Probabilistic assessment of dynamic instability of frame structures under seismic excitations

Transcription

1 Probabilisic assessmen of dynamic insabiliy of frame srucures under seismic exciaions D. Deniz & J. Song Universiy of Illinois a Urbana-Champaign, Urbana, IL, USA J.F. Hajjar & T.H. Nguyen Norheasern Universiy, Boson, MA, USA ABSTRACT: Miigaion of collapses of srucural sysems caused by a srong earhquake shaking is crucial o reduce he poenial casualies, injuries and economic losses. Hence, accurae risk assessmen of srucural collapse under seismic exciaions is criical in effors o promoe hazard-resilience of he sociey. This paper summarizes he auhors recen effors for accurae predicion of srucural collapse wih sysemaic incorporaion of uncerainy. Compuaional simulaion models are developed for collapse es frames in he lieraure and validaed using experimenal daa. Through he validaed compuaional simulaions of collapse, alernaive collapse crieria are proposed in erms of dynamic insabiliy, i.e. he loss of he abiliy o susain he graviy loads. Using he new collapse crieria, key parameers ha govern collapse capaciy and collapse limi sae funcions are idenified for more effecive risk assessmen. A probabilisic framework is also being developed for sysemaic reamen of uncerainies in he ground moion ime hisories and for risk-informed design of frame srucures under earhquake hazards. 1 INTRODUCTION Hazard-resilience of a srucure can be defined as he abiliy o recover he full funcionaliy quickly afer a hazardous even. In effors o enhance he resilience of srucures agains earhquake hazards, collapse prevenion is hus considered one of he mos imporan objecives. Therefore, i has become crucial o undersand he causes and effecs of seismic collapse of srucures in order o develop key documens such as naional building codes, regional emergency response plans, and risk managemen sraegies. While numerous research effors are repored in he lieraure o esimae collapse capaciy of srucures, accurae predicion of srucural collapse wih sysemaic incorporaion of uncerainy sill remains elusive. This is mainly due o he lack of collapse crieria based on dynamic insabiliy of he srucure, which are needed o idenify he impac of uncerainies in earhquake loads on he dynamic insabiliy. The incremenal dynamic analysis (IDA) approach (Vamvasikos & Cornell 2002, 2004, Zareian & Krawinkler 2007, Liel e al. 2009), and a similar approach adoped by a recen projec of he Applied Technology Council (ATC-63, 2009) are considered sae-of-he-ar approaches o accoun for he uncerainy in nonlinear dynamic response, including collapse predicion. However, here have been no horough invesigaions using validaed compuaional simulaions regarding he impacs of a srucural model selecion and he seleced se of he ground moions on he predicions of collapse capaciy, and poenial conribuions of various performance measures or predicive parameers o collapse predicions. The IDA-based approach idenifies he collapse capaciy of a srucural sysem for a given earhquake ground moion based on he behavior of he IDA curve, which is he relaionship beween an engineering demand parameer (EDP) (e.g., maximum iner-sory drif raio) and an inensiy measure (IM) (e.g., specral acceleraion of an earhquake ground moion) idenified by nonlinear dynamic analyses a incremenally increased inensiy levels. The main premise of he approach is ha he srucural sysem collapses when he IDA curve becomes almos fla, i.e. a sligh increase in IM causes an exceedingly large increase in EDP. However, he IDA curve could flaen due o large residual EDPs and hus may no necessarily indicae he inabiliy o susain graviy loads. I is also noed ha mos of he recen research effors based on he IDA-based approach used only one EDP (mosly maximum sory drif raio) while one migh need alernaive EDP or

