Eurocode compliant seismic analysis and design of r c buildings concepts commentary and worked examp

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Geotechnical, Geological and Earthquake Engineering

Ioannis Avramidis

Asimina Athanatopoulou

Konstantinos Mor dis

Anastasios Sextos

Agathoklis Giaralis

Eurocode-Compliant

Seismic Analysis and Design of R/C Buildings

Concepts, Commentary and Worked Examples with Flowcharts

Geotechnical,Geologicaland EarthquakeEngineering

Volume38

Serieseditor

AtillaAnsal,SchoolofEngineering,O ¨ zyeg ˘ inUniversity,Istanbul,Turkey

EditorialAdvisoryBoard

JulianBommer,ImperialCollegeLondon,U.K.

JonathanD.Bray,UniversityofCalifornia,Berkeley,U.S.A. KyriazisPitilakis,AristotleUniversityofThessaloniki,Greece SusumuYasuda,TokyoDenkiUniversity,Japan

Moreinformationaboutthisseriesathttp://www.springer.com/series/6011

IoannisAvramidis • AsiminaAthanatopoulou

KonstantinosMorfidis • AnastasiosSextos AgathoklisGiaralis

Eurocode-Compliant SeismicAnalysisand DesignofR/CBuildings

Concepts,CommentaryandWorked ExampleswithFlowcharts

IoannisAvramidis DepartmentofCivilEngineering AristotleUniversityofThessaloniki Thessaloniki,Greece

KonstantinosMorfidis InstituteofEngineeringSeismology andEarthquakeEngineering Thessaloniki,Greece

AsiminaAthanatopoulou DepartmentofCivilEngineering AristotleUniversityofThessaloniki Thessaloniki,Greece

AnastasiosSextos DepartmentofCivilEngineering UniversityofBristol&Aristotle UniversityofThessaloniki Bristol,UK&Thessaloniki,Greece AgathoklisGiaralis DepartmentofCivilEngineering CityUniversityLondon London,UK

ISSN1573-6059ISSN1872-4671(electronic) Geotechnical,GeologicalandEarthquakeEngineering ISBN978-3-319-25269-8ISBN978-3-319-25270-4(eBook) DOI10.1007/978-3-319-25270-4

LibraryofCongressControlNumber:2015940405

ThisbookisanextendedtranslationbasedontheoriginaleditioninGreek:“

”.Publisher:Theauthors(IoannisAvramidis,AsiminaAthanatopoulou,Konstantinos Morfidis,AnastasiosSextos),2011;Distributor:Techartbooks(http://www.techartbooks.gr)

SpringerChamHeidelbergNewYorkDordrechtLondon © SpringerInternationalPublishingSwitzerland2016

Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart ofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations, recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmission orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilaror dissimilarmethodologynowknownorhereafterdeveloped.

Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthis publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexempt fromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthis bookarebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernorthe authorsortheeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontained hereinorforanyerrorsoromissionsthatmayhavebeenmade.

Printedonacid-freepaper

SpringerInternationalPublishingAGSwitzerlandispartofSpringerScience+BusinessMedia (www.springer.com)

Preface

Thisbookaimstoserveasanessentialreferencetofacilitatecivilengineers involvedinthedesignofnewconventional(ordinary)reinforcedconcrete(r/c) buildingsregulatedbythecurrentEuropeanEurocode8orEC8(EN1998-1:2004) andEC2(EN1992-1-1:2004)codesofpractice.Itisaddressedtopractitioners workinginconsultinganddesigningengineeringcompaniesandtoadvanced undergraduateandpostgraduatelevelcivilengineeringstudentsattendingmodules andcurriculaintheearthquake-resistantdesignofstructuresand/orundertaking pertinentdesignprojects.Thebookconstitutesanupdatedandsignificantly extendedversionofatextbookco-authoredbythefirstfourauthorspublishedin 2011intheGreeklanguage.Thechangesandamendmentsincorporatedintothe currentbookdiscusstherecenttrendsinperformance-basedseismicdesignof structuresandprovideadditionalpracticalguidanceonfiniteelementmodelling ofr/cbuildingstructuresforcode-compliantseismicanalysismethods.

