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4. DERIVATION OF THE VULNERABILITY FUNCTIONThe procedure of calculating the probability of the maximum response exceeding agiven limit state (L.S.) is described as follows:1. Define the coefficient of variation (C.O.V.) and median of the maximum responseasC.O.V.: δ=σ/µMedian:µxm=(2)21+δwhere, σ is the standard deviation and µ is the mean value.2. Determine the displacement limit state (L.S.) associated with a specific damagelevel.3. Calculate the conditional cumulative probability for the log-normal distribution asln( L.S.)− λ2Φ() , λ = ln xm, ξ = ln(1 + δ )(3)ξ4. Calculate the probability of maximum displacement exceeding a given limit stateasln( L.S.)− λProb (max. displ. > L.S.) = 1- Φ()ξ(4)Whilst the effect of stiffness and strength change on the vulnerability curves areconsidered by response using the Response Database, the effect of ductility change(∆u i ) can be implemented into the calculation procedure of conditional probability bychanging the limit states (L.S.), as shown in Fig. 6.60∆u i1Original L.S.Changed L.S.Base shear (kN)4020Original L.S. Changed L.S.00 50 100 150Displacement (mm)Prob. (Sd > L.S.)0.80.60.40.200 0.1 0.2 0.3 0.4 0.5PGA (g)Figure 6. Effect of ductility change on vulnerability functions.192
Sample derivation of vulnerability functions corresponding to variousdisplacement limit states, for the same structures shown in Fig. 5 (elastic-perfectlyplastic,T=0.8 sec. and S.R.=0.1; 0.2;0.3), are presented in Fig. 7.Prob. (x > 20mm)Prob. (x > 60mm)10.80.60.40.2010.80.60.40.20S.R.= 0.1S.R.= 0.2S.R.= 0.30 0.1 0.2 0.3 0.4 0.5PGA (g)(a) L.S. = 20 mmS.R.= 0.1S.R.= 0.2S.R.= 0.30 0.1 0.2 0.3 0.4 0.5PGA (g)Prob. (x > 40mm)Prob. (x > 80mm)10.80.60.40.2010.80.60.40.20S.R.= 0.1S.R.= 0.2S.R.= 0.30 0.1 0.2 0.3 0.4 0.5PGA (g)(b) L.S. = 40 mmS.R.= 0.1S.R.= 0.2S.R.= 0.30 0.1 0.2 0.3 0.4 0.5PGA (g)(c) L.S. = 60 mm(d) L.S. = 80 mmFigure 7. Vulnerability functions for various limit states (L.S.).Sources of uncertainty can be categorized as (i) errors of ignorance andsimplification, (ii) measurement errors and (iii) statistical errors (Geysken et al.,1993). In each category, various uncertainties exist and their quantification iscomplex (Singhal and Kiremidjian 1998). The uncertainties can be implemented inthe derivation of vulnerability function as below:Prob (max. displ. > L.S.) = 1- Φ (ln( L.S.m) − λ)(5)2 22β + β + ⋅⋅⋅ + β1 2nwhere L.S. m is the median value of a displacement limit state and β i (i=1, 2, · · ·, n)represent various uncertainties. These can be demand uncertainty, capacityuncertainty and modeling uncertainty as in (Wen et al. 2004) or simply response andcapacity uncertainty (Dimova and Hirata 2000). Modeling of uncertainty is notpresented in this paper, though its importance in seismic loss assessment cannot beover-emphasized.193
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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
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 172 and 173: Figure 3a, shows an example of frag
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 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
Page 222 and 223: of sliding thresholds, are desirabl
Page 224 and 225: Retrofit of Nonstructural Component
Page 226 and 227: was developed to accommodate these
Page 228 and 229: tested by Meinheit and Jirsa are us
Page 230 and 231: where D is the maximum drift and N
Page 232 and 233: in predicting damage as well as rep
Page 234 and 235: 4.2.2 Modeling the Data Using Stand
Page 236 and 237: that the defining demand using a no
Page 238 and 239: • The influence on the dynamic re
Page 240 and 241: deviations σ and correlation coeff
Page 242 and 243: The first three modes of vibration
Page 244 and 245: Details about the ten records selec
Page 246 and 247: to allow a quantitative assessment
Page 248 and 249: Cornell A. C., F. Jalayer, R. Hambu
Page 250 and 251: limited possibilities of overcoming
Page 252 and 253: uildings, up to five stories high (
Page 254 and 255: Efficiency η, %100806040203D-RWBW-
Page 256 and 257: 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
Page 494 and 495:
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
Page 514 and 515:
DISPLACEMENT(m)DISPLACEMENT (m)DISP
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The results for all 100 earthquake
Page 518 and 519:
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
Page 534 and 535:
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.............
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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