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Figure 3a, shows an example of fragility function for the first damage state of areinforced concrete column in the building. It is observed that the EDP, which in thiscase corresponds to the interstory drift ratio, associated to certain damage states ofstructural components exhibits a very large scatter. In order to reduce the uncertaintyin damage estimation for these damage states fragility surfaces were developed(Aslani and Miranda 2004a). In a fragility surface the mean and standard deviation ofEDP corresponding to a damage state are evaluated as a function of a new parameter,α, which allows the incorporation of additional information. The parameter α canincorporate information on the element (e.g., geometry, detailing, etc.), its loadingand or a combination of the two. The probability of exceeding the damage state isthen estimated as a function of the level of EDP in the component but also as afunction of the parameter α. Figures 3b and 3c present examples of the fragilitysurfaces developed to estimate the probability of experiencing a shear failure and orthe loss of vertical load carrying capacity in non-ductile reinforced concrete columnsFor more details on the fragility curves and fragility surfaces of structural componentsthe reader is referred to Aslani and Miranda 2004a.Consistent with parameters used in FEMA 356, fragility functions for nonstructuralcomponents were developed as a function of either IDR and PFA. Nonstructuralcomponents were assumed to be sensitive to only one of these parameters.Figure 4a presents an example of fragility functions developed for gypsum boardpartitions as a function of the level of the IDR imposed to the partition. Figure 4bpresents an example of fragility functions developed for suspended ceilings as afunction of the level of the PFA in the component. More details on the fragility ofnonstructural components are presented in Taghavi and Miranda (2003a).3.3 Estimation of the Probability of CollapseAs shown in Eqs (2) and (5) both the expected value of the losses and the dispersionof the losses for a given ground motion intensity require an estimate of the probabilityof collapse. Two different approaches were used to estimate the probability ofcollapse. In one approach collapse was produced by the occurrence of lateral dis-P(DM 1 |EDP i )Column1.00.80.60.40.20.00.000 0.010 0.020EDP [IDR]P (DM 2 | EDP i )1.00.50.00.080.04EDP [ IDR]0.000.300.150.00α shearP (DM 3 |EDP i )1.00.50.00.100.05EDP [ IDR]0.0020.010.00.0α AxialFigure 3. Fragility assessment of non-ductile reinforced concrete columns.155
P(DM i|EDP i=IDR)1.00.8Gypsum-board partitions(a)P(DM i |EDP i =P FA)1.00.8Suspended ceilings(b)0.60.60.40.20.0DM1DM2DM30.00 0.01 0.02 0.03EDP [IDR]0.40.20.0DM1DM2DM30.0 1.0 2.0 3.0 4.0EDP [PFA (g)]Figure 4. Fragility functions of drift-sensitive and acceleration-sensitive nonstructuralcomponents at different damage measures; (a) gypsum-boardpartitions, (b) suspended ceilings.placements that lead to a dynamic instability in the structure. In the second approachit was assumed that the structure could collapse even if the lateral displacements werenot very large but enough to cause damage states that could trigger the loss of verticalcarrying capacity in structural members. The second type of collapse triggeringmechanism is particularly important in the case of non-ductile structures. In order toget an estimate of the probability of collapse due to the loss of vertical carryingcapacity of structural components it was assumed that if a loss of vertical carryingcapacity occurred in either a column of a slab column connection, such failure wouldtrigger a progressive collapse of the structure. As shown in Aslani and Miranda(2004b), with this assumption the probability of collapse due loss of vertical carryingcapacity (LVCC), P(C LVCC |IM), is equal to the largest probability of any individualstructural element that can loose its vertical carrying capacityP( C | IM ) = max [ P ( LVCC IM )]LVCC i |∀iwhere ( LVCC IM )P i | is the probability of losing the vertical carrying capacity in theith component conditioned on IM and is computed asP( LVCC | IM ) P( LVCC | EDP ) ⋅ dP( EDP IM )=∫ ∞ (9)|i i ii0where P ( LVCC i | EDP i ) is the probability of the ith component losing its verticalcarrying capacity given that it is subjected to a deformation level equal to edp.P ( LVCC i | EDP i ) is computed from fragility surfaces, developed for LVCC damagedP EDPi | IMstates on the basis of experimental studies on structural components. ( )is the probability density function of EDP i conditioned on IM, which can be estimatedfrom a probabilistic response analysis. Figure 5, presents a graphical presentation ofthe steps to estimate P(C LVCC |IM), using Eqs. (8) and (9).(8)156
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PERFORMANCE-BASED SEISMIC DESIGNCON
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CONTENTSTable of Contents..........