2 muliple EDPs o predic he collapse more accuraely. I is also noeworhy ha he collapse capaciy of a srucure evaluaed by he IDA-approach may be sensiive o a paricular selecion of ground moions as well as possible chaoic behavior of he IDA curve such as srucural resurrecion. Alhough some deerminisic rules have been proposed o handle such unusual behaviors of IDA (Vamvasikos & Cornell 2002, 2004), i appears ha here is a need for developing collapse crieria based on simulaed collapse phenomena and a sysemaic procedure o idenify impac of uncerainies in ground moions on he collapse capaciy of a srucural sysem. In order o overcome hese challenges, a new probabilisic framework has been developed for accurae assessmen of collapse of frame srucures under sochasic ground moions. Firs, nonlinear dynamic analyses are performed for seleced experimenal case sudies repored in he lieraure (Kanvinde 2003, Rodgers & Mahin 2004, Lignos e al. 2008) by use of OpenSees, an objec-oriened sofware framework developed by Pacific Earhquake Engineering Cener (PEER). Using OpenSees compuaional models validaed by corresponding experimenal resuls, new dynamic-insabiliy-based collapse crieria are developed in erms of energy from he inpu ground moions and he graviy loads. The seleced case sudies are hen used o es he new collapse crieria and o idenify key parameers ha govern he collapse of a srucural sysem. Currenly, procedures are being developed for probabilisic predicion of collapse limi saes and corresponding srucural demands, and for idenificaion of criical parameers in collapse predicions. Using hese procedures, he impac of uncerain ground moion deails on he collapse limi saes and srucural demands is being invesigaed o provide guidelines on selecion of ground moions for IDAbased sudies and designs. This paper presens ongoing research aciviies in he proposed framework. Firs, he deails of compuaional simulaions of collapse es cases in he lieraure are presened. Second, he proposed collapse crieria based on dynamic insabiliy, i.e. he loss of he abiliy o susain he graviy loads are inroduced. Using he seleced experimenal case sudies, he new collapse crieria are compared wih he radiional IDA-based approach. Finally, he paper inroduces ongoing research aciviies for probabilisic assessmen of collapse limi saes, srucural demands a collapse levels and for idenificaion of criical parameers for collapse predicions. 2 VALIDATED COMPUTATIONAL SIMULATION OF COLLAPSE In order o develop he framework described in he previous secion, i is necessary o build compuaional simulaion models of collapse ha are validaed by available experimenal es resuls. This secion briefly describes he simulaion ool and provides deails of he compuaional simulaion models of he seleced collapse-case sudies considered in his sudy. 2.1 Simulaion ool OpenSees The Open Sysem for Earhquake Engineering Simulaion is a finie-elemen program developed by PEER o simulae he seismic behavior of srucural and geoechnical sysems (PEER 2004). OpenSees has been exensively used by many researchers in earhquake engineering for various finie-elemen applicaions because of is advanced capabiliies in consiuive models, elemens and soluion algorihms. Moreover, i is open-source sofware plaform ha allows researchers o conribue o he framework. Therefore, his sudy uses Open- Sees as he simulaion ool o perform nonlinear dynamic collapse analysis for seleced case sudies for which collapse or near-collapse level experimenal resuls are available. Advanced high-fideliy analyical models can accoun for many facors needed for accurae simulaion of srucural collapse process, bu are compuaionally demanding. These models are prone o convergence problems during nonlinear dynamic analysis because of he complexiy of he modeling deails. Therefore, hese advanced models can be impracical for he aforemenioned sochasic framework especially in design process. For his reason, his research employs macro-models available in OpenSees ha correlae well wih experimen resuls of seleced case sudies of collapse o achieve he aforemenioned research objecives and perform large-scale parameric sudies in collapse assessmen of srucures. 2.2 Case sudies on srucural collapse Nonlinear dynamic collapse analyses are performed for seleced experimenal case sudies repored in he lieraure by use of OpenSees. So far, hree case sudies have been explored using advanced capabiliies of OpenSees in consiuive models, elemens and soluion algorihms: Kanvinde (2003), Rodgers & Mahin (2004), and Lignos e al. (2008). In developing he compuaional simulaion models of he seleced case sudies, an emphasis was given on validaion of collapse a he sysem level by considering he maximum and residual sory drif responses as well as a he componen level by considering he momen-roaion response obained a he plasic locaions a he elemen ends. Two of hese case sudies (Kanvinde 2003, and Lignos e al. 2008) are presened in his paper for describing hese research aciviies.

