Skip to main content
SpringerLink
Log in

Analytical evaluation of structural component limit state probabilities

  • Original Research Paper
  • Published:
Bulletin of Earthquake Engineering Aims and scope Submit manuscript

Abstract

Probabilistic seismic assessment requires extensive computational effort resulting from variability both in input ground motions and mechanical properties. Nonetheless, such methodologies are of considerable importance, namely for pre-earthquake disaster planning or development of retrofitting programs. A framework for the analytical definition of closed form expressions for exceedance probabilities of structural component limit states, defined by limit values of structural response parameters, is proposed herein. The definition of these expressions is based on the probabilistic representation of the ground motion intensity and on the establishment of suitable expressions characterizing the evolution of structural demand with increasing earthquake intensity. Distinction is made between deformation-based and force-based structural parameters in the definition of such relations. Within the proposed framework, the limit states are defined by single deterministic thresholds of structural response quantities at the component level, as defined in structural codes. Different approaches are also discussed to account for the randomness of the mechanical properties and ground motion input within the proposed methodology. An application of the assessment of different limit state probabilities of members from a reinforced concrete building is presented, for which limit states and limit state capacities are defined according to the upcoming Part 3 of the Eurocode 8. Although the presented application only deals with member chord rotation and shear force limit state probabilities, the proposed methodology can be generalized to other deformation-based and force-based structural parameters.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Ambraseys N, Smit P, Sigbjornsson R, Suhadolc P, Margaris B (2002) Internet-Site for European strong-motion data. Euro Comm Research-Directorate General, Environ Climate Programme

  • Arêde A, Pinto AV (1996) Reinforced concrete global section modelling: definition of skeleton curves. Special Publication No.I.96.36. Institute for Systems, Informatics and Safety, Joint Research Center, Ispra, Italy

  • Aslani H (2005) Probabilistic earthquake loss estimation and loss disaggregation in buildings. PhD Thesis, John A. Blume Earthquake Engineering Center, Dept. of Civil and Environmental Engineering, Stanford University, Stanford, CA

  • ATC (1985) ATC-13: Earthquake damage evaluation data for California. Applied Technology Council, Redwood City, CA, USA

  • Au SK, Beck JL (2003) Subset simulation and its application to seismic risk based on dynamic analysis. J Eng Mech 129(8): 901–917

    Article  Google Scholar 

  • Carvalho EC, Coelho E, Campos-Costa A (1999) Preparation of the full-scale tests on reinforced concrete frames—Characteristics of the test specimens, materials and testing conditions. ICONS report, Innovative Seismic Design Concepts for New and Existing Structures, European TMR Network, LNEC, Lisbon

  • Castillo E (1988) Extreme value theory in engineering. Statistical Modeling and Decision Science. Academic Press, New York

    Google Scholar 

  • CEB (1996) RC frames under earthquake loading. Bulletin no. 231, Comité Euro-International du Béton

  • CEN (2004) European Committee for Standardization, Eurocode 8: Design of structures for earthquake resistance, Part 3: Assessment and retrofitting of buildings. Final draft

  • Cornell CA (1968) Engineering risk analysis. Bull Seismol Soc Am 58(5): 1583–1606

    Google Scholar 

  • Cornell CA, Jalayer F, Hamburger R, Foutch D (2000) Probabilistic basis for the 2000 SAC/FEMA steel moment frame guidelines. J Eng Mech 128(4): 526–533

    Google Scholar 

  • Der Kiureghian A (1996) Structural reliability methods for seismic safety assessment: a review. Eng Struct 18(6): 412–426

    Article  Google Scholar 

  • Dymiotis C, Kappos AJ, Chryssanthopoulos MC (1999) Seismic reliability of R/C frames with uncertain drift and member capacity. J Struct Eng 125(9): 1038–1047

    Article  Google Scholar 

  • Franchin P (2004) Reliability of uncertain inelastic structures under earthquake excitation. J Eng Mech 130(2): 180–191

    Article  Google Scholar 

  • Giannini R (2000) MATHazard: a program for seismic hazard analysis. University of Rome

  • Giovenale P, Cornell CA, Esteva L (2004) Comparing the adequacy of alternative ground motion intensity measures for the estimation of structural responses. Earthquake Eng Struct Dyn 33(8): 951–979

    Article  Google Scholar 

  • Hadjian AH (2002) A general framework for risk-consistent seismic design. Earthquake Eng Struct Dyn 31(3): 601–626

    Article  Google Scholar 

  • Haukaas T (2003) Finite element reliability and sensitivity analysis of hysteretic degrading structures. PhD Thesis, University of California, Berkeley, California

  • Hendawi S, Frangopol D (1994) System reliability and redundancy in structural design and evaluation. Struct Safety 16(1–2): 47–71

    Article  Google Scholar 

  • Jalayer F, Cornell CA (2000) Technical framework for probability-based demand and capacity factor (DCFD) seismic formats. RMS Technical Report No.43 to the PEER Center, Department of Civil and Environmental Engineering, Stanford University, Stanford, CA

  • Kennedy RC, Short SA (1994) Basis for seismic provisions of DOE-STD-1020. UCRLCR-111478 and BNL-52418, Lawrence Livermore National Laboratory and Brookhaven National Laboratory Report