Itisemphasizedthatthisbookisneitheracomprehensivetextonthedesignof earthquake-resistantstructuresnordoesitofferacompletecommentaryontheEC8 provisions.Tothisend,itpresumesthatthe“user”:

•Hassufficientknowledgeofthefundamentalconcepts,principles,andmethods ofstructuralanalysisforbothstaticanddynamicloadspertinenttothe earthquake-resistantdesignofstructuresandofr/cdesign

•HasaccesstoandappreciationoftheEC8(EN1998-1:2004)andEC2 (EN1992-1-1:2004)codesofpractice

Thebookissplitnotionallyintotwoparts.Thefirstpartcomprisesthefirstthree chaptersinwhich:

•Thefundamentalprinciplesforearthquake-resistantdesignareintroducedand discussionandcommentsareincludedonhowtheseprinciplesreflectonthe

currentEC8(EN1998-1:2004)codeandonseveralinternationalguidelinesfor performance-basedseismicdesignofstructures(Chap. 1).

•Importantpracticalaspectsontheconceptualdesign,finiteelementmodelling, analysis,anddetailingofcode-compliantearthquake-resistantr/cbuildingsare discussedandtherelevantrequirementsprescribedbytheEC8(EN19981:2004)provisionsarecriticallycommentedupon(Chap. 2).

•Alltherequiredlogicsteps,computations,andverificationchecksforthedesign (seismicanalysisandstructuralmemberdetailing)ofordinaryr/cbuildings accordingtotheEC8(EN1998-1:2004)andEC2(EN1992-1-1:2004)are presentedinasequentialandmethodologicalmannerbymeansofself-contained flowchartsandadditionalexplanatorycomments(Chap. 3).

Thesecondpartofthebook(Chap. 4)includesthreenumericalexample problems,solvedindetail,toillustratetheimplementationofvariousclausesof theEC8fortheseismicanalysisanddesignofthreedifferentmultistoreybuildings. Thepropertiesandstructurallayoutsoftheconsideredbuildingsarejudicially chosentoachievethenecessarysimplicitytoserveasgeneralbenchmarkstructures whilemaintainingimportantfeaturescommonlyencounteredinreal-lifedesign scenarios.Inthisregard,thesebenchmarkexampleproblemsprovidefor:

•Acomprehensiveillustrationofcompleteanddetailednumericalapplicationsto gainabetterappreciationoftheflowandthesequenceoftherequiredlogicand computationalstepsinvolvedintheearthquake-resistantdesignofstructures regulatedbytheEC8

•Verificationtutorialstocheckthereliabilityofcustom-madecomputerprograms andofcommercialfiniteelementsoftwaredeveloped/usedforthedesignof earthquake-resistantr/cbuildingscomplyingwiththeEC8

ThebookiscomplementedbyanAppendixdiscussingtheinelasticstatic (pushover)analysisoftheEC8whichisallowedtobeusedasanalternativemethod tothestandardequivalentlineartypesofanalysisforthedesignofEC8compliant r/cbuildingstructures.InasecondAppendix,theconceptsoftorsionalsensitivity aredelineatedusinganalyticalformulaeandnumericalexamples.Lastly,tofurther facilitatepractitioners,allrequirementsposedbyboththeEC2(EN1992-1-1:2004) andtheEC8(EN1998-1:2004)codesregardingthedetailingofr/cstructural membersarecollectedinaconcisetabular/graphicalformatinathirdAppendix. Notably,pertinentselectedbibliographyisincludedattheendofeachchapterto directthereadertoappropriatesourcesdiscussingsomeofthehereinintroduced materialingreaterdetail.

Asafinalnote,wearethankfultoThanasisSpiliopoulos(SchoolBuildings OrganizationSA,Athens,Greece)andtoProf.PloutarchosGiannopoulos(National TechnicalUniversityofAthens,Greece)whoprovideduswithvariousphotosfrom theirpersonalarchiveandallowedustoincludetheminthebook.Wefurther acknowledgeallcolleaguesoftheacademiccommunityandpractisingengineers whocontributedtotheenhancementoftheoriginalmanuscriptthroughdiscussions, reviewing,andindependentnumericalverificationchecks.