3 Figure 1. Specimen configuraion (Kanvinde 2003). Figure 2. Displacemen ime hisory resuls by OpenSees for he es case by Kanvinde (2003) under he es ground moion record of he 1994 Norhridge a Obregon Park. sof and radi in he plo refer o he sofening amoun and radius of ransiion from elasic o plasic branches in he springs respecively. Kanvinde (2003) conduced shake able ess on a single-sory specimen configuraion measured 12 by 24 in plan (he longer dimension aligned in he direcion of moion) and 10 in heigh o invesigae he concep of dynamic insabiliy of srucures during earhquakes. The specimen configuraion was in he form of four fla columns conneced o he base plae and a seel mass on op served as a rigid diaphragm as shown in Figure 1. For he proposed asks described in his paper, a srucural model was buil in OpenSees using he 2-D analyical model deails given in Kanvinde (2003). Elasic elemens were assigned o he columns and beam, and he beam was assumed o behave rigidly. Concenraed nodal masses were placed a he ends of op beam. Inelasic single-degree-of-freedom (SDOF) zero-lengh roaional springs were modeled a he plasic locaions a he ends of he columns by assuming Giufré- Menegoo-Pino plasiciy model (Menegoo & Pino 1973) for he spring hysereic response. The co-roaional formulaion was used in order o include he nonlinear geomeric effecs hrough he specimen. Nonlinear dynamic collapse analyses under he es ground moion of Obregon Park were performed o provide he OpenSees resul for he es case no. 11 in Figure 2, which almos coincides wih available experimen daa even a he near-collapse level. Lignos e al. (2008) performed a series of collapse shake-able ess of a 4-sory, 2-bay seel frame wih reduced-beam secions (RBS) in 1/8 scale. Figure 3 shows he seup of he es frame on he NEES mass simulaor a he Universiy a Buffalo, which consiss of elasic members wih plasic hinges a he ends. The mass simulaor is conneced o he es frame by means of axially rigid horizonal links hrough which he simulaor ransfers P-Dela effecs acing as a leaning column on he es frame. An analyical model for he 1/8 scale 4-sory es frame was developed in OpenSees based on he deerioraion parameers and mahemaical model properies given in Lignos e al. (2008). The roaional springs were used o analyically model he plasic hinges in he frame wih a modified Ibarra-Krawinkler deerioraion model (Lignos e al. 2008) available in OpenSees, calibraed based on a seel componen daabase of seel beams wih RBS under cyclic loading. Panel zones were modeled a he connecions considering he shear disorions. Furhermore, offses from he panel zones were applied o ake RBS ino accoun following he mehod used by he researchers. Effecs of he panel zones on he srucural response were explored comparing o hose of a developed clear span model. Time hisory analysis and IDA were performed using he OpenSees model and he resuls were compared wih hose by experimen (See Figure 4), which show good agreemen. Noe ha a se of nonlinear dynamic analyses wih four differen levels of seismic inensiy scales were performed sequenially o simulae he acual loading sequences of he ess. Figure 3. Shake-able-es of a 1/8 scale 4-sory, 2-bay seel frame wih reduced beam secions (Lignos e al. 2008).

4 corresponding experimenal resuls, new dynamicinsabiliy-based collapse crieria have been developed in erms of he energy from he inpu ground moions and he graviy loads. The seleced case sudies are hen used o es he new collapse crieria of a srucural sysem. Figure 4. Comparison of experimenal es resuls and simulaion resuls of laeral displacemen ime hisory a he op of he frame for he es case by Lignos e al. (2008). Noe ha he simulaion model here depends on he clear span model, and was coninuously subjeced o he ground moion record of he 1994 Norhridge earhquake a Canoga Park wih a scale facor of 0.4, 1.0, 1.5,1.9, and 2.2 following he es procedure. 2.3 Virual collapse simulaions In order o develop a new sochasic framework for idenifying collapse limi-sae and imporan parameers in he collapse assessmen of srucures subjeced o seismic loads, exensive IDAs are performed using validaed OpenSees simulaion models o obain a large sample for muliple DMs and corresponding IM and for muliple ground moions. Since he ground moions considered in he mehodology of ATC-63 projec were seleced in such a way ha he mehodology can be generally applied o building srucures a any sie, he Far-Field record se of ATC-63 projec have been chosen in he developmen of he sochasic framework. This record se consiss of weny-wo ground moion pairs (wolaeral componens) recorded a sies locaed wihin 10km of faul rupure. Records were seleced from srong earhquake ground moions wih a magniude changing from 6.5 o 7.9. As a fuure work in he sudy, virual collapse simulaions considering a wide array of geomeric and maerial parameers (Seelman & Hajjar 2009) will also be performed using he validaed analyical models o accoun for he impacs of a srucural model selecion on he collapse predicion of srucures. 