Floor Acceleration Spectra Estimation in Reinforced Concrete Frames

Transcription

1 Paper 88 Civil-Comp Pre, 2015 Proceeding of the Fifteenth International Conference on Civil, Structural and Environmental Engineering Computing, J. Krui, Y. Tompanaki and B.H.V. Topping, (Editor), Civil-Comp Pre, Stirlinghire, Scotland Floor Acceleration Spectra Etimation in Reinforced Concrete Frame A. Lucchini, P. Franchin and F. Mollaioli Department of Structural and Geotechnical Engineering Sapienza Univerity of Roma, Italy Abtract Non-tructural element that are conidered primarily enitive to and ubject to damage from inertial loading are claified a acceleration-enitive element. The repone of acceleration-enitive non-tructural component in building i therefore directly affected by the floor acceleration demand that they experience during ground haking. Reducing eimic damage to thee element i of primary importance not only for economic reaon, but alo for maintaining the functionality of the building immediately after the earthquake. The purpoe of thi paper i to tudy the floor acceleration demand variation along the height of concrete frame building and how the ophitication of the tructural modeling can be reduced in uch etimation. In fact, development of probabilitic eimic demand model, that uually involve the ue of method uch a the incremental dynamic analyi, the cloud analyi, and multiple tripe analyi require a large number of non-linear analye of the tructure to be run. To reduce the numerical effort, a implified methodology baed on the modal puhover analyi procedure will be propoed and ued for the characterization of floor pectra. To thi purpoe the eimic repone of a elected cae tudy, coniting in a ix-torey three-bay frame of a reinforced concrete building, dimenioned to be repreentative of an exiting tructure deigned according to a pat eimic code (uing the one in force in Italy between 1996 and 2008), will be analyzed. The etimate of peak abolute acceleration and repone pectra at each floor level will be compared and contrated. Keyword: nontructural component, probabilitic eimic demand model, correlated engineering demand parameter, intertory drift, floor repone pectra. 1 Introduction The continued functionality of critical facilitie in the face of natural or manmade diater i eential to community reilience. Performance-baed eimic 1

2 aement of thee facilitie i baed on the evaluation of the probability of functionality lo in a period of interet. Functionality can be expoed to earthquakeinduced damage to tructural a well a non-tructural component (NSC). Once the tate of damage to all component i known, aement of reidual functionality require the evaluation of a fault tree (FT) for the function, with baic event coniting of component failure. The FT depend on the topology and propertie of the ytem performing the function. Within a PBEE framework [8, 4], the aumption of conditional independence allow the ubdiviion of the performance aement into a equence of tep: 1) hazard; 2) tructural repone given eimic intenity; 3) damage of component given tructural repone; 4) functionality given damage. One uch model i needed for lo aement tudie, where Step 4 i imply replaced by a ummation of economic value of component damage over the tructure [11]. In the latter cae uually component are claified into o-called performance group, which lump together all component that are imilarly affected by the ame repone quantity, or engineering demand parameter (EDP). NSC are uually claified into drift-enitive (e.g. piping) and acceleration-enitive (e.g. equipment reting on floor or hanging from ceiling) component. The latter may be rigid or flexible. A complete eimic demand model mut include both intertory drift and floor pectra, or at leat drift and ome floor acceleration parameter [2]. Thi paper dicue iue related to the etimation and ue of a multivariate eimic demand model for NSC in term of drift and floor acceleration pectra. A model to generate realization of floor repone pectra baed on few parameter derived from the full PSDM i alo propoed. 2 Methodology A detailed etimation of the functionality lo require a imulation approach and a relatively large number of realization. In thi cae, the evaluation of the tructural repone and tate of ytem functionality in the ame inelatic repone hitory analyi (IRHA) it i not practicable becaue the number of the latter would be too large to be affordable. Thu, the common approach i to exploit a reduced number of IRHA to obtain a reaonable et of repone to etablih a urrogate model to be ued in a following Monte Carlo imulation of ytem tate [8, 11]. The PSDM adopted in thi work i a multivariate lognormal model, uch a that in [11]. The tructural repone quantitie are intertory drift and floor acceleration pectral ordinate at elected period, or floor repone pectra (FRS). The ue of a lognormal ditribution for drift i well etablihed, and there i upport for it ue alo for acceleration repone [11, 9]. The FRS are calculated from floor acceleration recorded in the IRHA of the tructure (alone). Structure-component interaction effect, in fact, are aumed negligible, which i acceptable in the cae the ma of the component i ignificantly maller than that of the tructure (le than 1%, baed on the reult of the invetigation carried out by [12]). The ue of elatic FRS for acceleration-enitive NSC ret on the aumption that both component and their upport and attachment to the tructure remain in the linear elatic range. 2