Thessaloniki,GreeceIoannisAvramidis Thessaloniki,GreeceAsiminaAthanatopoulou Thessaloniki,GreeceKonstantinosMorfidis Bristol,UK&Thessaloniki,GreeceAnastasiosSextos London,UKAgathoklisGiaralis

January2015

1FundamentalPrinciplesfortheDesignofEarthquake-Resistant Structures .............................................1

1.1PartialProtectionAgainstStructuralDamageastheUnderlying DesignPhilosophyforEarthquakeResistance. ..............2

1.1.1TheUncertainNatureoftheSeismicAction..........2

1.1.2Canan“Absolute”LevelofProtectionAgainst theSeismicHazardBeAchieved?... ..............3

1.1.3FullandPartialProtectionAgainstStructuralDamage foraGivenDesignSeismicAction. ................3

1.1.4DesignObjectivesandRequirementsforPartial ProtectionAgainstStructuralDamageinCurrent SeismicCodesofPractice .......................5

1.1.5Stiffness,Strength,andDuctility:TheKeyStructural PropertiesinEarthquakeResistantDesign ...........8

1.2ImplementationofthePartialProtectionAgainstStructural DamageSeismicDesignPhilosophyinCurrent CodesofPractice ....................................14

1.2.1DuctilityDemandandDuctilityCapacity............16

1.2.2The“Interplay”BetweenDuctilityCapacityandForce ReductionorBehaviourFactor. ...................18

1.2.3TheRelationshipAmongtheBehaviourFactor, theDuctilityCapacityandtheOverstrength ofR/CBuildings... ...........................26

1.2.4Force-BasedSeismicDesignUsingaLinear Single-Seismic-Action-LevelAnalysis ..............28

1.2.5AdditionalQualitativeRequirementsforDuctile EarthquakeResistantDesign... ..................32

1.2.6TheRationaleofCapacityDesignRequirements.......34 ix

1.3TheConceptofPerformance-BasedSeismicDesign: ARecentTrendPointingtotheFutureofCodeProvisions......40

1.3.1TheNeedforPerformance-BasedSeismicDesign ......40

1.3.2EarlyGuidelinesforPerformance-BasedSeismic DesignandTheirRelationtotheTraditionalDesign Philosophy ..................................43

1.3.3RecentGuidelinesonPerformance-BasedSeismic DesignforNewStructures(MC2010andATC-58) .....49

1.4OntheSelectionofaDesiredPerformanceLevel inCode-CompliantSeismicDesignofNewR/CBuildings......51 References.............................................55

2DesignofR/CBuildingstoEC8-1:ACriticalOverview ..........59

2.1ConceptualDesignPrinciplesforEarthquake-Resistant Buildings..........................................64

2.1.1DesirableAttributesoftheLateralLoad-Resisting StructuralSystemandFundamentalRules............64

2.1.2FrequentlyObservedDeficienciesinStructuralLayouts..70

2.2DuctileBehaviorConsiderationsandPreliminarySizing ofR/CStructuralMembers.. ...........................73

2.2.1TheFundamentalQuestionattheOnsetofSeismic Design:WhatPortionoftheDuctilityCapacity ShouldBe“Utilized”?..........................73

2.2.2LocalandGlobalDuctilityCapacity ................76

2.2.3FactorsInfluencingtheLocalDuctilityCapacity ofR/CStructuralMembers ......................78

2.2.4CapacityDesignRulesforDuctileGlobalCollapse Mechanisms .................................82

2.3StructuralandLoadingModelingforSeismicDesignofR/C BuildingsUsingLinearAnalysisMethods ..................91

2.3.1EC8-CompliantLoadingModeling forSeismicDesign ............................91

2.3.2EC8-CompliantModelingofSuperstructure, Foundation,andSupportingGround................99

2.3.3CommonStructuralFEModelingPractices ofMultistoreyR/CBuildingsforLinearMethods ofAnalysis..................................109

2.4StructuralAnalysisMethodsforSeismicDesignofR/C BuildingStructures ...................................136

2.4.1SelectionofStructuralAnalysisMethods forSeismicDesign ............................138

2.4.2OverviewofEC8StructuralAnalysisMethods ........146

2.4.3DiscussionandRecommendationsonEC8Analysis Methods....................................147

2.4.4OverstrengthDistributionVerificationandSensitivity Analyses....................................156

2.5OntheUseofCommercialSoftwareforRoutine SeismicDesign... ..................................160

2.5.1VerificationofCommercialStructuralAnalysis SoftwareviaBenchmarkStructuralAnalysis andDesignProblems ...........................160

2.5.2DesirableAttributesandUseofGood QualitySoftware.. ............................162 References.............................................165