3 COLLAPSE CRITERIA BASED ON DYNAMIC INSTABILITY OF FRAME STRUCTURES This secion presens new collapse crieria of frame srucures based on he dynamic insabiliy, i.e. he loss of he abiliy o susain he graviy loads. Using he OpenSees compuaional models validaed by 3.1 Tradiional IDA-based collapse limi saes The flaening of IDA curves may be caused by large residual displacemen, no by he occurrence of collapse necessarily. I is also noed ha unusual behaviors of IDA curves such as non-monoonic behavior and disconinuiies may occur (Vamvasikos & Cornell 2002). As a resul, he collapse capaciy idenified from he IDA-based approach migh no accoun for he impac of he uncerainies in ground moion appropriaely. To idenify collapse capaciies from he behavior of IDA curves, some rules have been proposed (Vamvasikos & Cornell 2002). According o he IM-based rule (Figure 5a), a building reaches is collapse capaciy when he slope of he curve is reduced o 20% of he iniial slope. If an IDA curve does no fulfill he IM-based rule, hen one checks if he drif raio exceeds an assumed global drif capaciy, say 10% (DM-based rule; see Figure 5b). However, hese IDA-based collapse idenificaion rules depend on assumed hreshold values on IM and DM, herefore no sufficien for objecive and physicsbased idenificaion of a srucural collapse based on acual dynamic insabiliy of a srucure. Therefore, new dynamic-insabiliy-based collapse crieria are developed in erms of energies from he inpu ground moions, and he graviy loads. Firs, energy balance of a srucural sysem under seismic exciaion is inroduced in he following secion. Then, deails of he new dynamic-insabiliy-based collapse crieria are presened. (a) (b) Figure 5. a) IM-based and b) DM-based rules.

5 3.2 Energy balance of a srucural sysem subjeced o seismic forces The equaion of moion a ime for a muli-degreeof-freedom (MDOF) srucure under horizonal earhquake loads and graviy loads is given as M u() + C u() + F S () = M u F () (1) where u is he relaive nodal displacemen vecor, u is he relaive nodal velociy vecor, u is he relaive nodal acceleraion vecor, M is he srucural mass marix, C is he srucural damping marix, F S is he srucural resoring force vecor, and u F is he acceleraion vecor of he applied loads. An insigh ino he dynamic insabiliy of srucures can be gained by considering energy balance of a srucural sysem under dynamic and graviy forces. If each erm in Equaion 1 is inegraed wih respec o u, he energy balance of he srucural sysem can be derived as (Uang & Berero 1990): M u() du + C u() 0 du + F 0 S () du = M u 0 F () du (2) 0 The inegrals in Equaion 2 give he following energy componens of a srucural sysem respecively, i.e. EK + ED + ES = EI (3) where EK is he relaive kineic energy, ED is he damping energy, ES is he srain energy, and EI is he relaive dynamic inpu energy. Using du = u()d, he inpu energy componen can be decomposed as follows: E I = M u F () u() d (4) 0 If he srucure is subjeced o he horizonal earhquake exciaion and he graviy loads only, hen he inpu energy can be separaed ino dynamic inpu energy due o horizonal seismic acions, EEQ, and graviy energy due o applied graviy loads on he srucure, EG, i.e. E EQ = M u () u EQ x () d (5) 0 E G = M g u 0 y () d = Mgu y () (6) Where u EQ is he acceleraion of he horizonal earhquake exciaion, u x is he relaive nodal velociy vecor in x-direcion, u y is he relaive nodal displacemen vecor in y-direcion, and g denoes he graviy acceleraion, which is consan. The earhquake energy applied on he srucure is dissipaed hrough he work done by he damping and hysereic forces. Therefore, he damping and hyseric energies are irrecoverable while he elasic and kineic energies are recoverable vibraional energy. If all he individual energy componens are gahered ogeher, he energy balance of a srucure in Equaion 3 is now defined as: EK + ED + ES = EG + EEQ (7) Akiyama (2002) saed ha he graviy energy can be considered as a release of he poenial energy as a resul of he P-Dela effecs, and akes a par in he oal resisance of a srucure agains a seismic exciaion. Therefore, he graviy energy can be alernaively shown on he lef side of he energy