3 The PSDM i ued in a PBEE framework to evaluate the mean annual frequency of lo of functionality λ, uing the total probability theorem expreion: ( ) ( ) S( ) ( ) S( ) λ = pfd pdsdd dλ = pfsdλ (1) S d where: p(f d) i the probability of lo of functionality given a et of NSC demand d (which require evaluation of the correponding NSC capacitie from their repective fragility function and evaluation of the FT) p(d S) i the joint denity of NSC demand given eimic intenity S, output of Step 3 (the multivariate lognormal PSDM) p(f S) i the outcome of Step 4, and i the integral over the demand d of the product p(f d)p(d S), carried out by Monte Carlo-like imulation State-of-the-art correct evaluation of the probability denity of d conditional on intenity S require the ue of a et of recorded ground motion time-erie elected to reflect the conditional ditribution of ground motion given that S =. Thi can be done according e.g. to the election procedure in [1], [7], and [6]. The multipletripe analyi [5] i adopted herein, a it provide the eaiet mean to account for the variation in ground motion propertie with the conditioning intenity meaure S in the total probability theorem expreion above. In the following, unle otherwie pecified, reference i implicitly made to one of the intenity level (i.e. a ingle tripe) S =. At each intenity S =, the adopted PSDM i completely pecified through the two N 1 vector µ ln and σ ln of the mean and tandard deviation of the logarithm of the repone, and through the N N correlation matrix R lnln of the pair-wie correlation coefficient among the logarithm of the repone. The length N of the repone vector can be expreed a: (2) where: n f i the number of floor (and multiplied by one yield the number of intertory drift of interet, for 2D problem n T i the number of period at which the FRS i evaluated n ξ i the number of component damping ratio of interet The ue of multiple component damping ratio may be needed when, a already mentioned, type and propertie of the component are not known at the tructural analyi tage. The number of period ued to dicretize the FRS ha only computational implication, but thi i a relatively minor iue ince the FRS are elatic, thu n T can be in principle a large a deired. On the other hand, uing a limited number of pectral ordinate to decribe the full pectrum i alo an option, being attractive epecially in thoe cae where both n f and n ξ are large. Other tudie have ued a S 3

4 limited number of pectral ordinate to characterize the FRS [2], introducing peak component acceleration (PCA) demand in three period range: peak floor acceleration region (PFAR, for the component vibration period T C = 0 ), hort period region (SPR, 0 < T C < 0.5T 1 ) and fundamental period region (FPR, 0.5T 1 < T C < 2.0T 1 ). In that tudy, however, PCA demand in each period range are characterized independently, without conideration of correlation and the final outcome i a et of (marginal) uniform component hazard pectra obtained combining the eimic hazard curve with the PCA ditribution. The latter uniform hazard pectra cannot be ued for Monte Carlo imulation ince they would not provide probabilitically conitent et of component damage tate to be ued for ytemic evaluation. Further, FRS ordinate for component at period away from the fundamental one or a lower period of the building may have coniderably lower acceleration demand. Figure 1: Model propoed to generate approximate realization of FRS. Intead of uing a et of (n f x n T x n ξ ) pectral ordinate, the FRS can be alternatively imulated with the propoed model hown in Figure 1. According to thi model, the acceleration demand S a,nsc of NSC located at different floor level of the building, and characterized by different period of vibration and damping ratio, can be approximately predicted by mean of few parameter by uing the following equation: TNSC / Ti 1 βi, f max ( α0, f, ηξ ( NSC ) αi, f e ) 0 < TNSC < Tn m Sa, NSC ( T, ξ, ) = approx NSC NSC f TNSC / Ti 1 βi, f max ηξ ( NSC ) αi, f e Tn < T m NSC 1<< i nm (3) α ( ( )) = PCA = max S T, ξ = 2%, f (4) i T min ( ) max( ) NSC Ti region Ti region i, f T, f a, NSC NSC NSC 4

