DRAFT: US-JAPAN PBEE PAPER BY CORDOVA ... - PEER
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spectral acceleration is an accurate index for structures that respond elastically, this singleparameter does not reflect many of the aspects of earthquake ground motions that affect inelasticstiffness and strength degradation. An objective of this paper is to examine a new two-parameterhazard intensity index that can improve the accuracy of structural performance predictions basedon inelastic time history analyses. A related objective is the development of reliability-basedequations for interpreting the performance limit state to compare the effect of using a singleversus two-parameter intensity measure.The scope and approach of this paper is as follows. First, the general concepts of earthquakeground motion intensity measures are introduced, including an overview of traditional measuresand the development of attenuation functions for the new proposed index. Second, a series ofcase study buildings are introduced and analyzed to determine their collapse limit state usingincremented inelastic time-history analyses coupled with a post-earthquake stability analysis.Results of the case study analyses are used to calibrate the new earthquake intensity measure.Next, a probability-based assessment procedure is developed to describe the collapseperformance in terms of mean annual probability of exceedance and an equivalent load andresistance format. Finally, the probabilistic assessment procedure is demonstrated through anapplication to one of the case study buildings.2. HAZARD INTENSITY MEASURESTraditionally, building codes have quantified earthquake intensity as a function of either peakground motions (acceleration or velocity) or linear response spectrum quantities (acceleration,velocity, or displacement). As implied by their name, linear response spectrum quantities do agood job at characterizing earthquake effects in structures that respond elastically, but they donot necessarily capture inelastic behavior. More elaborate indices, which seek to improvecharacterization of earthquake ground motions, have been the subject of continuing studies. Forexample, Housner (1975) proposed combining spectral acceleration together with strong motionduration. More recently, Luco (2001) has proposed extending linear spectral quantities into thenonlinear realm through the use of inelastic spectral response demands. While they are generallymore accurate, one drawback of the nonlinear spectral values is that they imply a couplingbetween the earthquake hazard definition and the inelastic structural properties. This complicates2
development of seismic hazard maps for general use. Another topic of recent research concernsnear fault directivity effects and whether these warrant specialized treatment in earthquakehazard characterization (e.g., Alavi & Krawinkler 2000). These are just a few examples ofresearch to investigate the damaging features of earthquake ground motions and developimproved hazard intensity measures to represent these effects.Common to most studies of improved intensity measures is the goal to characterize groundmotion hazards in a statistically meaningful way for predicting structural performance. Thisimplies that the best intensity measures are those that result in the least record-to-recordvariability, measured with respect to a common intensity index, when evaluating structuralperformance to multiple earthquake records. Of course, even with the best ground motioncharacterization, uncertainties will persist in characterizing the geologic earthquake hazard andin simulating inelastic structural performance.αImproved Hazard Intensity Measure - S a (T 1 )R SaThe International Building Code (ICC 2000) and most other earthquake engineering designstandards in the United States define hazard intensity as the spectral acceleration of the groundmotion, typically calculated at the fundamental (first mode) period of the structure. A knownshortcoming of this measure is that it does not account for inelastic lengthening of the period asthe structure softens under stiffness degradation. As illustrated in the response spectra plots ofFig. 1, two ground motionscharacterized on the basis of their firstmodespectral response may result insignificantly different inelasticresponse, depending on the slope ofthe spectra at lengthened periods. Forexample, when normalized withrespect to S a (T 1 ), record #2 willinevitably produce larger inelasticdeformations than record #1. Thistrend is not accounted for in the singlespectral quantity, S a (T 1 ).3S aRecord #1S a (T 1 )Record #2As damage occursT 1T FS a (T F )T, PeriodFigure 1 – Effects of structural softening.
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development of seismic hazard maps for general use. Another topic of recent research concernsnear fault directivity effects and whether these warrant specialized treatment in earthquakehazard characterization (e.g., Alavi & Krawinkler 2000). These are just a few examples ofresearch to investigate the damaging features of earthquake ground motions and developimproved hazard intensity measures to represent these effects.Common to most studies of improved intensity measures is the goal to characterize groundmotion hazards in a statistically meaningful way for predicting structural performance. Thisimplies that the best intensity measures are those that result in the least record-to-recordvariability, measured with respect to a common intensity index, when evaluating structuralperformance to multiple earthquake records. Of course, even with the best ground motioncharacterization, uncertainties will persist in characterizing the geologic earthquake hazard andin simulating inelastic structural performance.αImproved Hazard Intensity Measure - S a (T 1 )R SaThe International Building Code (ICC 2000) and most other earthquake engineering designstandards in the United States define hazard intensity as the spectral acceleration of the groundmotion, typically calculated at the fundamental (first mode) period of the structure. A knownshortcoming of this measure is that it does not account for inelastic lengthening of the period asthe structure softens under stiffness degradation. As illustrated in the response spectra plots ofFig. 1, two ground motionscharacterized on the basis of their firstmodespectral response may result insignificantly different inelasticresponse, depending on the slope ofthe spectra at lengthened periods. Forexample, when normalized withrespect to S a (T 1 ), record #2 willinevitably produce larger inelasticdeformations than record #1. Thistrend is not accounted for in the singlespectral quantity, S a (T 1 ).3S aRecord #1S a (T 1 )Record #2As damage occursT 1T FS a (T F )T, PeriodFigure 1 – Effects of structural softening.
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