Skip to main content
SpringerLink
Log in

Seismic Fragility Functions Grounded on State-Based Philosophy: Application to Low to Midrise Steel Frame Buildings

  • Structural Engineering
  • Published:
KSCE Journal of Civil Engineering Aims and scope

Abstract

In this study, a new formulation for structural fragility function based on the theory of state-based philosophy (SBP) is introduced. In this innovative approach, gradual changes in stiffness (or flexibility) of the structure is considered as a firm base for describing changes in the state of the structure due to damage from various sources. In this study, the source of damage data is considered ground motions. After formulating state changes by using SBP theory, a new fragility function is proposed. Therefore, this new function is based on observations of various failure stages of the structure and, besides, it is organized specifically for the structural damage data. In order to prove the accuracy of this method, some special moment frames (SMFs) are modeled, and incremental dynamic analysis (IDA) is performed on them. Thus damage data are provided as initial input to the fragility function. After that, the final results of the SBP fragility function are compared with the results of the conventional methods of plotting the fragility curve, and lastly, the fragility curve’s accuracy obtained by using this new function is verified. This new fragility function is called ‘SBP fragility function’ and has some advantages over the ordinary fragility functions, which are discussed in this article.

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

Abbreviations

CDF:

Cumulative distribution function

CP:

Collapse prevention

CV:

Coefficient of variation

CVerr:

Cross-validation error

EDP:

Engineering demand parameter

Err:

Error

F R :

SBP fragility function

IDA:

Incremental dynamic analysis

IO:

Immediate occupancy

IM:

Intensity measure

k N :

Dimensionless stiffness of the structure (structural stiffness coefficient)

K S :

Dimensioned stiffness of the structure

k S :

Stiffness of the intact structure

LS:

Life safety

MDOF:

Multi degree of freedom

MLE:

Maximum likelihood estimation

MM:

Method of moments

NC:

Not considered

p :

First SBP power factor

PBEE:

Performance-based earthquake engineering

PDF:

Probability distribution function

PEER:

Pacific earthquake engineering research

PGA:

Peak ground acceleration

PGV:

Peak ground velocity

P(ξ):

First SBP auxiliary function

q :

Second SBP power factor

Q(ξ):

Second SBP auxiliary function

SBP:

State-based philosophy

SD:

Standard deviation

SDOF:

Single degree of freedom

SMF:

Special steel moment frame

St:

Story

SSE:

Sum of squared error

ξ :

State variable

References

  • AISC (2010) Seismic provisions for structural steel buildings. AISC 341-10, American Institute of Steel Construction, Chicago, IL, USA

    Google Scholar 

  • Baharvand A, Ranjbaran A (2020) A new method for developing seismic collapse fragility curves grounded on state-based philosophy. International Journal of Steel Structures 20:583–599, DOI: 10.1007/s13296-020-00308-6

    Google Scholar 

  • Baker J (2005) Fitting fragility functions to structural analysis data using maximum likelihood estimation. Standford University, Stanford, CA, USA, 1–10

    Google Scholar 

  • Barbato M, Petrini F, Unnikrishnan VU, Ciampoli M (2013) Performance-Based Hurricane Engineering (PBHE) framework. Structural Safety 45:24–35, DOI: 10.1016/j.strusafe.2013.07.002

    Google Scholar 

  • Beheshti Aval SB (2015) Seismic rehabilitation of existing building. Khaje Nasirodin Toosi Univercity, Tehran, Iran

    Google Scholar 

  • Bojórquez E, Iervolino I (2011) Spectral shape proxies and nonlinear structural response. Soil Dynamics and Earthquake Engineering 31(7):996–1008, DOI: 10.1016/j.soildyn.2011.03.006

    Google Scholar 

  • Bojórquez E, Iervolino I, Reyes-Salazar A, Ruiz SE (2012) Comparing vector-valued intensity measures for fragility analysis of steel framesin the case of narrow-band ground motions. Engineering Structures 45:472–480, DOI: 10.1016/j.engstruct.2012.07.002

    Google Scholar 

  • Buratti N (2012) A comparison of the performances of various ground-motion intensity measures. Proceedings of the 15th World Conferenceon Earthquake Engineering, September 24–28, Lisbon, Portugal, 24–28

    Google Scholar 

  • Cha Y-J, Bai J-W (2016) Seismic fragility estimates of a moment-resisting frame building controlled by MR dampers using performance-based design. Engineering Structures 116:192–202, DOI: 10.1016/j.engstruct.2016.02.055

    Google Scholar 

  • De Luca F, Verderame GM, Manfredi G (2015) Analytical versus observational fragilities: The case of Pettino (L’Aquila) damage data database. Bulletin of Earthquake Engineering 13(4):1161–1181, DOI: 10.1007/s10518-014-9658-1

    Google Scholar 

  • Deniz D, Song J, Hajjar JF (2018) Energy-based sidesway collapse fragilities for ductile structural frames under earthquake loadings. Engineering Structures 174:282–294, DOI: 10.1016/j.engstruct.2018.07.019