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REAL-TIME DYNAMIC HYBRID TESTING OF
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PREFACEThe workshop on “Seismic D
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LIST OF PARTICIPANTSSergio M. Alcoc
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RESOLUTIONSThe International Worksh
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CONCLUSIONS AND RECOMMENDATIONSThe
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nonlinear dynamic) and when they sh
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exists to develop testing protocols
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to be sent soon to the 28 members o
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factor γ I is 1.4 or 1.2 for essen
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i. The well-known relation µ θ -
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γ s =1.15. Values less than 1.0 me
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efore (factor α in Eq.(4)). Materi
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the force demand from the analysis,
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OVERVIEW OF A COMPREHENSIVE FRAMEWO
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ground motion Intensity Measure (IM
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2.2 Simulation of Engineering Deman
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describing the economic losses asso
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practice the localized gravity load
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Whereas financial and insurance org
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AN OUTLINE OF AIJ GUIDELINES FOR PE
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(7) a method of performance evaluat
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where, T: natural period of structu
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6. DAMAGE AND LIMIT DEFORMATIONSThe
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The limit inter-story deformations
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DirectionX-directionY-directionSkew
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HAZARD, GROUND MOTIONS AND PROBABIL
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of events with [X1>x 1 , X 2 >x 2 ,
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2.4 Option C: Sufficient IMs: Estim
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predictions and hence required samp
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PEER has put forward PBSA methodolo
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3.2.1 A DCF Displacement-Based Form
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parameter k (the slope of the hazar
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POST-EARTHQUAKE FUNCTION OF HIGHWAY
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ln( EDP) a b ln ( IM )= + (1)Probab
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terms of global and local bridge pe
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Figure 3. Bridge column component d
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5.2 Method B: MDOF Residual Displac
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calculated using a 2 dimensional mu
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MODELING CONSIDERATIONS IN PROBABIL
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location. Transverse reinforcement
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2.50.1000Spectral Accel. (g)2.01.51
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Results indicate that 33% of the re
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4.1.2 Elastic vs. Inelastic ModelsF
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The increased dispersion leads to h
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AN ANALYSIS ON THE SEISMIC PERFORMA
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The survey stood on the condition t
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who decide the design force levels
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It is interesting to clarify whethe
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concluded that the dependence of in
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Table 10. Problems of performance-b
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DEVELOPMENT OF NEXT-GENERATION PERF
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ground shaking hazard, probable str
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Vulnerability of buildings to losse
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Peak Interstory Drfit Ratio0.120.10
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Conditional Probability ofDamage St
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Probability of Non-Exceedance10.80.
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APPLICATIONS OF PERFORMANCE-BASED E
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PRACTICAL ADAPTATION FOR STAKEHOLDE
Page 122 and 123: cost premium for the more expensive
Page 124 and 125: The future techniques will improve
Page 126 and 127: Benefit-cost ratio(BCR) 2.5UC Berke
Page 128 and 129: motivation to change the way they w
Page 130 and 131: CHANGING THE PARADIGM FOR PERFORMAN
Page 132 and 133: Ideally, the preliminary design of
Page 134 and 135: ModelM1M2M3Table 1. Description of
Page 136 and 137: Sample results from the response-hi
Page 138 and 139: In FEMA 273/356, the intersection o
Page 140 and 141: (M8 and M9) and the isolated frames
Page 142 and 143: THE ATC-58 PROJECT PLAN FOR NONSTRU
Page 144 and 145: The development of next-generation
Page 146 and 147: for these flexible nonstructural co
Page 148 and 149: spectra is several times larger tha
Page 150 and 151: The variability is associated with
Page 152 and 153: functions for a wide variety of non
Page 154 and 155: SIMPLIFIED PBEE TO ESTIMATE ECONOMI
Page 156 and 157: One can show (Porter et al. 2004) t
Page 158 and 159: ( )FDM| EDP= xdm = 1 −FRdm , + 1,
Page 160 and 161: 1. Facility definition. Same as in
Page 162 and 163: Table 1. Approximation of seismic r
Page 164 and 165: The EAL values shown in Figure 3 mi
Page 166 and 167: ASSESSMENT OF SEISMIC PERFORMANCE I
Page 168 and 169: where e -λτ is the discounted fac
Page 170 and 171: IDR 3[rad]σPFAIDR34(g)σ PFA4media
Page 174 and 175: P(C LVCC i |IM )1.00.80.60.40.20.00
Page 176 and 177: E [ L T | IM ]$ 10 M$ 8 M$ 6 M$ 4 M
Page 178 and 179: SEISMIC RESILIENCE OF COMMUNITIES
Page 180 and 181: 2. RESILIENCE CONCEPTSResilience fo
Page 182 and 183: quantification tools could be used
Page 184 and 185: structure remains elastic. This is
Page 186 and 187: of Figure 7a will be used. It is as
Page 188 and 189: Nigg, J. M. (1998). Empirical findi
Page 190 and 191: acceleration with a 475-year return
Page 192 and 193: limit states, the suggestions given
Page 194 and 195: ∆NSLsi= SϑH(5)iTFor column-sway
Page 196 and 197: Pinto et al., 2004). The probabilit
Page 198 and 199: The main difficulty in assigning a
Page 200 and 201: Crowley, H., R. Pinho, and J. J. Bo
Page 202 and 203: analytical models generally have si
Page 204 and 205: Figure 2. Structure of the response
Page 206 and 207: can be used as a random variable of
Page 208 and 209: 4. DERIVATION OF THE VULNERABILITY
Page 210 and 211: 5. CONCLUSIONSDerivation of vulnera
Page 212 and 213: REFERENCESAbrams, D. P., A. S. Elna
Page 214 and 215: In general, these types of bench-mo
Page 216 and 217: where & x&(t ) = acceleration at th
Page 218 and 219: science building. The lateral load-
Page 220 and 221: emain the same, the magnitude of sl
