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5.2 Performance Levels and Limit States of StructureThe performance objective given by the Chinese “Code for seismic design ofbuildings” (GBJ11-89) is as follows. For frequently occurring earthquakes ofintensity lower than the seismic strengthening intensity of the region, buildingsdesigned according to the code shall not be damaged and/or shall be able to be inservice; for occasionally occurring earthquakes of intensity corresponding to theseismic strengthening intensity of the region, buildings may be damaged but shouldbe restorable to service with minor repairs; for rarely occurring earthquakes ofintensity higher than the seismic strengthening intensity of the region, buildings shallnot collapse or incur severe life-threatening damage. So, on the basis of the seismicstrengthening objective, three performance levels are specified: for frequentlyoccurring, occasionally occurring and rarely occurring earthquakes, which are the socalled“no damage during frequently occurring earthquakes, repairable duringoccasionally occurring earthquakes, and no collapse during rarely occurringearthquakes”.In order to conduct reliability analysis, the limit states of a structure need to begiven. Usually, five limit states are considered: representing initial cracking damage,slight damage, moderate damage, severe damage and collapse of the structure. Wecan see from the definition of three performance levels as mentioned above that thefirst one corresponds to the initial cracking damage; the second one corresponds toslight to moderate damage; the third one corresponds to severe damage.In this analysis, the limit state of a structure is defined in terms of the structuralductility factor. For each limit state, a corresponding capacity in terms of the ductilityfactor can be established. The ductility factor of the brick wall is defined as the ratioof the maximum deformation to the cracking deformation. The structural capacity canbe usually modeled by a lognormal distribution. According to Zhang (2002), on thebasis of the cracking features of walls in each hysteretic skeleton curve stage andcompared with the true earthquake damage degree of buildings, the median µ~R andlogarithmic standard deviation σ can be obtained, as shown in Table 3.RTable 3. Ductility factor capacityLimit statesBrick wall withoutconstructional columnBrick wall withconstructional column~ µRσ RRσRµ ~Initial cracking damageSevere damageCollapse1.0 0.31.6 0.32.6 0.31.0 0.32.6 0.34.8 0.3414
The collapse capacities of the brick wall with and without constructional columns aretaken as 90% and 85% of ultimate strength, respectively. The capacity for the severedamage is related to the ultimate strength. The capacity for the initial crackingdamage is related to the cracking strength. The capacities for slight damage andmoderate damage are taken as the values at 1/5 and 3/5 points between the capacitiesfor the initial cracking damage and severe damage, respectively. The median andlogarithmic standard deviation of story capacity of the brick buildings are obtained bycomposing the mean and standard deviation of the brick wall with and withoutconstructional columns according to their cross section ratio.5.3 Probabilistic Response of Earthquake Load-Structure SystemThe hysteretic model used in nonlinear seismic response analysis includes a negativestiffness branch. In order to avoid the probable unstable phenomenon in the iterationmethod and probable non-definite abnormal matrix in the variable stiffness matrixmethod during dealing with the negative stiffness, we use the method of nonlineardynamic response analysis based on pattern of self-equilibrating stresses (Zhang1998, Zhang 1997b) to analyze the response of multistory brick buildings.For each earthquake load-structure system, the nonlinear seismic responseanalysis is carried out. The i-th story ductility ratio is:U max,iµ i =U(7)c,iwhere U max,i is the maximum absolute inter-story deformation of the i-th story and U c,iis the cracking deformation of the i-th story.For the results of 81 samples, statistical analysis is utilized to determine mean,standard deviation and distribution function of the maximum response. According toZhang (2002), the maximum structural response can be modeled by a lognormaldistribution.5.4 Reliability AnalysisThe structural seismic reliability analysis is used to determine the limit stateprobability PF with respect to a particular limit state during the structure’s servicelife. It can be expressed as:10PF = ∑ λ I ⋅ Pj=6jf(Ij)where j=6, 7, 8, 9, 10, is the number of intensity. The structural reliability index withrespect to a particular limit state is:−1β = −Φ (PF)(8)(9)415
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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
Page 378 and 379: in X-direction pushover curves prac
Page 380 and 381: As an example, an idealized force-d
Page 382 and 383: The IN2 curve can be used in the pr
Page 384 and 385: HORIZONTALLY IRREGULAR STRUCTURES:
Page 386 and 387: Dutta and Das (2002, 2002b and refs
Page 388 and 389: They tested the procedure on three
Page 390 and 391: Table 1. Properties of the 4 WallsW
Page 392 and 393: The following is a summary of two s
Page 394 and 395: ectangular concrete deck supported
Page 396 and 397: REFERENCESAlmazan, J. L., and J. C.
Page 398 and 399: Rosenblueth, E. (1957). “Consider
Page 400 and 401: instantaneous period of vibration a
Page 402 and 403: value of the maximum plastic deform
Page 404 and 405: (a) elastic-perfectly plastic type(
Page 406 and 407: where a is the constant peculiar to
Page 408 and 409: Referring to Eq. (15), the natural
Page 410 and 411: -The effective period obtained by u
Page 412 and 413: eal damage data, rather than theore
Page 414 and 415: liquefaction-induced damage. This i
Page 416 and 417: Figure 5. Selected damage distribut
Page 418 and 419: Figure 6. Idealized capacity spectr
Page 420 and 421: I’ for the ductile case, as expec
Page 422 and 423: This study has shown that a modific
Page 424 and 425: thickness of the inner wall is usua
Page 426 and 427: 4. EARTHQUAKE GROUND MOTION INPUT A
Page 430 and 431: where λ I jis the occurrence rate
Page 432 and 433: intensity VI because the number of
Page 434 and 435: and thus are not considered in seis
Page 436 and 437: The values of the displacement modi
Page 438 and 439: constant amplitude loading (CA) or
Page 440 and 441: deterioration. These are the type o
Page 442 and 443: members, is the main feature of the
Page 444 and 445: RESULTS, DISCUSSIONS AND CONCLUSION
Page 446 and 447: systems, where FEMA estimations are
Page 448 and 449: The case study is a Hospital in the
Page 450 and 451: Table 1. Dimensions and amount of r
Page 452 and 453: 4.2 Incremental AnalysisBase shear
Page 454 and 455: When adding jackets to columns, the
Page 456 and 457: storyShear in interior Column [ton]
Page 458 and 459: PERFORMANCE-BASED SEISMIC ASSESSMEN
Page 460 and 461: 2. HYBRID FRAME BUILDINGSTwo precas
Page 462 and 463: 15’ - 0” 15’ - 0”Hybrid fra
Page 464 and 465: and maximum residual inter-story fr
Page 466 and 467: As the first step in understanding
Page 468 and 469: Table 3. Comparison of calculated m
Page 470 and 471: NEW MODEL FOR PERFORMANCE BASED DES
Page 472 and 473: (a) interior beam-column joint(b) k
Page 474 and 475: yxVN =VADjDBABLD jDOV cOVCN= VLV bV
Page 476 and 477: 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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