20% (base-isolated equivalent) has spectral accelerations approximately 50–60% lower than a ζ=5% reference. Typical design damping ratios are 2% for steel frames, 5% for reinforced concrete, and 20–30% for seismically isolated structures. The reduction is most pronounced in the acceleration-controlled plateau region of the spectrum.

Question 3

What is the difference between Sa, Sv, and Sd spectra?

Accepted Answer

Sa (spectral acceleration), Sv (spectral velocity), and Sd (spectral displacement) are interrelated through the natural period T: Sv = Sa·T/(2π) and Sd = Sa·(T/2π)². For example, at T=1 s and Sa=5 m/s², we get Sv≈0.796 m/s and Sd≈0.127 m. Sa is used for force calculation in superstructure design; Sd is critical for base isolation design where large relative displacements must be accommodated by isolation bearings.

Question 4

How does soil class affect the response spectrum shape?

Accepted Answer

Soil class modifies both the spectral amplitude and the dominant period range. Type I (rock/stiff soil) applies a factor of 0.8 and favors short-period response. Type II (normal soil) is the reference at factor 1.0. Type III (soft soil) amplifies the spectrum by factor 1.4 and shifts the peak toward longer periods. Tall buildings with long natural periods (T > 2 s) are particularly vulnerable on soft soil because the spectral values remain elevated in the long-period range.

Seismic Response Spectrum Calculator

Theory Notes — How to Read a Response Spectrum