Encyclopedia of Earthquake Engineering

Editors: Michael Beer, Ioannis A. Kougioumtzoglou, Edoardo Patelli, Ivan Siu-Kui Au

Conditional Spectra

Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-36197-5_386-1

Synonyms

Introduction

The conditional spectrum (CS) is a response spectrum that specifies the probability distribution of spectral accelerations, Sa, over a range of periods of vibration, Ti, conditioned on spectral acceleration at a conditioning period, T*, of interest. The conditional spectrum utilizes the correlations between spectral accelerations at different periods (e.g., Baker and Jayaram 2008) to compute the expected (logarithmic mean) response spectrum (Baker and Cornell 2006; Baker 2011) and additionally account for the variability (variance) of the response spectra (Jayaram et al. 2011; Lin et al. 2013a). Assuming the distribution of logarithmic spectral accelerations is multivariate normal (Jayaram and Baker 2008), then the first two moments (i.e., the means, standard deviations, and correlations) fully describe the conditional spectrum. The CS...

This is a preview of subscription content, log in to check access

References

  1. Abrahamson NA, Al Atik L (2010) Scenario spectra for design ground motions and risk calculation. In: 9th US National and 10th Canadian conference on earthquake engineering, Toronto, 12 pGoogle Scholar
  2. Abrahamson NA, Bozorgnia Y, Boore D, Atkinson G, Campbell K, Silva W, Chiou B, Idriss IM, Youngs R (2008) Comparisons of the NGA ground-motion relations. Earthq Spectra 24(1):45–66CrossRefGoogle Scholar
  3. ASCE (2010) Minimum design loads for buildings and other structures. ASCE 7–10. American Society of Civil Engineers/Structural Engineering Institute, RestonGoogle Scholar
  4. Baker JW (2011) Conditional mean spectrum: tool for ground-motion selection. J Struct Eng 137(3):322–331CrossRefGoogle Scholar
  5. Baker JW, Cornell CA (2006) Spectral shape, epsilon and record selection. Earthq Eng Struct Dyn 35(9):1077–1095CrossRefGoogle Scholar
  6. Baker JW, Jayaram N (2008) Correlation of spectral acceleration values from NGA ground motion models. Earthq Spectra 24(1):299–317CrossRefGoogle Scholar
  7. Bradley BA (2010) A generalized conditional intensity measure approach and holistic ground-motion selection. Earthq Eng Struct Dyn 39(12):1321–1342Google Scholar
  8. Bradley BA (2012) A ground motion selection algorithm based on the generalized conditional intensity measure approach. Soil Dyn Earthq Eng 40:48–61CrossRefGoogle Scholar
  9. Carlton B, Abrahamson N (2014) Issues and approaches for implementing conditional mean spectra in practice. Bull Seismol Soc Am 104(1):503–512Google Scholar
  10. Cornell CA (1968) Engineering seismic risk analysis. Bull Seismol Soc Am 58(5):1583–1606Google Scholar
  11. Cornell CA, Krawinkler H (2000) Progress and challenges in seismic performance assessment. PEER Center News 3(2):1–3Google Scholar
  12. Gulerce Z, Abrahamson NA (2011) Site-specific design spectra for vertical ground motion. Earthq Spectra 27(4):1023–1047CrossRefGoogle Scholar
  13. Haselton CB, Deierlein GG (2007) Assessing seismic collapse safety of modern reinforced concrete frame buildings. Technical report, 2007/08. Pacific Earthquake Engineering Research Center, University of California, BerkeleyGoogle Scholar
  14. Jayaram N, Baker JW (2008) Statistical tests of the joint distribution of spectral acceleration values. Bull Seismol Soc Am 98(5):2213–2243CrossRefGoogle Scholar
  15. Jayaram N, Lin T, Baker JW (2011) A computationally efficient ground-motion selection algorithm for matching a target response spectrum mean and variance. Earthq Spectra 27(3):797–815CrossRefGoogle Scholar
  16. Katsanos EI, Sextos AG, Manolis GD (2010) Selection of earthquake ground motion records: a state-of-the-art review from a structural engineering perspective. Soil Dyn Earthq Eng 30(4):157–169CrossRefGoogle Scholar
  17. Lin T, Baker JW (2011) Probabilistic seismic hazard deaggregation of ground motion prediction models. In: 5th international conference on earthquake geotechnical engineering, Santiago, 12 pGoogle Scholar
  18. Lin T, Baker JW (2013) Introducing adaptive incremental dynamic analysis: a new tool or linking ground motion selection and structural response assessment. In: 11th international conference on structural safety and reliability. CRC Press, New York, 8 pGoogle Scholar
  19. Lin T, Harmsen SC, Baker JW, Luco N (2013a) Conditional Spectrum computation incorporating multiple causal earthquakes and ground-motion prediction models. Bull Seismol Soc Am 103(2A):1103–1116CrossRefGoogle Scholar
  20. Lin T, Haselton CB, Baker JW (2013b) Conditional spectrum-based ground motion selection. Part I: hazard consistency for risk-based assessments. Earthq Eng Struct Dyn 42(12):1847–1865CrossRefGoogle Scholar
  21. Lin T, Haselton CB, Baker JW (2013c) Conditional spectrum-based ground motion selection. Part II: intensity-based assessments and evaluation of alternative target spectra. Earthq Eng Struct Dyn 42(12):1867–1884CrossRefGoogle Scholar
  22. Loth C, Baker JW (2013) Reliability-based calibration of design seismic response spectra and structural acceptance criteria. In: 11th international conference on structural safety and reliability. CRC Press, New York, 8 pGoogle Scholar
  23. McGuire RK (1995) Probabilistic seismic hazard analysis and design earthquakes: closing the loop. Bull Seismol Soc Am 85(5):1275–1284Google Scholar
  24. Naeim F, Lew M (1995) On the use of design spectrum compatible time histories. Earthq Spectra 11(1):111–127CrossRefGoogle Scholar
  25. NIST (2011) Selecting and scaling earthquake ground motions for performing response-history analyses. NIST GCR 11-917-15 (ATC 82). Prepared by the NEHRP Consultants Joint Venture for the National Institute of Standards and Technology, Gaithersburg, 256 pGoogle Scholar
  26. Wang G (2011) A ground motion selection and modification method capturing response spectrum characteristics and variability of scenario earthquakes. Soil Dyn Earthq Eng 31(4):611–625CrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Civil, Construction and Environmental EngineeringMarquette UniversityMilwaukeeUSA
  2. 2.Stanford UniversityStanfordUSA