    Google Scholar 

  • Dumova-Jovanoska E (2000) Fragility curves for reinforced concrete structures in Skopje (Macedonia) region. Soil Dynamics and EarthquakeEngineering 19(6):455–466, DOI: 10.1016/S0267-7261(00)00017-8

    Google Scholar 

  • Elkady A, Lignos DG (2014) Modeling of the composite action in fully restrained beam-to-column connections: Implications in the seismic design and collapse capacity of steel special moment frames. Earthquake Engineering & Structural Dynamics 43(13):1935–1954, DOI: 10.1002/eqe.2430

    Google Scholar 

  • FEMA (2000) Prestandard and commentary for the seismic rehabilitation of buildings. Federal Emergency Management Agency, Washington, DC, USA, 1–518

    Google Scholar 

  • FEMA (2009) Quantification of building seismic performance factors. FEMA P695, Federal Emergency Management Agency, Washington, DC, USA

    Google Scholar 

  • Ghosh S, Ghosh S, Chakraborty S (2017) Seismic fragility analysis in the probabilistic performance-based earthquake engineering framework:An overview. International Journal of Advances in Engineering Sciences and Applied Mathematics DOI: 10.1007/s12572-017-0200-y

    Google Scholar 

  • Hartloper A, Lignos D (2017) 11.29: Updates to the ASCE-41-13 provisions for the nonlinear modeling of steel wide-flange columns for performance-based earthquake engineering. ce/papers 1(2-3):3072–3081, DOI: 10.1002/cepa.359

    Google Scholar 

  • Huang Q, Gardoni P, Hurlebaus S (2010) Probabilistic seismic demand models and fragility estimates for reinforced concrete highway bridges with one single-column bent. Journal of Engineering Mechanics 136(11):1340–1353, DOI: 10.1061/(ASCE)EM.1943-7889.0000186

    Google Scholar 

  • Huang YN, Whittaker AS, Hamburger RO (2017) A simplified analysis procedure for performance-based earthquake engineering of buildings. Engineering Structures 150:719–735, DOI: 10.1016/j.engstruct.2017.07.048

    Google Scholar 

  • Ibarra LF, Medina RA, Krawinkler H (2005) Hysteretic models that incorporate strength and stiffness deterioration. Earthquake Engineeringand Structural Dynamics 34(12):1489–1511, DOI: 10.1002/eqe.495

    Google Scholar 

  • Inel M, Ozmen HB (2006) Effects of plastic hinge properties in nonlinearanalysis of reinforced concrete buildings. Engineering Structures 28(11):1494–1502, DOI: 10.1016/j.engstruct.2006.01.017

    Google Scholar 

  • Jeong SH, Elnashai AS (2007) Probabilistic fragility analysis parameterized by fundamental response quantities. Engineering Structures 29(6): 1238–1251, DOI: 10.1016/j.engstruct.2006.06.026

    Google Scholar 

  • Ji J, Elnashai AS, Kuchma DA (2009) Seismic fragility relationships of reinforced concrete high-rise buildings. Structural Design of Tall and Special Buildings 18(3):259–277, DOI: 10.1002/tal.408

    Google Scholar 

  • Kircher C, Deierlein G, Hooper J, Krawinkler H, Mahin S, Shing B, Wallace J (2010) Evaluation of the FEMA P-695 methodology for quantification of building seismic performance factors. NIST GCR 10-917-8, National Institute of Standards and Technology, Gaithersburg, MD, USA

    Google Scholar 

  • Kwag S, Gupta A (2018) Computationally efficient fragility assessment using equivalent elastic limit state and Bayesian updating. Computersand Structures 197:1–11, DOI: 10.1016/j.compstruc.2017.11.011

    Google Scholar 

  • Lallemant D, Kiremidjian A, Burton H (2015) Statistical procedures for developing earthquake damage fragility curves. Earthquake Engineering & Structural Dynamics 44(9):1373–1389, DOI: 10.1002/eqe.2522

    Google Scholar 

  • Lin T, Haselton CB, Baker JW (2013) Conditional spectrum-based ground motion selection. Part I: Hazard consistency for risk-based assessments. Earthquake Engineering and Structural Dynamics 42(12):1847–1865, DOI: 10.1002/eqe.2301

    Google Scholar 

  • Liu XS, Ning JG, Tan YL, Gu QH (2016) Damage constitutive model based on energy dissipation for intact rock subjected to cyclic loading. International Journal of Rock Mechanics and Mining Sciences 85:27–32, DOI: 10.1016/j.ijrmms.2016.03.003

    Google Scholar 

  • Málaga-Chuquitaype C, Elghazouli AY, Enache R (2016) Contribution of secondary frames to the mitigation of collapse in steel buildings subjected to extreme loads. Structure and Infrastructure Engineering 12(1):45–60, DOI: 10.1080/15732479.2014.994534

