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The peak modal demands r n are then combined by an appropriate modal combinationrule—SRSS for symmetric-plan buildings and CQC for unsymmetric-plan systems—to estimate the total demand. This procedure is directly applicable to the estimation ofdeformation demands (e.g., floor displacements and story drifts) but computation ofplastic hinge rotations and member forces requires additional consideration.Although modal analysis theory is strictly not valid for inelastic systems, the factthat elastic modes are coupled only weakly in the response of inelastic systems tomodal inertia forces (Chopra and Goel, 2002, 2004) permitted development of MPA,an approximate procedure.3.2 Summary of ProcedureThe MPA procedure has been summarized as a sequence of computational steps toestimate floor displacements and story drifts for symmetric-plan buildings (Goel andChopra, 2004a) and unsymmetric-plan buildings (Chopra and Goel, 2004).3.3 Plastic Hinge Rotations and Member ForcesAlthough the total floor displacements and story drifts are computed by combiningthe values obtained from gravity load and “modal” pushover analyses for all modescontributing significantly to the demand, the plastic hinge rotations and memberforces are not computed by this procedure. The rotations of plastic hinges can beestimated from the story drifts by a procedure presented earlier by Gupta andKrawinkler (1999). The member forces are computed from the total memberdeformations using the member force-deformation (or moment rotation) relationship,recognizing P-M interaction in columns. These procedures to compute member forcesare described in Goel and Chopra (2004b).4. EVALUATION OF MPA: SYMMETRIC-PLAN BUILDINGS4.1 Higher Mode Contributions in Seismic DemandsFigures 3 and 4 show the median values of story drift and beam plastic rotationdemands, respectively, including a variable number of “modes” in MPAsuperimposed with the “exact” result from nonlinear RHA. The first “mode” alone isinadequate in estimating story drifts, but with a few “modes” included, story driftsestimated by MPA are generally similar to the nonlinear RHA results.The first “mode” alone fails to identify the plastic hinging in the upper floors ofall buildings and also in the lower floors of the Seattle 20-story building. Includinghigher-“mode” contributions also improves significantly the estimate of plastic hingerotations. In particular, plastic hinging in upper stories is now identified, and the MPAestimate of plastic rotation is much closer—compared to the first-“mode” result—tothe “exact” results of nonlinear RHA.337
9BostonSeattleLos AngelesFloor63NL−RHAMPA1 "Mode"2 "Modes"3 "Modes"9−StoryG0 0.5 1 1.5 2200 1 2 3 4 50 1 2 3 4 5Floor16128NL−RHAMPA1 "Mode"3 "Modes"5 "Modes"420−StoryG0 0.5 1 1.5 20 1 2 3 4 5Story drift, ∆ MPAor ∆ NL−RHA(%)0 1 2 3 4 5Figure 3. Median story drifts determined by nonlinear RHA and MPA withvariable number of “modes”; P-∆ effects due to gravity loads are included.9SeattleLos AngelesFloor63NL−RHAMPA1 "Mode"2 "Modes"3 "Modes"9−StoryG0 0.02 0.04 0.06 0 0.02 0.04 0.0620Floor16128NL−RHAMPA1 "Mode"3 "Modes"5 "Modes"4G20−Story0 0.02 0.04 0.06Beam Plastic Rotation (rad)0 0.02 0.04 0.06Beam Plastic Rotation (rad)Figure 4. Median plastic rotations in interior beams determined by nonlinearRHA and MPA with variable number of “modes”; P-∆ effects due to gravityloads are included.338
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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
Page 302 and 303: 15001000500Shear [kN]0-8.0 -6.0 -4.
Page 304 and 305: 5.1 3D Tests on a Torsionally Unbal
Page 306 and 307: Non-linear substructuring was recen
Page 308 and 309: PERFORMANCE BASED ASSESSMENT — FR
Page 310 and 311: 4 x 50 m = 200 mC1 C2 C3h u = 7 mh
Page 312 and 313: some procedures are (contrary to th
Page 314 and 315: 5 th floor disp. [cm]0.60.0-0.6CC =
Page 316 and 317: While the global drift of the build
Page 318 and 319: the use of such connections in eart
Page 320 and 321: I d = 0.25elastic limitmaximum resi
Page 322 and 323: As regards the influence of differe
Page 324 and 325: ON GROUND MOTION DURATION AND ENGIN
Page 326 and 327: time between the first and last acc
Page 328 and 329: FyFyFyFFFkk0.03kδδδcover a large
Page 330 and 331: T5b, T13a, T13b, T20a and T20b can
Page 332 and 333: Tabled results show that in the cas
Page 334 and 335: 0 0.25 0.5 0.75 1Dkin PfSa[g]0 0.25
Page 336 and 337: ON DRIFT LIMITS ASSOCIATED WITH DIF
Page 338 and 339: BehaviourElasticInelasticCollapseDa
Page 340 and 341: Other factors such as the applied l
Page 342 and 343: 4. MOMENT RESISTING FRAMES4.1 Ducti
Page 344 and 345: 5Ductility factor432100 0.2 0.4 0.6
Page 346 and 347: 5.1 Flexural Structural WallsAn exa
Page 348 and 349: MODAL PUSHOVER ANALYSIS: SYMMETRIC-
Page 350 and 351: Floor963SeattleNonlinear RHAFEMA1st
Page 354 and 355: 9BostonSeattleLos AngelesFloor63RSA
Page 356 and 357: 5. EVALUATION OF MPA: UNSYMMETRIC-P
Page 358 and 359: Without additional conceptual compl
Page 360 and 361: AN IMPROVED PUSHOVER PROCEDURE FOR
Page 362 and 363: for a response governed by the fund
Page 364 and 365: 2.2 Modal ScalingThe principal aim
Page 366 and 367: 2.3 Pushover-History AnalysisSubsti
Page 368 and 369: (3) Calculate cumulative scale fact
Page 370 and 371: 46.4 58 58 58 58 58 58 58 58 58 58
Page 372 and 373: EXTENSIONS OF THE N2 METHOD — ASY
Page 374 and 375: The strength reduction factor due t
Page 376 and 377: 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
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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
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
Page 524 and 525:
There are many questions to be answ
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assess expected NSASS losses. For t
Page 528 and 529:
3.2.2 Design for Tolerable Mean Ann
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
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AUTHOR INDEXH. Akiyama.............
Page 544 and 545:
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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