5 2 / β TNSC Ti 1 x = α ( ξ = ) i, f arg min i, f e Sa, NSC TNSC, NSC 2%, f (5) x ( ) < < ( ) min T max i region TNSC Ti region min ( Ti region ) 0 i = 0 0 i= nm =... exp( 0.5log( T2 T3) ) i= 2 exp( 0.5log( T1 T2) ) i= 1 0 i = 0 exp( 0.5log( Tn 1 T )) = m n i n m m max ( Ti region ) =... exp( 0.5log( T1 T2) ) i= 2 max( TNSC ) i= 1 (6) (7) ( ) ηξ NSC = 2 ξ NSC (8) and where: S a, NSC i the approximated value of the (peudo) acceleration of the approx NSC produced by a eimic intenity level S=; T NSC i the period of vibration of the NSC; ξ NSC i the NSC damping ratio (expreed a a percentage); f i the floor level where the NSC i located; T i i the i th period of vibration of the tructure; T i region i the period region of the FRS containing the i th period of vibration of the tructure; n m i the number of (conidered) ignificant mode of vibration of the tructure; η i a damping correction factor (different from 1 for ξnsc 2% ). In the cae thi propoed model i ued to generate the FRS, the number of parameter which characterize the PSDM become ( 1 ) N = nf + np (9) in which np = 1+ 2 nm (10) where: n P i the number of parameter of the propoed model (coniting in α, 0, f α, ). i f, and β i f, Feaibility of a further reduction of the number of parameter needed to decribe the FRS in the cae the law for prediction the variation of α, and β i, f i, f with the floor level i aumed a-priori i dicued later. 5

6 Once the vector µ ln and σ ln and the correlation matrix R lnln for each intenity level S= have been etablihed baed on the reult of the IRHA, imulation of any number of realization of the NSC demand vector proceed with the well-known formula to generate a multivariate lognormal vector from a vector of tandard Normal variable: d = exp μ + diag σ Lu ( ln ( ln ) ) (11) where: diag(σ ln ) i the N N diagonal matrix with diagonal σ ln L i the lower triangular matrix reulting from the Choleky decompoition of the correlation matrix of the logarithm LL T = R lnln u i a N 1 vector of tandard Normal variable 3 Illutrative Example 3.1 Structural model The methodolgy i illutrated by mean of 6-torey reinforced concrete plane frame dimenioned o a to be repreentative of an exiting tructure deigned according to a pat eimic code (a the one in force in Italy between 1996 and 2008). Information on the pan length and the tory height of the frame, and detail on cro-ection dimenion and reinforcement of the tructural member are given in Figure 2. The tructure i uppoed to be located in a high eimic zone in Italy. Figure 2: Studied reinforced concrete tructure. The model ued to analyze the frame i built in OpenSee [13] with beam and column modelled with elatic beam element connected in erie to zero-length nonlinear rotational pring located at member end for repreenting platic hinge. The material model ued for the nonlinear pring i the hyteretic material of OpenSee, with the pinch and the damage parameter et to have a peak oriented behavior and no in-cycle degradation, repectively. A Rayleigh damping proportional to the ma and the initial tiffne matrix (with the rotational pring 6

7 being not included) i conidered, with coefficient calibrated to provide a 2% damping at the firt and third mode period. Second-order effect due to geometric nonlinearity are accounted for through p-delta tranformation. The firt three period of the frame model are 1.3, 0.44 and 0.25, with correponding participating ma equal to 80%, 11%, and 3%. In Figure 3, the puhover curve obtained with a load vector proportional to the inertia force ditribution of the firt mode of vibration of the tructure i reported. Figure 3: Reult of a puhover analyi of the frame. The puhover curve i expreed in term of bae hear V bae, normalized with repect to the total weight W, and roof drift ratio RDR. 3.2 Ground Motion In thi tudy, eimic hazard i repreented with ground motion record elected uing the algorithm of Bradley [1] baed on the generalized conditional intenity meaure approach [18]. The vector of intenity meaure adopted in the election procedure conit in a et of (peudo) acceleration pectral ordinate S a (computed at 14 different period of vibration T i, uing a damping ratio equal to 5%), and the Aria Intenity AI [21]. Among the conidered pectral acceleration, that correponding to a vibration period equal to 1 i ued a the conditioning intenity meaure (i.e., S = S a (1)). Even if alternative intenity meaure than the pectral acceleration were found to be good predictor for eimic demand on non-tructural component (epecially for the cae of floor acceleration, a hown e.g. in [23, 24, 25]), S a i elected in thi tudy becaue of it computability (i.e., availability of ground motion prediction equation, and correlation equation a well). The prediction equation of Boore and Atkinon [19] and Campbell Bozorgnia [19] are ued to predict the S a (T i ) and AI value, repectively, while the equation of Baker and Jayaram [22] and that of Campbell and Bozorgnia [19] i ued for the prediction of the S a (T i ) - S a (T j ) correlation and the S a (T i ) - AI correlation, repectively. In order to account for ite effect, record are elected by auming rock condition, and then modified through a ite-repone analyi. In thi cae, a linear filter 7

