Bulletin of Earthquake Engineering

, Volume 17, Issue 4, pp 1941–1960 | Cite as

Improving FEMA P-58 non-structural component fragility functions and loss predictions

  • Gemma CremenEmail author
  • Jack W. Baker
Original Research


Fragility functions are an important tool in earthquake engineering, used to compute the probabilities of different damage states as a function of seismic response. They can be developed for large systems like buildings and bridges, as well as for individual structural and non-structural components, such as those used in the FEMA P-58 Seismic Performance Assessment Procedure. There are currently a number of problems associated with some P-58 non-structural mechanical component fragility functions and related loss predictions, including non-convergence when fitting the fragility functions in some cases and non-monotonic loss predictions. In this study, we recommend improvements to these fragility functions and loss predictions. Firstly, we recommend using the maximum likelihood method to fit the fragility functions to the underlying empirical data. This mitigates the non-convergence problems when fitting and makes predictions that better align with damage observed in past events. To compute predicted losses for anchored mechanical components, it is necessary to additionally consider anchorage damage, which can be predicted using fragility functions based on building code provisions. We recommend refining the current FEMA P-58 method for predicting anchored mechanical component losses, such that component and anchorage damage are calculated directly according to their corresponding fragility functions. The proposed method yields more intuitive loss predictions that vary monotonically with anchorage capacity. It also leads to better predictions of losses relative to damage observed in previous events. If implemented, the recommendations made in this paper would enhance the FEMA P-58 Seismic Performance Assessment Procedure.


Non-structural components Fragility functions Loss predictions FEMA P-58 



We thank an anonymous reviewer for comments that improved the quality of this manuscript. We appreciate helpful feedback received from Dustin Cook, Curt Haselton, Katie Fitzgerald Wade, and Brendon Bradley. We thank Farzad Naeim for providing a copy of the SMIP Information System, and for feedback on typical equipment installation conditions.


