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3.2.2 Design for Tolerable Mean Annual Frequency of CollapseA different way to express desired collapse performance is to target a tolerable meanannual frequency (MAF) of collapse, λ Coll . This performance target is more general(it permits the estimation of the probability of collapse over an expected life time),but it is more difficult to implement because the “accurate” computation of a MAFrequires integration over the S a hazard curve. An approximate implementation ispossible by means of the simplified closed form expression proposed by Cornell(Cornell 1996), which estimates the MAF of collapse as follows:1 2 2λ Coll = ∫ FC|S( c | sa)| dλS a(sa)| = λS( ηC)exp( k β RC )(3)aa2SaThe simplified expression on the right-hand side contains the MAF of the spectralacceleration associated with the median collapse capacity, λ Sa (η C ), and a term thataccounts, in an approximate manner, for the uncertainties inherent in the computationof the collapse capacity. This term contains the slope of the hazard curve at thereferenced spectral acceleration value, k, and the dispersion(s) in the collapse fragilitycurve, β (the σ of the log of the data if a log-normal distribution is assumed for theprobability of collapse given the spectral acceleration). In the example illustratedhere only record-to-record (RTR) variability if considered, which is explicitlycontained in the fragility curves shown in Figure 5 (these fragility curves are obtainedby using an “expected” structural model subjected to 40 ground motions). Thus, theterm β RC in equation (3) expresses the effect of RTR variability only (“Randomness incollapse Capacity”), and is found to be on the order of 0.4 to 0.5 (except for longperiod structures for which it is smaller because of the dominance of P-delta effects).As an example, let us target a tolerable annual frequency of collapse of 0.0002(i.e., a tolerable probability of collapse of approximately 0.0002x50 = 0.01 in a 50year life). This criterion could be used, together with median collapse capacityspectra of the type shown in Figure 6(b), to arrive at effective design solutions. Againusing the example of a 9-story frame structure, the following design alternatives couldbe explored. If a period of 0.9 sec. and a component ductility capacity of δ c /δ y = 4 areassumed, then the median [S a (T 1 )/g]/γ value from Figure 6(b) is 7.7. For the sitespecific hazard curve of the previously illustrated example the slope of the S a hazardcurve in the neighborhood of a MAF of 0.0001 to 0.0004 is about 2.2, and the β RCvalue is about 0.4 (from collapse fragility analyses, Ibarra 2003). Thus, fromequation (3), the MAF of the S a associated with the median collapse capacity, λ Sa (η C ),is equal to 0.0002/exp(0.5x2.2 2 x0.4 2 ) = 0.000136. From the S a hazard curve for thesite of the example problem, the corresponding S a is 2.8g, and the corresponding γvalue is 2.8/7.7 = 0.36. Again, this is a larger value than that based on loss-controlledperformance targets. Alternatives are to increase the component ductility capacity (ifit is increased from 4 to 6, [S a (T 1 )/g]/γ is 8.9, and for the same λ Sa (η C ) of 0.000136the γ value becomes 2.8/8.9 = 0.31), or to increase the structure period. If, for515
instance, T 1 is 1.8 sec., the [S a (T 1 )/g]/γ value from Figure 6(b) is 5.4 (for δ c /δ y = 4),and, using the site specific k value of 2.4 for the T = 1.8 sec. hazard curve, λ Sa (η C )becomes 0.000126, the S a value for this MAF is 1.4g, and the base shear strengthparameter γ becomes 1.4/5.4 = 0.26.4. CONCLUSIONSConceptual PBD implies a decision process that leads to the selection of one orseveral effective design alternatives based on performance targets for acceptablelosses and a tolerable probability of collapse. In this context, two challenges have tobe addressed. One is to develop data on EDP limits associated with these performancetargets. The other is to select structural systems that efficiently accommodate theseEDP limits. This necessitates the development of MDOF “design decision aids” thatfacilitate the design decision process, or of global criteria that can be translated intostrength and stiffness requirements. This paper proposes a process to accomplisheffective PBD and illustrates how these two challenges can be met.ACKNOWLEDGEMENTSThis research was carried out as part of a comprehensive effort at Stanford's John A.Blume Earthquake Engineering Center to develop basic concepts for PBEE andsupporting data on seismic demands and capacities. This effort is supported by theNSF sponsored Pacific Earthquake Engineering Research (PEER) Center.REFERENCESCornell, C. A. (1996). Calculating building seismic performance reliability; a basis formulti-level design norms. Proc. 11 th WCEE, Acapulco, Mexico.Cornell, A., and H. Krawinkler. (2000). Progress and challenges in seismic performanceassessment. PEER