3PracticalImplementationofEC8forSeismicDesignofR/C Buildings–FlowchartsandCommentary .....................169

3.1EC8-CompliantSeismicAnalysisStepsandFlowcharts ........174

3.1.1ConditionsandVerificationChecks forStructuralRegularity. .......................176

3.1.2ClassificationofaLateralLoad-Resisting StructuralSystem .............................181

3.1.3SelectionofDuctility(Capacity)Class..............186

3.1.4DeterminationoftheMaximumAllowed BehaviourFactor..............................188

3.1.5SelectionandImplementationofEquivalentLinear MethodsforSeismicAnalysis ....................195

3.1.6AccountingfortheVerticalComponentoftheSeismic Action ......................................204

3.2Deformation-BasedVerificationChecks...................206

3.2.1VerificationCheckforSecondOrder(P- Δ)Effects (FC-3.10a andFC-3.10b)........................209

3.2.2VerificationCheckforMaximumInterstoreyDrifts (FC-3.11a andFC-3.11b)........................215

3.3SpecialRequirementsforInfillWallsinR/CBuilding Structures .........................................216

3.4PracticalRecommendationsforEC8CompliantSeismic AnalysisandVerificationChecks ........................218

3.5DeterminationofDesignSeismicEffectsforr/cWalls.........219

3.5.1EnvelopeBendingMomentDiagramforSeismic Designofr/cWalls ............................220

3.5.2EnvelopeShearForceDiagramforSeismicDesign ofr/cWalls..................................223

3.6DetailingRequirementsandVerificationChecksforr/c StructuralMembers ..................................225 References.............................................245

4EC8-CompliantSeismicAnalysisandDesignExamples ..........247

4.1ExampleA:Five-StoreySingleSymmetricIn-PlanBuilding withDualLateralLoad-ResistingStructuralSystem ...........251

4.1.1Geometric,Material,andSeismicActionData ........251

4.1.2ModelingAssumptions.........................253

4.1.3VerificationChecksforRegularityforBuildingA ......255

4.1.4ClassificationoftheLateralLoad-ResistingStructural SystemofBuildingA. .........................260

4.1.5SelectionofDuctility(Capacity)ClassofBuildingA...262

4.1.6DeterminationoftheMaximumAllowedBehaviour FactorforBuildingA..........................263

4.1.7SelectionofanEquivalentLinearMethodofSeismic AnalysisforBuildingA .........................268

4.1.8StaticAnalysisforGravityLoadsoftheDesignSeismic LoadingCombination(G“+” ψ2Q)forBuildingA.....268

4.1.9SeismicAnalysisofBuildingAUsingtheModal ResponseSpectrumMethodandDeformation-Based VerificationChecks. ...........................269

4.1.10SeismicAnalysisofBuildingAUsingtheLateral ForceMethodandDeformation-Based VerificationChecks ............................294

4.1.11ComparisonofDesignSeismicEffectsforBuilding AObtainedfromtheMRSMandtheLFM ...........314 4.2ExampleB:Five-StoreyTorsionallySensitiveBuilding withDualLateralLoad-ResistingStructuralSystem ...........318

4.2.1Geometric,Material,andSeismicActionData ........318

4.2.2ModelingAssumptions.........................321

4.2.3VerificationChecksforRegularityforBuildingB......323

4.2.4ClassificationoftheLateralLoad-ResistingStructural SystemofBuildingB..........................330

4.2.5SelectionofDuctility(Capacity)ClassofBuildingB...331

4.2.6DeterminationoftheMaximumAllowedBehaviour FactorforBuildingB ...........................331

4.2.7SelectionofanEquivalentLinearMethodofSeismic AnalysisforBuildingB. ........................331

4.2.8StaticAnalysisforGravityLoadsoftheDesignSeismic LoadingCombination(G“+” ψ2Q)forBuildingB. ....332

4.2.9SeismicAnalysisofBuildingBUsingtheModal ResponseSpectrumMethodandDeformation-Based VerificationChecks. ...........................333

4.3ExampleC:Four-StoreyBuildingwithCentralR/CCore andaBasementonCompliantSupportingGround ............356

4.3.1Geometric,Material,andSeismicActionData ........356

4.3.2ModelingAssumptions.........................360

4.3.3VerificationChecksforRegularityforBuildingC......374

4.3.4ClassificationoftheLateralLoad-resistingStructural SystemofBuildingC..........................378