8 repreenting a uniform oil layer overlying a half-pace of elatic rock i ued to modify the record. Seimic hazard i etimated auming the frame to be located in Lamezia Terme (Italy). Three eimic intenity level, correponding to a return period equal to 100, 500 and 2500 year, are ued in the multiple-tripe analyi. Through the analyi of thee three tripe, the variation of the PSDM propertie with the nonlinearity level of the tructural repone i evaluated. Studie have hown, in fact, that FRS ignificantly change both in amplitude and hape when the tructure get into the nonlinear range (e.g., ee [26, 27, 17]). 4 Reult In the conidered cae tudy, the repone vector ued to develop the PSDM for the NSC conit in n f = 6 intertory drift, and, for each floor level, n T = 301 ordinate of floor pectral acceleration (correponding to period uniformly ditributed in the range 0-3 ) calculated for n ξ =10 damping value (ranging from 0.5% to 5%). Thu, the length N of the repone vector i equal to It i worth noticing that the number of component period n T ued to calculate the floor pectral acceleration, which i quite large, wa etimated o that to accurately identify the maximum value of the FRS (whoe hape i ignificantly peaked, epecially in the linear range of repone of the tructure). In the following figure, where FRS and PCA plot are hown, unle otherwie pecified, reference i implicitly made to the conidered cae of ξ NSC =2%. Figure 4-5 plot the marginal ditribution of intertory drift (normalized by the tory height) and floor repone pectra (at elected floor level) obtained for the three conidered earthquake intenity level. It i intereting to oberve that, for the cae of the intertory drift, the eimic demand ditribution, within the building, lightly change in hape with the variation of the earthquake intenity. For the cae of the floor repone pectra, intead, the eimic demand ditribution change. Figure 4: Percentile of the marginal ditribution of the intertory drift ratio IDR (i.e., intertory drift normalized by tory height) obtained for the three conidered et of record (correponding to different value of the earthquake return period T R ). 8

9 With the increae of the earthquake intenity, the acceleration repone in the hort period region (SPR) of the pectra increae, while in the fundamental period region (FPR) the pectral acceleration initially increae and then lightly decreae. A a conequence, in ome cae (e.g., ee at the roof when T R = 2500 year), the peak value of the FRS are recorded in the SPR intead of the FPR. Therefore, in the cae of acceleration-enitive NSC i very important to conider everal eimic intenitie to obtain an accurate etimate of the demand in term of both level and ditribution within the building. Correlation among drift and component acceleration i much lower than the correlation between the drift at adjacent torie, and become almot negligible for high eimic intenity level. Thi mean that in drift- and acceleration-enitive NSC demand tend to become uncorrelated when the tructure enter the nonlinear range of repone. Figure 5: Percentile of the marginal ditribution of 2%-damped FRS ordinate calculated at two different floor level of the tructure. T NSC and T 1 denote the component period and the fundamental period of the tructure, repectively. The correlation coefficient among FRS ordinate which correpond to NSC located at the ame floor level, are reported in the plot of Figure 6 and 7. By comparing the plot of Figure 6 and Figure 7, it can be oberved that, imilarly to what found for the cae of the drift, correlation decreae with the increae of the earthquake intenity. In particular, in the nonlinear range of the tructural repone, only when T NSC < T 2 and T NSC > T 1 the correlation remain ignificant. 9

10 Figure 6: Correlation coefficient among the logarithm of FRS ordinate correponding to NSC located at the ame floor level. T R = 100 year et of record. Red line define the period value of the firt three mode of vibration. Figure 7: Correlation coefficient among the logarithm of FRS ordinate correponding to NSC located at the ame floor level. T R = 2500 year et of record. Red line define the period value of the firt three mode of vibration. 10

