Baker JW

Chandramohan R

Deierlein GG

UC Research Repository

Accounting for ground motion duration and spectral shape in structural design and assessmentReagan Chandramohan, Jack W. Baker, and Gregory G. DeierleinJohn A. Blume Earthquake Engineering Center, Stanford UniversityBackground and MotivationI The equivalent lateral force (ELF) procedure is the most widelyused structural design procedure in practice todayI This procedure considers only the Sa(T1) of the anticipatedground motions, while ignoring their durations and responsespectral shapesI Recent studies by the authors and others have, however,demonstrated that both duration and spectral shape significantlyinfluence structural collapse capacityObjectivesI Develop a framework to characterise the influence of durationand spectral shape on structural collapse riskI Propose a method to account for the eects of duration andspectral shape in the ELF structural design procedureExamples of long and short duration ground motions0 100 200 300a(t)Ds5−75 = 80 sLong duration record from 2011 Tohoku (MW = 9.0)0 100 200 300t (s)a(t)Ds5−75 = 5 sShort duration record from 1989 Loma Prieta (MW = 6.9)I Significant duration Ds was shown to be an eective metric ofstrong motion duration in a previous study by the authorsExamples of records with dierent spectral shapes0.1 0.2 1 3 6T (s)0.010.1110S a(T)(g)SaRatio = 0.88SaRatio = 2.95I SaRatio is a dimensionless scalar metric of response spectralshape, similar to εSaRatio(T , Tstart, Tend ) =Sa(T )Sa,avg (Tstart, Tend )Structural modelI Eight-story reinforced concrete moment frame building with afundamental period 1.76 s, designed for a site in SealeI Model incorporates the strength and stiness deterioration ofstructural components and destabilizing P − ∆ eects: bothcharacteristics required to capture the eect of durationColumnhingeBeam hingeJointpanelLeaningcolumnRotationMomentCyclicdeteriorationIn-cycledeteriorationHazard-consistent incremental dynamic analysis (H-IDA)I Traditional incremental dynamic analysis (IDA) is conductedusing a generic set of 88 recordsI The following linear regression model is fit to the estimatedground motion collapse intensitiesln Sa(T1) at collapse = c0 + cdur ln Ds + css ln SaRatio + ϵI R2 is 0.81 using both Ds and SaRatio as predictors, 0.40 using Dsalone, and 0.45 using SaRatio aloneI Ground motions with long durations and low SaRatio valuescause collapse when scaled to lower intensity levelsI The regression coeicients cdur and css quantify the sensitivity ofthe structure to duration and spectral shape respectivelyI The failure surface quantifies the probability a ground motionwith a certain Ds and SaRatio, when scaled to an intensity Sa(T1),will cause collapse: P [collapse | ln Ds, ln SaRatio, ln Sa(T1)]I The probability of collapse at an Sa(T1) level is computed byintegrating site-specific conditional distributions of Ds andSaRatio: f [ ln Ds, ln SaRatio | ln Sa(T1)], over the failure domainP [collapse | ln Sa(T1)] ="P [collapse | ln Ds, ln SaRatio, ln Sa(T1)]f [ ln Ds, ln SaRatio | ln Sa(T1)] d (ln Ds) d (ln SaRatio)I Linear contours represent P [collapse | ln Ds, ln SaRatio, ln Sa(T1)],elliptical contours represent f [ ln Ds, ln SaRatio | ln Sa(T1)], andthe degree of overlap represents P [collapse | ln Sa(T1)]I A hazard-consistent collapse fragility curve is computed byevaluating the reliability integral at dierent Sa(T1) levels0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Sa(1.76 s) (g)0.00.10.20.30.40.50.6Probabilityofcollapse02468Meanannualfrequencyofexceedance(×10−4)H-IDA: Using Sa(T1),SaRatio, and DsMSA: Using responsespectra and DsIDA: Using Sa(T1) onlyIDA: Using Sa(T1) andFEMA P695 spectralshape adjustmentHazard curveI The fragility curve computed using H-IDA agrees well with thatcomputed using hazard-consistent multiple stripe analysis (MSA)Design strength adjustment factorsI A structure designed using the ELF procedure is assumed topossess an x % (usually 10 %) probability of collapse at the MCERlevel, under ground motions possessing a reference duration Dsrefand spectral shape SaRatiorefI Dsref and SaRatioref are defined here as the median duration andspectral shape of the ground motions expected in Los AngelesI If the structure is actually located at site where ground motionsof duration Dstarget and spectral shape SaRatiotarget are expected,to maintain an x % collapse probability at the MCER level, it mustbe designed to a adjusted base shearV = k′durk′ssCSWk′dur =(DsrefDstarget)cdurk′ss =(SaRatiorefSaRatiotarget)cssI This method can be extended to nonlinear response historyanalysis (NLRHA) as well, by adjusting the MCER value insteadI cdur and css values are characterised for dierent structuralsystems by conducting similar analyses on a suite of models0.0 0.5 1.0 1.5 2.0 2.5 3.00.00.10.20.3−cdurRC ductile MFsSteel ductile MFsSteel BRBFsSteel SCBFs0.0 0.5 1.0 1.5 2.0 2.5 3.0T1 (s)0.00.51.0c ssI k′dur and k′ss values of 1 s reinforced concrete moment frames arecomputed for a number of dierent sites in Western USA−125˚−125˚−120˚−120˚−115˚−115˚−110˚−110˚35˚ 35˚40˚ 40˚45˚ 45˚50˚ 50˚EugeneSeattlePortlandBerkeleySan FranciscoLos Angeles0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6k’dur−125˚−125˚−120˚−120˚−115˚−115˚−110˚−110˚35˚ 35˚40˚ 40˚45˚ 45˚50˚ 50˚EugeneSeattlePortlandBerkeleySan FranciscoLos Angeles0.9 1.0 1.1 1.2 1.3 1.4 1.5k’ssCity Dstarget5−75 (s) k′dur SaRatiotarget k′ss k′durk′ssEugene 29.4 1.50 2.16 1.11 1.67San Francisco 10.2 1.20 2.02 1.19 1.43Portland 11.2 1.23 2.16 1.11 1.36Seale 9.6 1.18 2.20 1.09 1.29Berkeley 4.9 1.03 2.38 1.01 1.04Los Angeles 4.3 1.00 2.40 1.00 1.00I Structures at sites located near the Cascadia subduction zone andalong large crustal faults should be designed to higher baseshears to maintain a geographically uniform risk of collapseConclusionsI Developed a hazard-consistent incremental dynamic analysis(H-IDA) procedure that can be used to compute ahazard-consistent collapse fragility curve by post-processing theresults of IDA conducted using a generic record setI Developed a framework to account for the eects of duration andspectral shape in the structural design, and thereby ensure auniform risk of structural collapse over dierent geographicalregions and structural systems

Accounting for ground motion duration and spectral shape in structural design and assessment

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Accounting for ground motion duration and spectral shape in structural design and assessment

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