4.3.5SelectionofDuctility(Capacity)ClassofBuildingC...380

4.3.6DeterminationoftheMaximumAllowedBehaviour FactorforBuildingC ...........................380

4.3.7SelectionofanEquivalentLinearMethodofSeismic AnalysisforBuildingC. ........................382

4.3.8StaticAnalysisforGravityLoadsoftheDesignSeismic LoadingCombination(G“+” ψ2Q)forBuildingC. ....382

4.3.9SeismicAnalysisofBuildingBUsingtheModal ResponseSpectrumMethodandDeformation-Based VerificationChecks. ...........................383

4.3.10DeterminationofNormalStressesTransferred fromPadFootingstoSupportingGround........ ....392

4.3.11DetailingandDesignVerificationsofTypical StructuralMembersofBuildingC.................401

4.3.12EnvelopeBendingMomentandShearForce DiagramfortheDuctileWallW3XofBuildingC ......445 References.............................................450

AppendixA–QualitativeDescriptionofEC8Non-linear Static(Pushover)AnalysisMethod .............................453

AppendixC–ChartFormofEurocode2and8Provisionswith RespecttotheSectionalDimensionsandtheReinforcement ofStructuralMembers ......................................473

Chapter1

FundamentalPrinciplesfortheDesign ofEarthquake-ResistantStructures

Abstract Thischapterprovidesaconcisequalitativeoverviewofthephilosophy forearthquakeresistantdesignofordinarystructuresadoptedbyrelevantinternationalcodesofpractice,includingEurocode8.Theaimistofacilitatepracticing engineerswiththeinterpretationofthecode-prescribeddesignobjectivesand requirementsfortheseismicdesignofordinaryreinforcedconcrete(r/c)building structureswhichallowforstructuraldamagetooccurforanominaldesignseismic actionspecifiedinaprobabilisticmanner.Inthisregard,thestructuralpropertiesof stiffness,strength,andductilityareintroducedalongwiththestandardcapacity designrulesandrequirements.Further,theroleofthesestructuralpropertiesinthe seismicdesignofr/cbuildingstructuresfollowingaforce-basedapproachin conjunctionwithequivalentlinearanalysismethodsisexplained.Emphasisis placedondelineatingtheconceptofthebehaviourfactor,orforcereductionfactor, whichregulatestheintensityoftheseismicdesignloadsandductilitydemands. Moreover,thedevelopmentandcurrenttrendsintheemergingperformance-based designapproachforearthquakeresistancearebrieflyreviewed.Lastly,practical recommendationstoachievehigher-than-the-minimum-requiredbycurrentcodes ofpracticestructuralperformancewithintheforce-baseddesignapproachare provided.

Keywords Seismicdesignobjectives•Stiffness•Strength•Ductility•Capacity design•Force-baseddesign•Performance-baseddesign•Behaviourfactor

Despiteminordifferences,currentcodesofpracticeandguidelinesregulatingthe earthquakeresistantdesignofstructuresshareacommonrationaleinsettingand achievingtherequirementsforstructuralperformanceunderstrongearthquake shaking.Developingasufficientleveloffamiliaritywiththisrationale,sometimes calledthe“philosophyofearthquakeresistantdesign”,isessentialbefore embarkingonconceptualdesignforearthquakeresistancefollowedbytherequired structuralanalysisanddetailingcalculationsprescribedbyseismiccodesof practice.

Inthisregard,thisfirstchapteraimstoprovidethereaderwithaconcise qualitativeoverviewofthephilosophyforearthquakeresistantdesignasiscurrentlyimplementedbycodesofpracticeincludingEurocode8,hereafterEC8(CEN

© SpringerInternationalPublishingSwitzerland2016 I.Avramidisetal., Eurocode-CompliantSeismicAnalysisandDesignofR/C Buildings,Geotechnical,GeologicalandEarthquakeEngineering38, DOI10.1007/978-3-319-25270-4_1

21FundamentalPrinciplesfortheDesignofEarthquake-ResistantStructures

2004a).Itfurtherprovidessomerecommendationsastohowthecurrentprescriptiveregulationsandrequirementscanbeusedtoaddressthemorerecenttrendsin earthquakeresistantdesigntowardsaperformance-basedapproach.Inthisrespect, thischapterformsabasisuponwhichsubsequentchaptersfocusingexclusivelyon EC8builds.