11 The weak correlation oberved in the T 1 - T 2 region, which decreae when the difference in the component period increae and when the component are located at different floor level, can be explained by the following conideration: when T 1 < T NSC < T 2, the repone of the NSC i not dominated by a ingle mode of vibration of the tructure only, but by both the fundamental and the higher mode of vibration; the correlation among the repone to the earthquake of two different mode of vibration of the tructure rapidly reduce when the difference in the period of vibration of the two mode increae (e.g., ee the reult of the tudy of Baker and Jayaram [22] on the correlation of pectral acceleration value); the contribution to the acceleration repone of the building of the different mode of vibration varie with the conidered floor level. Once the PSDM i built, realization of the NSC demand vector can be imulated by uing Equation (11). A expected, when the pectral ordinate are aumed uncorrelated, the hape of the FRS i much more peaked; a a conequence, depending on the conidered value of the component period, the eimic demand of the NSC can be ignificantly overetimated or underetimated. 5 Propoed model to generate FRS In alternative to the full et of pectral ordinate, a reduced number of parameter can be ued to build the PSDM in the cae the FRS are imulated with the propoed model decribed in Equation (3). In Figure 8, the predictive ability of the damping correction factor η i evaluated by comparing the η value obtained with Equation (8) with the (mean) PCA value of the FRS derived from the reult of the IRHA. In order to compare η with the PCA demand, the latter, calculated for different ξ NSC value, are then normalized with repect to the PCA value obtained for ξ NSC = 2%. Three period region correponding to the period value of the firt three mode of vibration of the tructure are conidered to calculate PCA (n m = 3). By oberving the plot of Figure 8, it can be noted that the variation of the PCA with the component damping ratio doe not ignificantly change with the conidered period region, earthquake intenity, and floor level where PCA i calculated. Except for few cae (i.e., for low value of ξ NSC, and the earthquake intenity correponding to T R = 2500 year), the prediction obtained with the propoed model perfectly match the actual normalized PCA value. In the cae the propoed model to generate the FRS i ued, the number of parameter needed to develop the PSDM can be further reduced if the following equation are ued to etimate the variation of α, and β i, f i, f with the floor level α = α φ i, f i, roof i (12) i, f c (13) β = where: φ i i the hape of the i th mode of vibration of the tructure (normalized with repect to the diplacement at the roof level); c i a contant value aumed for β which doe not change with the conidered floor level and earthquake intenity. 11

12 Figure 8: Damping correction factor η (defined a PCA divided by PCA for ξ NSC = 2%) for different period region T i : comparion between mean value obtained with the et of record, and predicted value uing a propoed model. In Figure 9, the ditribution in elevation of the (mean) PCA obtained from the analyi i compared with that predicted uing Equation (12). At the different floor level, the value of both the actual and the predicted PCA are normalized with repect to the PCA value calculated at the roof (the actual, and the predicted value, repectively). It i intereting to oberve that the ditribution in elevation of the normalized PCA doe not ignificantly change with the increae of the earthquake intenity. Thi i due to the fact that the tudied building i regular: becaue of thi, while the contribution to the repone given by the different mode of vibration of the tructure change in intenity getting in the nonlinear range, their ditribution within the tructure remain nearly unchanged. 12

13 Figure 9: Prediction model for the variation of the PCA with the floor level: comparion between mean value (black line), and predicted value (blue line). A a conequence, for each period region, the ditribution in elevation of the normalized PCA demand matche the hape of the correponding mode of vibration of the tructure. Actually, it can be noted that in the cae of the T 1 and the T 2 region, the match i almot perfect. In the cae of the T 3 region, intead, there are ome difference. The latter are explained by the fact that in thi illutrative example only three period region have been conidered to calculate the PCA demand. However, for ome of the ued record, the peak of the FRS in the SPR i produced by the fourth mode of vibration of the tructure rather than by the third one. By looking at Equation (3), it i clear that β i the parameter which quantifie, in the i th period 13

