A Probability-based Approach for the Definition of the Expected Seismic Damage Evaluated with Non-linear Time-History Analyses

ABSTRACT The seismic damage evaluated through Nonlinear Time-History Analyses is significantly affected by the response quantity chosen to represent the seismic responses. Starting from the theory of tolerance regions, a generic upper limit of the seismic responses is proposed. The method is applied to a reinforced concrete structure subjected to different record combinations. For each considered damage index and record combination, the upper limit damage is compared with the average value suggested by seismic codes. The proposed method yields a higher seismic damage than the average response and an increase in the damage indices as the number of records decreases.

[1]  Aníbal Costa,et al.  Assessment of the Statistical Distributions of Structural Demand Under Earthquake Loading , 2011 .

[2]  Derek Bissell,et al.  Sampling Inspection in Statistical Quality Control. , 1977 .

[3]  S. S. Wilks Determination of Sample Sizes for Setting Tolerance Limits , 1941 .

[4]  Zdeněk P. Bažant,et al.  Mechanics of solid materials , 1992 .

[5]  K. Krishnamoorthy,et al.  Handbook of Statistical Distributions with Applications, Second Edition , 2015 .

[6]  E. Miranda,et al.  Probabilistic estimation of residual drift demands for seismic assessment of multi-story framed buildings , 2010 .

[7]  A. Ang,et al.  Seismic Damage Analysis of Reinforced Concrete Buildings , 1985 .

[8]  Gaetano Manfredi,et al.  The use of damage functionals in earthquake engineering: A comparison between different methods , 1993 .

[9]  Lucia Luzi,et al.  ITACA (ITalian ACcelerometric Archive): A Web Portal for the Dissemination of Italian Strong-motion Data , 2008 .

[10]  Vitelmo V. Bertero,et al.  An Evaluation of Inelastic Seismic Design Spectra , 1981 .

[11]  L. Ibarra Global collapse of frame structures under seismic excitations , 2003 .

[12]  Y Bozorgnia,et al.  IMPROVED DAMAGE PARAMETERS FOR POST-EARTHQUAKE APPLICATIONS , 2002 .

[13]  Y. K. Wen,et al.  Method of Reliability-Based Seismic Design. I: Equivalent Nonlinear Systems , 1997 .

[14]  Ahmet S. Cakmak,et al.  Evaluation of Seismic Damage Indices for Reinforced Concrete Structures , 1990 .

[15]  Fatemeh Jalayer,et al.  The probabilistic basis for the 2000 SAC/FEMA steel moment frame guidelines , 2002 .

[16]  Nicolas Luco,et al.  EFFECTS OF CONNECTION FRACTURES ON SMRF SEISMIC DRIFT DEMANDS , 2000 .

[17]  J. Mander,et al.  Theoretical stress strain model for confined concrete , 1988 .

[18]  Peter Fajfar,et al.  Equivalent ductility factors, taking into account low‐cycle fatigue , 1992 .

[19]  D. Brillinger,et al.  Handbook of methods of applied statistics , 1967 .

[20]  C. Allin Cornell,et al.  Probabilistic Basis for 2000 SAC Federal Emergency Management Agency Steel Moment Frame Guidelines , 2002 .

[21]  D. G. Beech,et al.  Handbook of Statistical Tables. , 1962 .

[22]  Bruce R. Ellingwood,et al.  Probability-based codified design for earthquakes , 1994 .

[23]  Masanobu Shinozuka,et al.  Seismic Damage Assessment of Reinforced Concrete Members , 1987 .

[24]  Homayoon E. Estekanchi,et al.  CORRELATION BETWEEN STRUCTURAL PERFORMANCE LEVELS AND DAMAGE INDEXES IN STEEL FRAMES SUBJECTED TO EARTHQUAKES , 2009 .

[25]  Andreas J. Kappos,et al.  Seismic damage indices for RC buildings: evaluation of concepts and procedures , 1997 .

[26]  Kabir Sadeghi Energy based structural damage index based on nonlinear numerical simulation of structures subjected to oriented lateral cyclic loading , 2011 .

[27]  Martin S. Williams,et al.  Seismic Damage Indices for Concrete Structures: A State-of-the-Art Review , 1995 .

[28]  J. Douglas,et al.  Internet site for European strong-motion data , 2004 .

[29]  M. Menegotto Method of Analysis for Cyclically Loaded R. C. Plane Frames Including Changes in Geometry and Non-Elastic Behavior of Elements under Combined Normal Force and Bending , 1973 .

[30]  Julio J. Hernández,et al.  Structural Design for Multicomponent Seismic Motion , 2002 .

[31]  Jonathan P. Stewart,et al.  Response-history analysis for the design of new buildings: A fully revised chapter 16 methodology proposed for the 2015 NEHRP provisions and the ASCE/SEI 7-16 standard , 2014 .

[32]  W. G. Howe Two-Sided Tolerance Limits for Normal Populations—Some Improvements , 1969 .

[33]  J. Wolfowitz,et al.  Tolerance Limits for a Normal Distribution , 1946 .

[34]  C. Allin Cornell,et al.  Probabilistic seismic demand analysis of nonlinear structures , 1999 .

[35]  Enrico Spacone,et al.  FIBRE BEAM–COLUMN MODEL FOR NON‐LINEAR ANALYSIS OF R/C FRAMES: PART I. FORMULATION , 1996 .

[36]  S. S. Wilks Statistical Prediction with Special Reference to the Problem of Tolerance Limits , 1942 .

[37]  Sashi K. Kunnath,et al.  IDARC Version 3.0: A Program for the Inelastic Damage Analysis of Reinforced Concrete Structures , 1992 .

[38]  John Aitchison,et al.  Statistical Prediction Analysis , 1975 .

[39]  A. Ang,et al.  Mechanistic Seismic Damage Model for Reinforced Concrete , 1985 .

[40]  Robert L. Perry Sampling Inspection in Statistical Quality Control , 1979 .

[41]  C. Cornell,et al.  Disaggregation of seismic hazard , 1999 .

[42]  Enrico Spacone,et al.  Seismic Demand Sensitivity of Reinforced Concrete Structures to Ground Motion Selection and Modification Methods , 2014 .

[43]  Sonia E. Ruiz,et al.  Energy-based damage index for steel structures , 2010 .

[44]  Edward Cohen,et al.  Minimum Design Loads for Buildings and Other Structures , 1990 .

[45]  J. K. Ord,et al.  Statistical Tolerance Regions: Classical and Bayesian , 1971 .

[46]  K. Krishnamoorthy Handbook of statistical distributions with applications , 2006 .

[47]  B. Bradley Design Seismic Demands from Seismic Response Analyses: A Probability-Based Approach , 2011 .

[48]  N. Null Minimum Design Loads for Buildings and Other Structures , 2003 .

[49]  Joseph Penzien,et al.  CHARACTERISTICS OF 3-DIMENSIONAL EARTHQUAKE GROUND MOTIONS , 1974 .

[50]  Fabrizio Mollaioli,et al.  Characterization of displacement demand for elastic and inelastic SDOF systems , 2003 .

[51]  Roberto Paolucci,et al.  Overview of the Italian strong motion database ITACA 1.0 , 2010 .

[52]  Gaetano Manfredi,et al.  Damage indices and damage measures , 2000 .

[53]  Abraham Wald,et al.  An Extension of Wilks' Method for Setting Tolerance Limits , 1943 .

[54]  J. Bommer,et al.  Relationships between Median Values and between Aleatory Variabilities for Different Definitions of the Horizontal Component of Motion , 2006 .