Inparticular,Sect. 1.1 providesabriefintroductionontherationaleofthe fundamentaldesignobjectivesandrequirementssetbycurrentcodesofpractice. Section 1.2 introducesthecommonforce-basedseismicdesignapproachadopted bycodesofpracticetoachievethesoughtrequirementsforearthquakeresistance. Next,Sect. 1.3 providesabriefoverviewonthedevelopmentandcurrenttrendsin theemergingperformance-baseddesignapproachforearthquakeresistance.Lastly, Sect. 1.4 listspracticalrecommendationstoachievehigher-than-the-minimumrequiredstructuralperformancelevelsasprescribedbycurrentcodesofpractice withinthetraditionalforce-baseddesignframework.

1.1PartialProtectionAgainstStructuralDamage

1.1.1TheUncertainNatureoftheSeismicAction

Theuniquenessoftheearthquakeinduced(seismic)actioncomparedtoother actions,suchasgravitationalliveloads,whichbuildingstructuresmustresist duringtheirlifetime,stemsfromthefollowingfacts:

1.Manyimportantparametersoftheseismicactionaffectingthestructural responseare inherentlystronglyuncertain suchas(ElnashaiandDiSarno 2008):

•theearthquakemagnitude(relatedtotheenergyreleasedalongtheseismic fault),

•thefocal(hypo-central)depthoftheearthquake, •thedistanceofthestructuresitefromthesourceortheepicenter, •thedirectivity,thefrequencycontent,andthedurationoftheearthquake inducedgroundmotionatthefoundationofthestructure.

2.Theprobabilityofacertainstructurebeingexposedto“extreme”seismicground motionaccelerations(andtoconsequent“extreme”lateralinertialforces)during itsconventionallifetime(typicallyestimatedtobe50years)isrelativelylowdue totheconsiderablegeographic(spatial)dispersionofhighseismicintensities.In otherwords,asevere(destructive)earthquakeisconsideredtobea“rare”event whichwill,mostlikely,affectarelativelysmallpercentageofthestructural stockofaregionorofacountry.Still,itspotentialconsequencestothebuilt environmentmaybetoohightobeneglected.

1.1.2Canan“Absolute”LevelofProtectionAgainst theSeismicHazardBeAchieved?

Animportantimplicationofthe uncertain natureoftheseismicactionisthatthe designandconstructionofstructuresthatare“seismicallyinvulnerable” under any futureearthquakeisnotpracticallyfeasiblesincethelocation,thetimeinstant,and theleveloftheearthquake-induceddemandonthestructurescannotbedeterministicallydefined.

However,theexpectedlevelofearthquakegroundmotioncanbequantifiedby the seismichazard inagivengeographicalarea,whichnaturally,isexpressedina statistical/probabilistic sense(McGuire 1995).Tothisend,theseismicintensity thatthestructureisdesignedforaccordingtocurrentseismiccodesofpracticeand designguidelines(mostcommonlydenotedasthe“designearthquake”)istypically definedintermsoftheprobabilitytobeexceededwithinaspecifictimeinterval (e.g.,10%probabilitytobeexceededin50years).

Further,theuncertainnatureoftheearthquakeinducedactiononstructures necessitatesmakingacritical decision regardingthe desired levelofprotection againststructuraldamage.Thisisachievedbydefiningthe minimum levelof protectionorelse,aminimum performance,inrelationtoprescribedspecificlevels ofseismicaction,anissuethatisfurtherdiscussedinthefollowingsection.

1.1.3FullandPartialProtectionAgainstStructuralDamage

foraGivenDesignSeismicAction

Letusassumethat,basedonappropriateseismologicalstudies,thepeakseismic hazardofacertainregionisaccuratelymappedandthattheearthquakescenarios correspondingtothe“designearthquake”aredeterminedforallstructureswithin thisregioninastatistical/probabilisticcontext.Indecidingthesoughtlevelof protectionagainststructuraldamagefortheabovedesignearthquake,theperspectiveofdifferentstakeholdersneedtobeexaminedseparatelyasexplainedbelow.