  1. Agresti A (2013) Categorical data analysis. Wiley, HobokenGoogle Scholar
  2. Akkar S, Sucuoğlu H, Yakut A (2005) Displacement-based fragility functions for low-and mid-rise ordinary concrete buildings. Earthq Spectra 21(4):901–927CrossRefGoogle Scholar
  3. ASCE (2010) Minimum design loads for buildings and other structures, ASCE/SEI 7–10. American Society of Civil Engineers, RestonGoogle Scholar
  4. ASCE (2016) Minimum design loads for buildings and other structures, ASCE/SEI 7–16. American Society of Civil Engineers, RestonGoogle Scholar
  5. Badillo-Almaraz H, Whittaker AS, Reinhorn AM (2007) Seismic fragility of suspended ceiling systems. Earthq Spectra 23(1):21–40CrossRefGoogle Scholar
  6. Baker JW (2015) Efficient analytical fragility function fitting using dynamic structural analysis. Earthq Spectra 31(1):579–599CrossRefGoogle Scholar
  7. Bradley BA (2010) Epistemic uncertainties in component fragility functions. Earthq Spectra 26(1):41–62CrossRefGoogle Scholar
  8. Choe DE, Gardoni P, Rosowsky D, Haukaas T (2008) Probabilistic capacity models and seismic fragility estimates for RC columns subject to corrosion. Reliab Eng Syst Saf 93(3):383–393CrossRefGoogle Scholar
  9. Colombi M, Borzi B, Crowley H, Onida M, Meroni F, Pinho R (2008) Deriving vulnerability curves using Italian earthquake damage data. Bull Earthq Eng 6(3):485–504CrossRefGoogle Scholar
  10. FEMA (2012a) FEMA P-58-1: seismic performance assessment of buildings. Methodology, vol 1. Federal Emergency Management Agency, WashingtonGoogle Scholar
  11. FEMA (2012b) FEMA P-58-2: seismic performance assessment of buildings. Implementation guide, vol 2. Federal Emergency Management Agency, WashingtonGoogle Scholar
  12. Gardoni P, Der Kiureghian A, Mosalam KM (2002) Probabilistic capacity models and fragility estimates for reinforced concrete columns based on experimental observations. J Eng Mech 128(10):1024–1038CrossRefGoogle Scholar
  13. Huo Y, Zhang J (2012) Effects of pounding and skewness on seismic responses of typical multispan highway bridges using the fragility function method. J Bridge Eng 18(6):499–515CrossRefGoogle Scholar
  14. Kaufman RL (2013) Heteroskedasticity in regression: detection and correction, vol 172. Sage Publications, Thousand OaksCrossRefGoogle Scholar
  15. Kennedy R, Ravindra M (1984) Seismic fragilities for nuclear power plant risk studies. Nucl Eng Des 79(1):47–68CrossRefGoogle Scholar
  16. Lallemant D, Kiremidjian A, Burton H (2015) Statistical procedures for developing earthquake damage fragility curves. Earthq Eng Struct Dyn 44(9):1373–1389CrossRefGoogle Scholar
  17. Lopez Garcia D, Soong T (2003) Sliding fragility of block-type non-structural components. Part 1: unrestrained components. Earthq Eng Struct Dyn 32(1):111–129CrossRefGoogle Scholar
  18. Mosleh A, Apostolakis G (1986) The assessment of probability distributions from expert opinions with an application to seismic fragility curves. Risk Anal 6(4):447–461CrossRefGoogle Scholar
  19. Naeim F (1997) Seismic performance of extensively instrumented buildings an interactive information system. CSMIP reportGoogle Scholar
  20. Naeim F, Lobo R (1998) Performance of non-structural components during the January 17, 1994 Northridge Earthquake—case studies of six instrumented multistory buildings. In: Proceedings of the seminar on seismic design, retrofit, and performance of nonstructural components, ATC-29-1, San Francisco, CA, Citeseer, pp 107–119Google Scholar
  21. Nielson BG (2005) Analytical fragility curves for highway bridges in moderate seismic zones. Ph.D. thesis, Georgia Institute of TechnologyGoogle Scholar
  22. Pagni CA, Lowes LN (2006) Fragility functions for older reinforced concrete beam-column joints. Earthq Spectra 22(1):215–238CrossRefGoogle Scholar
  23. Porter K (2011) Fragility of mechanical, electrical and plumbing equipment considering installation conditions. BD-3.9.10. Federal Emergency Management Agency, WashingtonGoogle Scholar
  24. Porter K, Kennedy R, Bachman R (2007) Creating fragility functions for performance-based earthquake engineering. Earthq Spectra 23(2):471–489CrossRefGoogle Scholar
  25. Porter KA, Kiremidjian AS, LeGrue JS (2001) Assembly-based vulnerability of buildings and its use in performance evaluation. Earthq spectra 17(2):291–312CrossRefGoogle Scholar
  26. Rojahn C (2000) Database on the performance of structures near strong-motion recordings: 1994 Northridge, California, earthquake, vol 38. The Applied Technology Council, Redwood CityGoogle Scholar
  27. Rossetto T, Elnashai A (2005) A new analytical procedure for the derivation of displacement-based vulnerability curves for populations of RC structures. Eng Struct 27(3):397–409CrossRefGoogle Scholar
  28. Rota M, Penna A, Strobbia C, Magenes G (2008) Direct derivation of fragility curves from Italian post-earthquake survey data. In: Proceedings of the 14th world conference on earthquake engineering, Beijing, China, October, pp 12–17Google Scholar
  29. Rota M, Penna A, Magenes G (2010) A methodology for deriving analytical fragility curves for masonry buildings based on stochastic nonlinear analyses. Eng Struct 32(5):1312–1323CrossRefGoogle Scholar
  30. Sarabandi P, Pachakis D, King S, Kiremidjian A (2004) Empirical fragility functions from recent earthquakes. In: Proceedings of the 13th world conference on earthquake engineering, Vancouver, BC, Canada, August. Paper No. 1211Google Scholar
  31. Shinozuka M, Feng MQ, Lee J, Naganuma T (2000) Statistical analysis of fragility curves. J Eng Mech 126(12):1224–1231CrossRefGoogle Scholar
  32. Singhal A, Kiremidjian AS (1996) Method for probabilistic evaluation of seismic structural damage. J Struct Eng 122(12):1459–1467CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Stanford UniversityStanfordUSA
  2. 2.Stanford UniversityStanfordUSA

Personalised recommendations