News, April 2000.Deierlein, G. (2004). Overview of a comprehensive framework for earthquakeperformance assessment. Bled-04 proceedings.Ibarra, L. (2003). Global collapse of frame structures under seismic excitations. PhD.Dissertation Department of Civil Engineering, Stanford University, Stanford, CA.Krawinkler, H., and E. Miranda. (2004). Performance-based earthquake engineering.Chapter 9 of Earthquake Engineering: from engineering seismology to performancebasedengineering, CRC Press, 2004.Medina, R. A., and H. Krawinkler. (2003). Seismic demands for nondeteriorating framestructures and their dependence on ground motions. John A. Blume EarthquakeEngineering Center Report No. 144, Dept of Civil Eng’ng., Stanford U.Miranda, E., H. Aslani, and S. Taghavi. (2004). Assessment of seismic performance interms of economic losses. Bled-04 Proceedings.516
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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
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cost premium for the more expensive
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The future techniques will improve
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Benefit-cost ratio(BCR) 2.5UC Berke
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motivation to change the way they w
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CHANGING THE PARADIGM FOR PERFORMAN
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Ideally, the preliminary design of
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ModelM1M2M3Table 1. Description of
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Sample results from the response-hi
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In FEMA 273/356, the intersection o
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(M8 and M9) and the isolated frames
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THE ATC-58 PROJECT PLAN FOR NONSTRU
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The development of next-generation
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for these flexible nonstructural co
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spectra is several times larger tha
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The variability is associated with
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functions for a wide variety of non
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SIMPLIFIED PBEE TO ESTIMATE ECONOMI
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One can show (Porter et al. 2004) t
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( )FDM| EDP= xdm = 1 −FRdm , + 1,
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1. Facility definition. Same as in
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Table 1. Approximation of seismic r
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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
Page 478 and 479: 3.6 Failure ModeBased on the calcul
Page 480 and 481: Name ofSpecimenTable 2. Comparison
Page 482 and 483: EARTHQUAKE ACTIONS IN SEISMIC CODES
Page 484 and 485: examination of the risk implication
Page 486 and 487: Bozorgnia and Campbell (2004) find
Page 488 and 489: structure, the results of inelastic
Page 490 and 491: hazard curves will often vary throu
Page 492 and 493: large uncertainties associated with
Page 494 and 495: A PRAGMATIC APPROACH FOR PERFORMANC
Page 496 and 497: Relative Height20118160.8140.6 1210
Page 498 and 499: Yield Strength Coefficient, Cy2.01.
Page 500 and 501: Yield Strength Coefficient, Cy*1.61
Page 502 and 503: 2.6 Preliminary DesignIn the preced
Page 504 and 505: 4. CONCLUSIONSIn the space availabl
Page 506 and 507: EXAMINATION OF THE EQUIVALENT VISCO
Page 508 and 509: of the bilinear model with the ener
Page 510 and 511: 3. STUDY PARAMETERS AND ASSESSMENT
Page 512 and 513: decided to investigate the accuracy
Page 514 and 515: DISPLACEMENT(m)DISPLACEMENT (m)DISP
Page 516 and 517: The results for all 100 earthquake
Page 518 and 519: CONTRASTING PERFORMANCE-BASED DESIG
Page 520 and 521: Conceptual design is greatly facili
Page 522 and 523: 2. The availability of cost-of-repa
Page 524 and 525: There are many questions to be answ
Page 526 and 527: assess expected NSASS losses. For t
Page 530 and 531: THE PERFORMANCE REQUIREMENTS IN JAP
Page 532 and 533: 2.1 Law Enforcement and InspectionT
Page 534 and 535: Splices and development of reinforc
Page 536 and 537: as for the rising part of continuou
Page 538 and 539: compressive stress of concrete is t
Page 540 and 541: MOLIT Notification No. 1461 outline
Page 542 and 543: AUTHOR INDEXH. Akiyama.............
Page 544 and 545: F. Taucer .........................
Page 546 and 547: PEER 2003/06PEER 2003/05PEER 2003/0
Page 548 and 549: PEER 2001/13PEER 2001/12Modeling So
Page 550: PEER 1999/04 Adoption and Enforceme
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