balance: EK + ED + ES EG = EEQ (8) 3.3 Idenificaion of dynamic insabiliy by srucural graviy energy Dynamic insabiliy is a complex phenomenon, which canno be effecively prediced by a ground inensiy measure and/or an engineering parameer roughly represening srucural damage. The mos commonly used crierion for idenificaion of simulaed collapse under dynamic loads is boundless drifs owards collapse. However, his approach requires checking displacemen demands a each degree-of-freedom (DOF), bu mos sudies consider only he roof or sory drifs o check he sabiliy of he global srucural behavior. Therefore, he dynamic insabiliy of srucural sysems is invesigaed from he viewpoin of he energy balance because energy is an overall indicaor of he sysems. Progressive accumulaion of permanen laeral drifs during a srong ground shaking may render graviy forces he dominan forces and make he srucure collapse under significan P-dela effecs due o governing graviy forces (Jennings & Husid 1968). Therefore, new collapse crieria have been developed based on comparison beween he amoun of dynamic energy released by he earhquake o he srucure and he amoun of graviaional work done by he verical saic loads during he dynamic analysis. The sudden increase of he graviy energy, which evenually causes he graviy energy o exceed he dynamic energy, can be considered as an indicaor of he dominaion of graviy loads over dynamic loads. Figure 6 presens he inpu-energy-ime hisories for he validaed single-sory model of Kanvinde (2003) under he ground moion record of he 1994 Norhridge earhquake a Obregon Park, Los Angeles. If he inensiy of he ground moion is no srong enough o rigger he large geomeric effecs in he frame (e.g. he non-collapse case a he scale of 0.8), he srucure obains a seady sae in erms of he graviaional energy, which is found insignifican comparing o he quaniy of dynamic inpu energy coming from he ground moion (Figure 6a). A he inensiy scale of 1.0 (Figure 6b), geomeric non-

6 lineariies in he srucure become significan near he collapse, causing he frame o show very large displacemen in verical direcions and hus resul in a sudden increase in he graviaional energy as he srucure ges close o collapse. Since his approach employs sysem-level measures, i.e. graviy and dynamic inpu energies, one does no need o check each degree-of-freedom of he srucure o check he dynamic insabiliy. Moreover, he approach may faciliae developing a mahemaical descripion of dynamic insabiliy, which can be paricularly useful as limi-sae funcions during srucural reliabiliy analysis of collapse. (a) level of ground moion a which he srucure loses he dynamic sabiliy as he collapse capaciy. However, he srucural collapse capaciy should be evaluaed based on he maximum inensiy level before occurrence of dynamic insabiliy (Krawinkler e al. 2009, Haselon e al. 2009). The capaciy a his inensiy level is acual represenaion of he larges srucural resisance agains dynamic collapse. The validaed model for he case sudy by Lignos e al. (2008) is uilized here o perform nonlinear dynamic analyses using he ATC-63 far field se. Figure 7 shows he IDA curves of peak ground acceleraion (PGA) o op laeral displacemen obained from he validaed OpenSees model. Tradiional IDA-based rules are compared o he new crieria called energy rule based on he maximum inensiy level observed before he dynamic insabiliy occurs, i.e., graviy energy exceeds dynamic energy. Much variabiliy is observed in collapse capaciy level for all rules due o he effec of randomness in he seleced ground moions on srucural collapse. I is also noed ha he radiional IDA-based approach and he proposed crieria resul in significan differences in predicions of collapse capaciy (in PGA) and he srucural demand a he collapse level (in roof displacemen). (b) Figure 6. Inpu energy componens near collapse under he es earhquake of 1994 Norhridge earhquake a Obregon Park a) non-collapse case a he ground moion scale of 0.8 and b) collapse case a he ground moion scale of Comparison of new collapse crieria wih radiional IDA-based rules Tradiional IDA-based rules are compared o he new crieria called energy rule in erms of he maximum inensiy level observed before he dynamic insabiliy occurs, i.e., graviy energy exceeds dynamic energy. Mos recen research effors based on he IDA-based approach assume he inensiy Figure 7. IDA curves and comparison of collapse crieria for he es case of Lignos e al. (2008) subjeced o ATC-63 far field record se (44 ground moions). 4 PROBABILISTIC ASSESSMENT OF COLLAPSE USING NEW COLLAPSE CRITERIA Collapse assessmen of srucures based on IDA curves depends on he selecion of IM and DM used o consruc hese IDA curves as well as variabiliy in he se of ground moions considered in he analysis (Villaverde 2007). IDA curves usually reach a fla plaeau as an indicaion of collapse (i.e., a large increase in he srucural response corresponding o a small increase in he ground moion inensiy), bu

