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Probability of Non-Exceedance10.80.60.40.200 5000 10000 15000 20000 25000 30000Connection Repair Cost - $YieldingBucklingFracturingFigure 8. Example loss function for moment resisting steel frames.Loss functions for life losses can be developed by evaluating historical data onthe number of serious and fatal injuries in buildings of different constructioncharacteristics that experienced different levels of damage. Comparisons of this typetypically show that life losses are negligible unless partial or total collapse occurs. Byconvolving the likelihood that persons are in a portion of a building that is subject tocollapse at the time an earthquake occurs, with the statistical rate that collapse hasresulted in various levels of injury in the past, it is possible to develop loss functionsthat relate the probability of serious injury and life loss to the collapse damage state.Once the hazard function, structural and nonstructural response functions, anddamage and loss functions for a building have been formed it is possible to completethe performance assessment process by estimating the risk of the various losses interms meaningful to the different decision makers who must select the desiredbuilding performance that will serve as the basis for .design. The simplest form ofloss prediction consists of determining the expected value of a loss (deaths, dollars, ordown time) given that the structure experiences a specific intensity of ground motionthat may for example, represent an event with a 10% probability of exceedance in 50years. The process starts by determining the conditional probability that structuralresponse, in our previous example interstory drift (δ i ), will be to a given level, if thestructure experiences this level of ground motion intensity. This is determined byevaluating the response function for the structure (e.g., Figure 4) at the given intensitylevel. The next step is to determine the total probability that the structure will bedamaged to each of the possible damage states (DS j ). This is performed byintegrating the conditional probability of experiencing each of the damage statesP(DS j |δ i ) as a function of interstory drift, δ i , e.g., from Figures 5, 6 and 7, with theprobability of experiencing different levels of δ I obtained from the response function.Finally, the expected loss is computed by summing the probable value of the loss(PV(Loss⏐DS j ), e.g., from loss functions such as Figure 8, given the occurrence of adamage state times the total probability of experiencing each of the damage statesP(DS) summed over all possible damage states, or in equation form:99
Expected Loss∫∫( Loss DS ) P( DS δ )= PVj j iP(δ ) d(DS)d(δ )(1)The average annual value of the loss can be obtained by realizing that theexpected loss calculated in equation (1) is actually the probable loss given that aspecific intensity of ground motion is experienced. Equation (1) can be used toevaluate the expected loss at each of a number of ground motion intensity levels, andthe average annual loss can be calculated as the sum of the expected loss at eachintensity level (EL k ) factored by the annual probability of experiencing each intensitylevel, and summing this over all possible intensity levels, or, in equation form:∫∫∫( Loss DS ) P( DS δ ) P( ( δ Sa ) P( Sa ) d(DS)d( ) d( Sa)Average Annual Loss = PVδ (2)jThe average annual loss can be summed, statistically, to provide the expectedloss over any desired interval of years. By calculating the combined uncertainty inthe losses associated with the hazard, response, damage and loss functions, it ispossible to estimate the expected losses at specified levels of confidence to produceother performance measures such as the popular Probable Maximum Loss (PML).3. SUMMARYWhen completed, the ATC-58 guidelines have the potential to revolutionize thepractice of performance-based design. They will introduce the practicing structuralengineer to the use of probabilistic structural reliability techniques and in the process,clarify the likelihood that performance-based designs will actually achieve intendedperformance. More important, they will enable the engineer to provide decisionmakers information that will be directly useful in selecting appropriate performancecriteria for building design and upgrade projects.REFERENCESAmerican Society of Civil Engineers (ASCE). 2002. Prestandard and Commentaryfor Seismic Rehabilitation of Buildings, Report No. FEMA-356, FederalEmergency Management Agency, Washington, D.C.Deierlein, G. G. 2004. “Overview of a Comprehensive Framework for EarthquakePerformance Assessment.” In Proceedings of the International Workshop onPerformance-Based Seismic Design, Bled, Slovenia, p.15.Earthquake Engineering Research Institute (EERI). 2000. Action Plan forPerformance-Based Seismic Design, Report No. FEMA-349, Federal EmergencyManagement Agency, Washington, D.C.Roeder, C. 2000. State of Art Report on Connection Performance, Report No. FEMA355D, Federal Emergency Management Agency, Washington, D.C.Structural Engineers Association of California (SEAOC). 1999. RecommendedLateral Force Requirements and Commentary, Appendix G, Performance-basedDesign, International Code Council, Whittier, CA, 1999.jiikk100
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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
Page 66 and 67: 3.2.1 A DCF Displacement-Based Form
Page 68 and 69: parameter k (the slope of the hazar
Page 70 and 71: POST-EARTHQUAKE FUNCTION OF HIGHWAY
Page 72 and 73: ln( EDP) a b ln ( IM )= + (1)Probab
Page 74 and 75: terms of global and local bridge pe
Page 76 and 77: Figure 3. Bridge column component d
Page 78 and 79: 5.2 Method B: MDOF Residual Displac
Page 80 and 81: calculated using a 2 dimensional mu
Page 82 and 83: MODELING CONSIDERATIONS IN PROBABIL
Page 84 and 85: location. Transverse reinforcement
Page 86 and 87: 2.50.1000Spectral Accel. (g)2.01.51
Page 88 and 89: Results indicate that 33% of the re
Page 90 and 91: 4.1.2 Elastic vs. Inelastic ModelsF
Page 92 and 93: The increased dispersion leads to h
Page 94 and 95: AN ANALYSIS ON THE SEISMIC PERFORMA
Page 96 and 97: The survey stood on the condition t
Page 98 and 99: who decide the design force levels
Page 100 and 101: It is interesting to clarify whethe
Page 102 and 103: concluded that the dependence of in
Page 104 and 105: Table 10. Problems of performance-b
Page 106 and 107: DEVELOPMENT OF NEXT-GENERATION PERF
Page 108 and 109: ground shaking hazard, probable str
Page 110 and 111: Vulnerability of buildings to losse
Page 112 and 113: Peak Interstory Drfit Ratio0.120.10
Page 114 and 115: Conditional Probability ofDamage St
Page 118 and 119: APPLICATIONS OF PERFORMANCE-BASED E
Page 120 and 121: 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
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ASSESSMENT OF SEISMIC PERFORMANCE I
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where e -λτ is the discounted fac
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IDR 3[rad]σPFAIDR34(g)σ PFA4media
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Figure 3a, shows an example of frag
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P(C LVCC i |IM )1.00.80.60.40.20.00
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E [ L T | IM ]$ 10 M$ 8 M$ 6 M$ 4 M
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SEISMIC RESILIENCE OF COMMUNITIES
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2. RESILIENCE CONCEPTSResilience fo
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quantification tools could be used
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structure remains elastic. This is
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of Figure 7a will be used. It is as
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Nigg, J. M. (1998). Empirical findi
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acceleration with a 475-year return
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limit states, the suggestions given
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∆NSLsi= SϑH(5)iTFor column-sway
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Pinto et al., 2004). The probabilit
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The main difficulty in assigning a
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Crowley, H., R. Pinho, and J. J. Bo
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analytical models generally have si
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Figure 2. Structure of the response
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can be used as a random variable of
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4. DERIVATION OF THE VULNERABILITY
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5. CONCLUSIONSDerivation of vulnera
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REFERENCESAbrams, D. P., A. S. Elna
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In general, these types of bench-mo
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where & x&(t ) = acceleration at th
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science building. The lateral load-
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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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