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of sliding thresholds, are desirabl
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Retrofit of Nonstructural Component
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was developed to accommodate these
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tested by Meinheit and Jirsa are us
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where D is the maximum drift and N
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in predicting damage as well as rep
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4.2.2 Modeling the Data Using Stand
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that the defining demand using a no
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• The influence on the dynamic re
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deviations σ and correlation coeff
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The first three modes of vibration
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Details about the ten records selec
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to allow a quantitative assessment
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Cornell A. C., F. Jalayer, R. Hambu
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limited possibilities of overcoming
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uildings, up to five stories high (
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Efficiency η, %100806040203D-RWBW-
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Table 1. Performance criteria for c
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Because the analytical model strong
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REFERENCESAguilar, G., R. Meli, R.
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tests of its type ever conducted. T
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end work-point to work-point). And
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Fig. 5 shows the actual application
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3Roof Disp. (mm)250200150100500-50-
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Base Shear (kN)Base Shear (kN)40002
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8. CONCLUSIONSBased on the test and
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REAL-TIME DYNAMIC HYBRID TESTING OF
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:::::2004) can be formulated using
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The structure to be simulated is di
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measurements, to the modeling of th
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Figure 8. Two stories (left) and hy
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ROLES OF LARGE-SCALE TEST FOR ASSES
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mid-height in the third story, at w
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cycles were repeated for each ampli
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the tests with ALC panels were excl
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the relationship between the moment
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attachment details adopted for inst
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FULL-SCALE LABORATORY TESTING: STRA
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economic losses resulting from the
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4. OBJECTIVES AND OUTCOME OF STRUCT
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15001000500Shear [kN]0-8.0 -6.0 -4.
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5.1 3D Tests on a Torsionally Unbal
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Non-linear substructuring was recen
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PERFORMANCE BASED ASSESSMENT — FR
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4 x 50 m = 200 mC1 C2 C3h u = 7 mh
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some procedures are (contrary to th
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5 th floor disp. [cm]0.60.0-0.6CC =
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While the global drift of the build
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the use of such connections in eart
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I d = 0.25elastic limitmaximum resi
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As regards the influence of differe
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ON GROUND MOTION DURATION AND ENGIN
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time between the first and last acc
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FyFyFyFFFkk0.03kδδδcover a large
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T5b, T13a, T13b, T20a and T20b can
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Tabled results show that in the cas
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0 0.25 0.5 0.75 1Dkin PfSa[g]0 0.25
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ON DRIFT LIMITS ASSOCIATED WITH DIF
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BehaviourElasticInelasticCollapseDa
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Other factors such as the applied l
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4. MOMENT RESISTING FRAMES4.1 Ducti
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5Ductility factor432100 0.2 0.4 0.6
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5.1 Flexural Structural WallsAn exa
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MODAL PUSHOVER ANALYSIS: SYMMETRIC-
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Floor963SeattleNonlinear RHAFEMA1st
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The peak modal demands r n are then
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9BostonSeattleLos AngelesFloor63RSA
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5. EVALUATION OF MPA: UNSYMMETRIC-P
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Without additional conceptual compl
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AN IMPROVED PUSHOVER PROCEDURE FOR
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for a response governed by the fund
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2.2 Modal ScalingThe principal aim
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2.3 Pushover-History AnalysisSubsti
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(3) Calculate cumulative scale fact
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46.4 58 58 58 58 58 58 58 58 58 58
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EXTENSIONS OF THE N2 METHOD — ASY
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The strength reduction factor due t
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The relations apply to SDOF systems
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in X-direction pushover curves prac
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As an example, an idealized force-d
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The IN2 curve can be used in the pr
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HORIZONTALLY IRREGULAR STRUCTURES:
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Dutta and Das (2002, 2002b and refs
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They tested the procedure on three
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Table 1. Properties of the 4 WallsW
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The following is a summary of two s
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ectangular concrete deck supported
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REFERENCESAlmazan, J. L., and J. C.