    Google Scholar 

  • Mazzoni S, McKenna F, Scott MH, Fenves GL (2006) The open system for earthquake engineering simulation (OpenSEES) user command-language manual

    Google Scholar 

  • Niño M, Ayala G, López S (2018) Uniform fragility spectra for the performance-based seismic design of structures considering variabilities in structural properties. Earthquake Engineering and Structural Dynamics 47(8):1742–1754, DOI: 10.1002/eqe.3038

    Google Scholar 

  • Patelli E, Beer M, Siu-Kui Au S-K, Kougioumtzoglou IA (2015) Encyclopedia of earthquake engineering. Springer, Berlin, Germany

    Google Scholar 

  • Pejovic J, Jankovic S (2016) Seismic fragility assessment for reinforced concrete high-rise buildings in Southern Euro-Mediterranean zone. Bulletin of Earthquake Engineering 14(1):185–212, DOI: 10.1007/s10518-015-9812-4

    Google Scholar 

  • Ranjbaran A, Ranjbaran M (2016) State functions: The milestone of fracture. Archive of Applied Mechanics 86(7):1311–1324, DOI: 10.1007/s00419-015-1115-3

    Google Scholar 

  • Ranjbaran A, Rousta H, Ranjbaran M, Ranjbaran M (2012) Dynamic stability of cracked columns; the stiffness reduction method. ScientiaIranica 20(1):57–64, DOI: 10.1016/j.scient.2012.11.005

    MATH  Google Scholar 

  • Ranjbaran A, Rousta H, Ranjbaran MO, Ranjbaran MA, Hashemi M, Moravej MT (2013) A necessary modification for the finite element analysis of cracked members detection, construction, and justification. Archive of Applied Mechanics 83(7):1087–1096, DOI: 10.1007/s00419-013-0736-7

    MATH  Google Scholar 

  • Sivaselvan MV, Reinhorn AM (2000) Hysteretic models for deterioratinginelastic structures. Journal of Engineering Mechanics 126(6):633–640, DOI: 10.1061/(ASCE)0733-9399(2000)126:6(633)

    Google Scholar 

  • Song JK, Pincheira JA (2000) Spectral displacement demands of stiffness-and strength-degrading systems. Earthquake Spectra 16(4):817–851, DOI: 10.1193/1.1586141

    Google Scholar 

  • Sugawara E, Nikaido H (2014) Properties of AdeABC and AdeIJK efflux systems of Acinetobacter baumannii compared with those of the AcrAB-TolC system of Escherichia coli. Antimicrobial Agents and Chemotherapy 58(12):7250–7257, DOI: 10.1128/AAC.03728-14

    Google Scholar 

  • Vamvatsikos D (2014) Accurate application and second-order improvementof SAC/FEMA probabilistic formats for seismic performance assessment. Journal of Structural Engineering 140(2):04013058, DOI: 10.1061/(ASCE)ST.1943-541X.0000774

    Google Scholar 

  • Vamvatsikos D, Cornell CA (2002) The incremental dynamic analysis and its application to performance-based earthquake engineering. Proceedings of the 12th European conference on earthquake engineering, September 9–13, London, UK

    Google Scholar 

  • Wu KC, Li B, Tsai KC (2011) The effects of explosive mass ratio on residual compressive capacity of contact blast damaged composite columns. Journal of Constructional Steel Research 67(4):602–612, DOI: 10.1016/j.jcsr.2010.12.001

    Google Scholar 

  • Yang TY, Moehle J, Stojadinovic B, Kiureghian A Der (2009) Seismic performance evaluation of facilities. Journal of Structural Engineering 135(10):1146–1154, DOI: 10.1061/(ASCE)0733-9445(2009)135:10 (1146)

    Google Scholar 

  • Zareian F, Krawinkler H (2012) Conceptual performance-based seismic design using building-level and story-level decision support system. Earthquake Engineering & Structural Dynamics 41(11):1439–1453, DOI: 10.1002/eqe.2218

    Google Scholar 

  • Zareian F, Medina RA (2010) A practical method for proper modeling of structural damping in inelastic plane structural systems. Computers & Structures 88(1–2):45–53, DOI: 10.1016/j.compstruc.2009.08.001

    Google Scholar 

  • Zentner I (2017) A general framework for the estimation of analytical fragility functions based on multivariate probability distributions. Structural Safety 64:54–61, DOI: 10.1016/j.strusafe.2016.09.003

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Civil and Environmental Engineering, Shiraz University, Shiraz, 8179976474, Iran

    Aref Baharvand & Abdolrasoul Ranjbaran

Authors
  1. Aref Baharvand
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Abdolrasoul Ranjbaran
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Aref Baharvand.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Baharvand, A., Ranjbaran, A. Seismic Fragility Functions Grounded on State-Based Philosophy: Application to Low to Midrise Steel Frame Buildings. KSCE J Civ Eng 24, 1787–1798 (2020). https://doi.org/10.1007/s12205-020-0350-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12205-020-0350-5

Keywords

Search

Navigation