  • Krawinkler H, Zareian F, Medina RA, Ibarra L (2006) Decision support for conceptual performance-based design. Earthquake Eng Struct Dyn 35(1): 115–133

    Article  Google Scholar 

  • Kurama YC, Farrow KT (2003) Ground motion scaling methods for different site conditions and structure characteristics. Earthquake Eng Struct Dyn 32(15): 2425–2450

    Article  Google Scholar 

  • LessLoss (2004) LessLoss—Risk mitigation for earthquakes and landslides. Integrated Research & Development Project of the European Commission, Contract No. GOCE-CT-2003–505448. http://www.lessloss.org/. Cited 22 Oct 2006

  • LessLoss (2006) LessLoss—Risk Mitigation for Earthquakes and Landslides. Applications of probabilistic seismic assessment methods to selected case studies. Technical Report No. 78. Integrated Research & Development Project of the European Commission

  • Luco N, Bazzurro P (2004) Effects of earthquake record scaling on nonlinear structural response. Report for PEER Center Lifelines Program—Task 1G00, Pacific Earthquake Engineering Research Center, UC Berkeley, Berkeley, California

  • Lupoi A, Franchin P, Schotanus MIJ (2003) Seismic risk evaluation of RC bridge structures. Earthquake Eng Struct Dyn 32(8): 1275–1290

    Article  Google Scholar 

  • Matlab (2006) The MathWorks, Inc. http://www.mathworks.com/. Cited 22 Oct 2006

  • McGuire RK (1976) A FORTRAN computer program for seismic risk analysis. United States Department of the Interior Geological Survey

  • McKay MD, Beckman RJ, Conover WJ (1979) A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21(2): 239–245

    Article  Google Scholar 

  • Medina RA, Krawinkler H (2004) Seismic demands for nondeteriorating frame structures and their dependence on ground motions. Report PEER 2003/15, Pacific Earthquake Engineering Research Center, UC Berkeley, Berkeley, California

  • Moses F (1990) New directions and research needs in system reliability. Struct Safety 7(2–4): 93–100

    Article  Google Scholar 

  • Pinto PE (2001) Reliability methods in earthquake engineering. Progress in Struct Eng Mate 3(1): 76–85

    Article  Google Scholar 

  • Pinto PE, Giannini R, Franchin P (2004) Seismic reliability analysis of structures. IUSS Press Istituto Universitario di Studi Superiori di Pavia: Pavia, Italy

  • Rocha P, Delgado P, Costa A, Delgado R (2004) Seismic retrofit of RC frames. Comput Struct 82(17–19): 1523–1534

    Article  Google Scholar 

  • Sabetta F, Pugliese A (1996) Estimation of response spectra and simulation of nonstationary earthquake ground motions. Bull Seismol Soc Am 86(2): 337–352

    Google Scholar 

  • Schotanus MIJ, Franchin P, Lupoi A, Pinto PE (2004) Seismic fragility analysis of 3D structures. Struct Safety 26(4): 421–441

    Article  Google Scholar 

  • Singhal A, Kiremidjian A (1998) Bayesian updating of fragilities with application to RC frames. J Struct Eng 124(8): 922–929

    Article  Google Scholar 

  • Shinozuka M, Feng MQ, Lee J, Naganuma T (2000) Statistical analysis of fragility curves. J Eng Mech 126(12): 1224–1231

    Article  Google Scholar 

  • Shome N, Cornell CA, Bazzurro P, Carballo IE (1998) Earthquakes, records and non-linear responses. Earthquake Spectra 14(3): 469–500

    Article  Google Scholar 

  • Stewart JP, Chiou SJ, Bray JD, Graves RW, Somerville PG, Abrahamson NA (2001) Ground motion evaluation procedures for performance-based design. Report PEER-2001/09, Pacific Earthquake Engineering Research Center, UC Berkeley, Berkeley, California

  • Thoft-Christensen P, Murotsu Y (1986) Application of structural systems reliability theory. Springer Verlag, Berlin, Germany

    Google Scholar 

  • Vamvatsikos D, Cornell CA (2002) Incremental dynamic analysis. Earthquake Eng Struct Dyn 31(3): 491–514

    Article  Google Scholar 

  • Varum H (1997) Numerical model for the seismic analysis of reinforced concrete plane frames. MSc Thesis, Faculty of Engineering of the University of Porto, Porto, Portugal (in Portuguese)

  • Zwillinger D, Kokoska S (2000) CRC standard probability and statistics tables and formulae. Chapman & Hall/CRC

Download references

Author information

Authors and Affiliations

  1. Civil Engineering Department, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal

    Xavier Romão, João Guedes & Raimundo Delgado

  2. Autonomous Civil Engineering Section, Universidade de Aveiro, Campus Universitário de Santiago, 3810-193, Aveiro, Portugal

    Aníbal Costa

Authors
  1. Xavier Romão
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. João Guedes
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Aníbal Costa
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Raimundo Delgado
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xavier Romão.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Romão, X., Guedes, J., Costa, A. et al. Analytical evaluation of structural component limit state probabilities. Bull Earthquake Eng 6, 309–333 (2008). https://doi.org/10.1007/s10518-007-9056-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10518-007-9056-z

Keywords

Search

Navigation