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Response-spectrum analysis (RSA) is a linear-dynamic statistical analysis method which measures the contribution from each natural mode of vibration to generate the likely maximum seismic response of an essentially elastic structure. Response-spectrum analysis provides insight into dynamic behavior by measuring pseudo-spectral acceleration, velocity, or displacement as a function of structural period for a given time history and level of damping. It is practical to envelope response spectra such that a smooth curve represents the peak response for each realization of structural period.

Response-spectrum analysis is useful for design decision-making because it relates structural type-selection to dynamic performance. Structures of shorter period experience greater acceleration, whereas those of longer period experience greater displacement. Structural performance objectives should be taken into account.


Damping and RSA:

  • RSA provides insight into damping application. A family of response curves may be developed for variable levels of damping. As damping increases, response spectra will shift downward.
  • The International Building Code (IBC) is based on 5% damping. This accounts for incidental damping from hysteretic behavior, which is not explicitly modeled during RSA.
  • Viscous dampers do not affect structural stiffness, therefore they are neither modeled during RSA, nor accounted for in the IBC provision for 5% damping.

Additional notes on RSA:

  • All response quantities are positive, therefore RSA is not suitable for torsional irregularity. A static lateral-load procedure is best for measuring accidental torsion. The same applies to uplift and compression during foundation design.
  • Modal response may be combined using SRSS, CQC, ABS, or GMC methods. CQC is best applied when periods are closely spaced, with cross-correlation between mode shapes. SRSS is suitable when periods differ by more than 10%.
  • Ritz vectors are recommended for analysis because this condensed and computationally-efficient formulation only identifies pertinent mode shapes which occur in the horizontal plane. Eigen vectors use the full stiffness and mass matrices, which also account for vertical modes. Eigen formulation is useful when considering floor vibration, out-of-plane vibration or shear-wall systems, locating modeling errors, etc.
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