14 region, how much the peak value of the FRS in that region exponentially decreae with the increae of ditance from the period value of the i th mode of vibration of the tructure. The higher i the value of β, the more ignificant i the decreae of the PCA demand from the peak. On the bai of the obtained reult, it can be noted that β in general change value with the conidered period region and earthquake intenity, but remain in many cae almot contant with the floor level. Baed on thi oberved trend, in order to reduce the number of parameter which define the PSDM, β can be approximately aumed contant with the floor level, equal for example to the etimated at the roof. A good fit with the data i obtained in thi cae tudy alo by auming β equal to 2. In Figure 10, a realization of FRS generated with the full PSDM (which include the et of all the conidered n f x n T x n ξ pectral ordinate), and with the propoed model are hown. It can be oberved that even when a reduced number of parameter i ued in the propoed model, the match with the realization generated with the full PSDM i very good, epecially for the cae in which the equation for the approximate etimation of α i, f only i ued. Figure10: Comparion between the 84 th of FRS obtained with the full PSDM and with the propoed model to generate approximate realization. 14

15 6 Concluion Thi paper propoe a probabilitic eimic demand model (PSDM) for the eimic evaluation of nontructural component in critical facilitie. The parameter ued in the model to meaure eimic demand are intertory drift, and floor acceleration pectral ordinate at elected component period and damping ratio. A multivariate lognormal ditribution i adopted for the demand vector. A model i alo propoed to generate realization of floor repone pectra baed on few parameter. When the latter model i ued, the number of parameter decribing the PSDM i ignificantly reduced. A 2D frame of a reinforced concrete building i ued to illutrate the implementation of the PSDM. The reported reult of the cae tudy are ued in the paper to how the importance of accounting for the correlation among the component of the demand vector when the PSDM i developed. It i hown that, in the cae of regular tructure, correlation decreae with the increae of the earthquake intenity. In particular, intertory drift- and floor acceleration pectral ordinate tend to become uncorrelated when the tructure enter the nonlinear range of repone. About intertory drift, only the correlation among thoe which correpond to adjacent torie remain ignificant. In the cae of floor repone pectra, correlation i weak for thoe ordinate lying in the region which i in between the period of the fundamental and the higher mode of vibration of the tructure. In thi period region, correlation decreae when the difference in the component period increae and when the component are located at different floor level. The variation of the peak component acceleration (PCA) with the component damping ratio i negligible when different period region, earthquake intenitie, and floor level are conidered. In addition, it ditribution in elevation doe not coniderably change with the increae of the earthquake intenity, and matche almot perfectly with the hape of that mode of vibration of the tructure with period in the region where PCA i calculated. The decreae of the pectral ordinate value at period cloe to the period value where the PCA i recorded, change in general with the conidered period region and earthquake intenity, but remain in many cae almot contant with the floor level. The reult of comparion between imulation obtained with the full PSDM and the propoed model to generate floor repone pectra howed the efficiency of the latter in the prediction of the nontructural demand of acceleration-enitive component. Acknowledgment Thi work wa upported in part by DPC-Relui and the Italian Minitry of the Intruction, Univerity and Reearch (MIUR). Thi upport i gratefully acknowledged. Any opinion, finding, and concluion or recommendation expreed in thi material are thoe of the author and do not necearily reflect thoe of the ponor. 15