7 his plaeau may occur a several differen inensiy levels of ground moions. Large dispersion observed in collapse-causing inensiies of ground moions and damage hresholds has iniiaed search for alernaive performance measures o assess collapse capaciy of srucures. However, mos of recen research on he IDA-based approach sill uses only one DM and one IM (mosly maximum sory drif raio and elasic specral acceleraion). This secion describes ongoing research effors o obain opimal selecion and/or combinaion of muliple performance measures ha describe he limi-sae mos effecively and he benefi of having more han one DM or IM for collapse capaciy predicion. 4.1 Saisical analysis on collapse capaciy by new crieria The collapse capaciy daa obained for he case sudy by Lignos e al. (2008) using ATC-63 far field se was invesigaed here o perform saisical analyses on he levels of IMs (denoed by IMcol) and he condiional disribuions of he corresponding DMs (denoed by DMcol) Empirical cumulaive disribuion funcions (CDF) for IMcol idenified by he energy rule are presened in Figure 8. CDFs of differen kinds of IMcol (normalized by heir means) such as peak ground acceleraion-velociy-displacemen (PGA- PGV-PGD), specral acceleraion for 2% damping (Sa (2%)), undamped inensiy of Arias (IA (0%), Arias 1970), roo of inegral of square of ground acceleraion-ime hisory (ars), average cycle of crossings over zero in he srong par of accelerogram (Tv, srong, where srong duraion is based on definiion by Trifunac & Brady 1975), and earhquake inpu energy (EEQ) were compared. These CDFs provide probabilisic esimaion of he collapse capaciies (in IM). In order o make a numerical comparison, heir normalized sandard deviaion, which is coefficien of variaion (cov), were obained in Table 1. IM wih he smalles cov is found o be ars from which collapse can be prediced wih more confidence comparing o oher candidaes. Currenly, he following linear combinaions of IMs and/or DMs in Equaion 9 or nonlinear combinaions are also being invesigaed o obain new performance measures (PM) ha can predic he collapse capaciies wih smaller covs: n PM = a i IM i + b i DM i (9) i=1 where a i and b i are he coefficiens of he IM and DM ha resul in smalles covs, found by saisical analysis. Condiional disribuion of srucural demand (DMcol) given IMcol is also being obained. Parial descripors such as condiional mean and variance of DMcol given IMcol can be obained hrough linear/nonlinear regression analysis. Such regression models provide probabilisic esimaion of he srucural demand a near-collapse level. 4.2 Effec of variabiliy in ground moions Effecs of uncerain characerisics of ground moions used for IDA on he probabilisic models described in secion 4.1 are being invesigaed o develop guidelines regarding selecion of a suie of ground moions o be used in nonlinear collapse analyses. Moreover, a new analysis framework is being developed for probabilisic evaluaion of collapse using arificial models represening possible ground moions a a given sie insead of a suie of seleced ground moions. This approach allows us o perform sie-specific probabilisic collapse assessmen. The approach will perform random vibraion analysis by employing a discree represenaion of a ground moion daabase (Rezaeian & Der Kiureghian 2008, 2010). The developed probabilisic mehod will be inegraed wih performance-based earhquake engineering (PBEE) framework, which will provide collapse fragiliy models hrough sysemaic reamen of uncerainies in seismic capaciy, demand and models. Figure 8. Cumulaive disribuion funcion of IM-collapse level for he es case of Lignos e al. (2008) subjeced o ATC-63 far field record se (44 ground moions). Table 1. Collapse-iniiaing inensiy measure and coefficien of variaions (cov) IM col cov ars 0.31 T v, srong 0.33 PGV 0.41 PGA 0.42 E EQ 0.48 Sa (2%) 0.56 IA 0.68 PGD 0.87