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Rosenblueth, E. (1957). “Consider
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instantaneous period of vibration a
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value of the maximum plastic deform
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(a) elastic-perfectly plastic type(
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where a is the constant peculiar to
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Referring to Eq. (15), the natural
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-The effective period obtained by u
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eal damage data, rather than theore
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liquefaction-induced damage. This i
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Figure 5. Selected damage distribut
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Figure 6. Idealized capacity spectr
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I’ for the ductile case, as expec
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This study has shown that a modific
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thickness of the inner wall is usua
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4. EARTHQUAKE GROUND MOTION INPUT A
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5.2 Performance Levels and Limit St
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where λ I jis the occurrence rate
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intensity VI because the number of
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and thus are not considered in seis
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The values of the displacement modi
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constant amplitude loading (CA) or
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deterioration. These are the type o
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members, is the main feature of the
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RESULTS, DISCUSSIONS AND CONCLUSION
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systems, where FEMA estimations are
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The case study is a Hospital in the
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Table 1. Dimensions and amount of r
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4.2 Incremental AnalysisBase shear
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When adding jackets to columns, the
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storyShear in interior Column [ton]
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PERFORMANCE-BASED SEISMIC ASSESSMEN
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2. HYBRID FRAME BUILDINGSTwo precas
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15’ - 0” 15’ - 0”Hybrid fra
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and maximum residual inter-story fr
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As the first step in understanding
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Table 3. Comparison of calculated m
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NEW MODEL FOR PERFORMANCE BASED DES
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(a) interior beam-column joint(b) k
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yxVN =VADjDBABLD jDOV cOVCN= VLV bV
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3.3.2 B-modeThe equilibrium conditi
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3.6 Failure ModeBased on the calcul
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Name ofSpecimenTable 2. Comparison
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EARTHQUAKE ACTIONS IN SEISMIC CODES
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examination of the risk implication
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Bozorgnia and Campbell (2004) find
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structure, the results of inelastic
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hazard curves will often vary throu
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large uncertainties associated with
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A PRAGMATIC APPROACH FOR PERFORMANC
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Relative Height20118160.8140.6 1210
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Yield Strength Coefficient, Cy2.01.
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Yield Strength Coefficient, Cy*1.61
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2.6 Preliminary DesignIn the preced
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4. CONCLUSIONSIn the space availabl
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EXAMINATION OF THE EQUIVALENT VISCO
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of the bilinear model with the ener
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3. STUDY PARAMETERS AND ASSESSMENT
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decided to investigate the accuracy
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DISPLACEMENT(m)DISPLACEMENT (m)DISP
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The results for all 100 earthquake
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CONTRASTING PERFORMANCE-BASED DESIG
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Conceptual design is greatly facili
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2. The availability of cost-of-repa
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There are many questions to be answ
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assess expected NSASS losses. For t
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3.2.2 Design for Tolerable Mean Ann
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THE PERFORMANCE REQUIREMENTS IN JAP
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2.1 Law Enforcement and InspectionT
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Splices and development of reinforc
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as for the rising part of continuou
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compressive stress of concrete is t
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MOLIT Notification No. 1461 outline
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AUTHOR INDEXH. Akiyama.............
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F. Taucer .........................
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PEER 2003/06PEER 2003/05PEER 2003/0
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PEER 2001/13PEER 2001/12Modeling So
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PEER 1999/04 Adoption and Enforceme
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