16 Reference [1] B.A. Bradley, Ground Motion Selection Algorithm Baed on the Generalized Conditional Intenity Meaure Approach, Soil Dynamic and Earthquake Engineering, 40(September), 48-61, [2] J.S. Clayton, R.A. Medina, Propoed Method for Probabilitic Etimation of Peak Component Acceleration Demand, Earthquake Spectra, 28(1), 55-75, [3] A.C. Cornell, F. Jalayer, R.O. Hamburger, D.A. Foutch, Probabilitic Bai for 2000 SAC Federal Emergency Management Agency Steel Moment Frame Guideline, Journal of Structural Engineering, 128(4), , [4] A.C. Cornell, H. Krawinkler, Progre and Challenge in Seimic Performance Aement, PEER Newletter 2000, 3(2). [5] F. Jalayer, A.C. Cornell, Alternative Non-Linear Demand Etimation Method for Probability-Baed Seimic Aement, Earthquake Engineering & Structural Dynamic, 38(8), , [6] T. Lin, S.C. Harmen, J.W. Baker, N. Luco, Conditional Spectrum Computation Incorporating Multiple Caual Earthquake and Ground-Motion Prediction Model, Bulletin of the Seimological Society of America, 103(2), , [7] T. Lin, C.B. Haelton, J.W. Baker, Conditional Spectrum-Baed Ground Motion Selection. Part I: Hazard Conitency for Rik-Baed Aement, Earthquake Engineering & Structural Dynamic, 42(12), , [8] Lupoi G, Franchin P, Lupoi A, Pinto PE. Seimic Fragility Analyi of Structural Sytem. Journal of Engineering Mechanic 2006; 132 (4): DOI: /(ASCE) (2006)132:4(385). [9] S. Taghavi, E. Miranda, Probabilitic Study of Peak Floor Acceleration Demand in Nonlinear Structure, Proceeding of the 15th World Conference on Earthquake Engineering, September 2012, Libon, Portugal. [10] D. Vamvatiko, A.C. Cornell, Incremental Dynamic Analyi, Earthquake Engineering & Structural Dynamic, 31(3), , [11] T.Y. Yang, J.P. Moehle, B. Stojadinovic, A. Der Kiureghian, Seimic Performance Evaluation of Facilitie: Methodology and Implementation, Journal of Structural Engineering, 135(October), , [12] S. Taghavi, E. Miranda, Effect of interaction between primary and econdary ytem on in-tructure repone pectra, Proceeding of the 14th World Conference on Earthquake Engineering, October 2008, Beijing, China. [13] F. McKenna, G.L. Fenve, M.H. Scott, OpenSee: Open Sytem for Earthquake Engineering Simulation, Verion PEER, Univerity of California, Berkeley, CA. [14] D. Bikini, M.N. Fardi, Deformation at flexural yielding of member with continuou or lap-pliced bar, Structural Concrete, 11(3), , [15] C.B. Haelton, A.B Liel, S. Taylor Lange, G.G. Deierlein, Beam-Column Element Model Calibrated for Predicting Flexural Repone Leading to Global Collape of RC Frame Building, PEER 2008; report 2007/03. 16

17 [16] CNR-DT 212/2013, Exiting building: the new Italian proviion for probabilitic eimic aement, Italian National Reearch Council (CNR), [17] A. Lucchini, F. Mollaioli, P. Bazzurro, Floor Repone Spectra for Bare and Infilled Reinforced Concrete Frame, Journal of Earthquake Engineering, 18(7), , [18] B. Bradley, A generalized conditional intenity meaure approach and holitic ground-motion election, Earthquake Engineering & Structural Dynamic, 39(12), , [19] D.M. Boore, G.M. Atkinon, Ground-motion prediction equation for the average horizontal component of PGA, PGV, and 5%-damped PSA at pectral period between 0.01 and 10.0, Earthquake Spectra, 24(1), , [20] K.W. Campbell, Y. Bozorgnia, A Comparion of Ground Motion Prediction Equation for Aria Intenity and Cumulative Abolute Velocity Developed Uing a Conitent Databae and Functional Form, Earthquake Spectra, 28(3), , [21] A. Aria, A meaure of earthquake intenity, in Seimic Deign for Nuclear Power Plant. R. J. Hanen (ed.), The MIT Pre: Cambridge, MA, 1970; [22] J.W. Baker, N. Jayaram, Correlation of Spectral Acceleration Value from NGA Ground Motion Model, Earthquake Spectra, 24(1), , [23] A. Lucchini, Y. Cheng, F. Mollaioli, L. Liberatore, Predicting Floor Repone Spectra for RC Frame Structure, Proceeding of the ECCOMAS Thematic Conference on Computational Method in Structural Dynamic and Earthquake Engineering, June 2013, Ko Iland, Greece. [24] F. Mollaioli, A. Lucchini, Y. Cheng, G. Monti, Intenity Meaure for the Seimic Repone Prediction of Bae-Iolated Building, Bulletin of Earthquake Engineering, 11(5), , [25] H. Ebrahimian, F. Jalayer, A. Lucchini, F. Mollaioli G. Manfredi, Relative Sufficiency of Alternative Scalar and Vector Intenity Meaure of Ground Shaking: Cae Studie, Bulletin of Earthquake Engineering, DOI: / , [26] S.R. Chaudhuri, R. Villaverde, Effect of building nonlinearity on eimic repone of nontructural component: a parametric tudy, Journal of Structural Engineering, 134(4), , [27] S.R. Chaudhuri, T.C. Hutchinon, Effect of nonlinearity of frame building on peak horizontal floor acceleration, Journal of Earthquake Engineering, 15(1), ,