1.1.3.1RegulatoryAgenciesandStateGovernments

Fromtheauthorities’ viewpoint,arequirementtodesign all structuresto remain elastic(i.e.,undamaged) underthedesign(“rare”)earthquake,andthereforeto ensurefullprotectionagainststructuraldamageforthedesignseismicaction,is consideredtobeeconomicallyprohibitive.Suchadecisionwouldinvolvechannelingexcessivefinancialresourcestoaddressarelativelylowriskintermsof casualtiescomparedtorisksassociatedwithothercriticalpublicfunctions(e.g., trafficsafety).Further,itisbelievedthatinmanycases,mandatingsuchastringent

levelofstructuralsafetymayleadto“bulky”andaestheticallydispleasingstructuresofreducedarchitecturalfunctionality.

Forthesereasons,Stateauthoritiesandregulatoryagenciessetforth minimum requirements fortheseismicdesignofstructuresdescribedintherelevantbuilding codesofpracticeandguidelineswhichaimtocompromisesocialwelfare(i.e.,life andpropertysafety)givenreasonablylimitedfinancialresources.Thisisachieved byadoptinganacceptablelevelofprotectionagainsttheseismichazard,bothin social/psychologicaltermsandincost-effectivenessterms.Tothisaim,structures arecommonlyclassifiedintotwocategories:(a)“special”structures,and (b)“ordinary”structures.

For“special”structures(e.g.,nuclearreactorcomplexesandpetrochemical facilitieshousingpoisonousgasandliquidmaterial),thatis,forstructureswhose potentialdamage,downtime,orevenglobalinstabilityandcollapse,wouldnegativelyaffectlargepopulationsandtheenvironmentoflargegeographicalregions (Fig. 1.1),a zerostructuraldamage requirementisprescribed.Inotherwords,itis requiredthatthesestructuressubjectedtothedesignearthquakebehavelinearlyand henceachievefullprotectionagainststructuraldamageforthedesignseismic action.

However,therequirementforfullprotectionagainsttheseismichazardis relaxedforthecaseof“ordinary”structures(e.g.,residential,retail,andoffice buildings,schools,hospitals,etc.),thatis,forstructureswhosepotentialdamage, downtime,orevenglobalinstability/collapse,wouldaffectinhabitantsandthe environmentwithintheirimmediatevicinityonly,despitetheir-maybe-different importance(Fig. 1.2).Suchordinarystructuresareallowedtoexhibitacertainlevel ofinelasticbehaviourandeventosustainirreversibleplasticdeformations(structuraldamage)underthedesignearthquake,whichshouldnot,however,leadto partialorglobalstructuralinstability/collapse(“partial”protectionagainststructuraldamageforthedesignseismicaction).

Therefore,structuraldamageunderthedesignearthquakeisconsideredacceptablebyStateauthoritiesforordinarystructuresaslongasthelifeoftheoccupants/ usersofstructuresisnotendangered(lifesafetyrequirement).Inthismanner,a minimumallowed levelofprotectionfromtheseismichazardissetwhich,presumably,constitutesasociallyandeconomicallyacceptablecompromiseinprioritizing limitedavailableresourcestomeetpublicneeds.Inthisregard,structuralengineers andinfrastructureownersshouldbeawarethattherequiredlevelofprotection againsttheseismichazardprescribedbyseismiccodesofpracticeconstitutessolely thelowestpermissiblelimit(lowerbound)ofstructuralsafetyandthatthereisno restrictioninchoosingtodesignaparticularstructuretoachieveahigherlevelof protectionorofseismicperformance,ifsodesired.

1.1.3.2BuildingOwners

Fromtheinfrastructureowner’sviewpoint,arequirementtoachievehigherthanthe minimumlevelofstructuralsafetyagainstanominal“designearthquake”setby

1.1PartialProtectionAgainstStructuralDamageastheUnderlyingDesign

Fig.1.2 Globalinstability (collapse)ofanordinary multistoreyresidential buildingunderastrong earthquakeaffectingthe neighboringstructures

codesofpracticeis,byallmeans,legitimate.Ofcourse,asthechoiceofahigher levelofsafetyagainsttheminimumrequiredbyseismiccodesisatthediscretionof theowner,theadditionalrequiredconstructioncostiscoveredbyhimselfandnot bytheState.Ithastobenotedatthispointthat,aswillbediscussedinmoredetail inSect. 1.4,theadditionalcostoffullearthquakeprotectionis(i)notashighasis oftendeemed,and(ii)doesnotnecessarilyleadtoundesirablylargestructural membersectionsanddysfunctionalbuildings.