8 5 CONCLUSIONS AND FUTURE WORK New collapse crieria were developed based on dynamic insabiliy of srucures near collapse hrough validaed compuaional simulaions of collapse es frames repored in he lieraure. Using he crieria, various quaniaive crieria are being explored o faciliae performing srucural reliabiliy analysis and idenifying criical measures. New collapse crieria based on compuaional simulaions of dynamic insabiliy give rise o new research opporuniies o gain beer undersanding of complex collapse of srucural sysems, idenify key parameers requiring more comprehensive and accurae measuremens during experimens, achieve more accurae and sysemaic predicion of collapse, and incorporae uncerainies ino collapse predicion. The sudy described here is expeced o have poenial impac across several srucural engineering research and pracice consiuencies seeking o improve building code provisions for prevening disproporionae collapse; regional emergency response plans and risk managemen sraegies ha rely on accurae assessmen of collapse wihin fragiliy analysis; and collapse assessmen of new srucural sysems. In addiion, hrough his work, life safey will be enhanced, as avoiding srucural collapse due o exreme loads is a criical componen o ensuring a safe infrasrucure and is resilience agains earhquake hazards. 6 ACKNOWLDEGEMENT The auhors would like o hank Naional Science Foundaion (NSF) for heir funding in his research under gran number CMMI Any opinions, findings and conclusions or recommendaions expressed in his maerial are hose of he auhors and do no necessarily reflec he views of NSF. REFERENCES Akiyama, H Collapse modes of srucures under srong moions of earhquake. Annals of Geophysics 45(6): Applied Technology Council, Quanificaion of building seismic performance facors. ATC-63 Projec Repor FE- MA. Arias, A A measure of earhquake inensiy. In R. J. Hansen (ed), Seismic design for nuclear power plans: Cambridge: M. I. T. Press. Haselon, C.B, Liel, A.B., & Deierlein, G.G Simulaing srucural collapse due o earhquakes: Model idealizaion, model Calibraion, and numerical soluion algorihms. 2nd Inernaional Conference on Compuaional Mehods in Srucural Dynamics and Earhquake Engineering, Rhodes, Greece, June. Jennings, P. C. & Husid, R Collapse of yielding srucures during earhquakes. Journal of Engineering Mechanics Division 94(5): Kanvinde, M Mehods o evaluae he dynamic sabiliy of srucures shake able ess and nonlinear dynamic analyses. EERI Annual Suden Paper Compeiion, Earhquake Engineering Research Insiue, Oakland, Calif. Krawinkler, H., Zareian, F., Lignos, D., & Ibarra, L. F Predicion of collapse of srucures under earhquake exciaions. 2nd Inernaional Conference on Compuaional Mehods in Srucural Dynamics and Earhquake Engineering, Rhodes, Greece, June. Liel, A.B., Haselon, C.B., Deierlein, G.G., & Baker, J.W Incorporaing modeling uncerainies in he assessmen of seismic collapse risk of buildings. Srucural Safey 31: Lignos, D.G., Krawinkler, H., & Whiaker, A.S Shaking able collapse ess of wo scale models of a 4-sory momen resising seel frame. Proceedings of he 14h World Conference on Earhquake Engineering, Beijing, China, Ocober. Menegoo, M., and Pino, E Mehod of analysis for cyclically loaded reinforced concree plane frames including changes in geomery and non-elasic behavior of elemens under combined normal force and bending. Proceedings of IABSE Symposium, Lisbon, Porugal. Pacific Earhquake Engineering Research Cener Open Sysem for Earhquake Engineering Simulaion. Universiy of California, Berkeley, CA. Rezaeian, S. & Der Kiureghian, A A sochasic ground moion model wih separable emporal and specral nonsaionariies. Earhquake Engineering and Srucural Dynamics 37: Rezaeian, S. & Der Kiureghian, A Simulaion of synheic ground moions for specified earhquake and sie characerisics. Earhquake Engineering and Srucural Dynamics 39: Rodgers, J.E., & Mahin, S.A Effecs of connecion hysereic degradaion on he seismic behavior of seel momen-resising frame. Pacfic Earhquake Engineering Research Cener Repor, PEER 2003/13. Seelman, J. S. & Hajjar, J. F Influence of inelasic seismic response modeling on regional loss esimaion. Engineering Srucures 31(12): Trifunac, M.D., & Brady, A.G On he correlaion of seismic inensiy scales wih he peaks of recorded ground moion. Bullein of he Seismological Sociey of America 65(1): Uang, C. M. & Berero, V. V Evaluaion of seismic energy in srucures. Earhquake Engineering and Srucural Dynamics 19: Vamvasikos, D. & Cornell, C.A Incremenal dynamic analysis. Earhquake Engineering and Srucural Dynamics 31 (3): Vamvasikos, D. & Cornell, C.A Applied incremenal dynamic analysis. Earhquake Specra 20(2): Villaverde, R Mehods o assess he seismic collapse capaciy of building srucures: Sae of he ar. Journal of Srucural Engineering 33(1): Zareian, F. & Krawinkler, H Assessmen of probabiliy of collapse and design for collapse safey. Earhquake Engineering and Srucural Dynamics 36(13):