1.1.4DesignObjectivesandRequirementsforPartial ProtectionAgainstStructuralDamageinCurrent SeismicCodesofPractice

Allowingforstructuraldamagetooccurforacertainlevelof“designseismic action”,liesatthecoreofallmodernseismicdesigncodesofpracticeforordinary structures.Inthisregard,code-compliantseismicdesignforordinarystructures,as

Fig.1.1 Specialstructuresforwhichzerostructuraldamagerequirementisspecified

definedinSect. 1.1.3.1,requiresapartialprotectionagainststructuraldamage.The practicalimplementationofthisseismicdesignphilosophycanbequalitatively framedviathethree fundamentalstructuraldesignobjectivesforearthquake resistance, asprescribedinearlyseismiccodes(seee.g.,thecommentaryofthe StructuralEngineersAssociationofCaliforniaBlueBook(SEAOC 1967)which introducedthegeneralphilosophyoftheearthquakeresistantdesignofbuildings thatisstillconceptuallyvalidtoday).Eachdesignobjectivecanbeimplicitly associatedwithaspecificlimitstateasfollows:

1.Structuresshouldwithstandminorlevelsofearthquakeinducedgroundmotion withoutanydamagetostructuralandtonon-structuralmembers.Thisdesign objectivesetsa nodamagerequirementforfrequentlyoccurringearthquakes duringthelifetimeofstructuresand correspondstothe“serviceability”limit state.

2.Structuresshouldwithstandmoderatelevelsofearthquakeinducedground motionwithnegligible(insignificantandreadilyrepairableifdeemedessential foraestheticalreasons)damagetostructuralmembers.Damagetonon-structural membersmayoccur(e.g.,Fig. 1.3).Thisdesignobjectivesetsa damage limitationrequirementforoccasionallyoccurringearthquakesduringthelifetimeofstructures.Itdefinesa“quasi”limitstatelyinginbetweentheserviceabilityandtheultimatelimitstateswhichmaybeviewedasa“cost”limitstate.

3.Structuresshouldwithstandmajorlevelsofearthquakeinducedgroundmotion withoutcollapsing.Damagetostructuralandnon-structuralmembersisacceptableaslongasitisnotlifethreateningandtheprobabilityofpartialorglobal collapseissufficientlylow(e.g.,Fig. 1.4).Thisdesignobjectivesetsa no collapserequirementforrareearthquakeswithrelativelylowprobabilityof occurrenceduringthelifetimeofstructures.Inreferencetomodernseismic codes(i.e.,ASCE 2010),itcanbefurtherapproximatelymappedontoadual requirementof“lifesafety”andcollapseprevention,andcorrespondstothe “ultimate”limitstate.

Afourthdesignobjectivecanbefurtheraddedforthecaseof“important” structures,whoseunobstructedoperationisessentialintheaftermathofamajor seismicevent(e.g.,hospitals,conventionalpowerplants,etc.)orwhosecollapse entailssignificantsocial,economic,orculturalloss(e.g.,schools,museums,etc.), asfollows:

4.Essentialandlargeoccupancystructuresshouldwithstandmajorlevelsof earthquakeinducedgroundmotionwithminororinsignificantdamagetostructuralmembers.Inotherwords,morestringentrequirementsfromthe“nocollapse”requirementshouldbeobserved.

Notethattheabove(1)–(3)designobjectivesandrelatedrequirementsareonly qualitativelydefined.Thatis,neitherthelimitingvaluesofthe“minor”,“moderate”,and“major”earthquakeshaking,northepermissiblelevelsofdamage correspondingtoeachoftheabovelevelsoftheinputseismicactionaredefined inanexplicitquantitativemanner.Infact,conventionaldesignofordinary

Fig.1.3 Requirementfor moderatelevelearthquakes: damagetonon-structural in-fillwallsisacceptable, yetonlyminor,repairable damagetostructural elementsispermitted

Fig.1.4 Requirementfor majorlevelearthquakes: damagetostructural elementsisaccepted,yet collapseprobabilitymust remainsufficientlylow

structuresforearthquakeresistanceinvolvestheconsiderationofonlyoneseismicaction-level(“designseismicaction”)correspondingtoarare“designearthquake”, typicallydefinedastheonehavinga10%probabilityofbeingexceededin 50years,thatis,havingareturnperiodofapproximately475years(seealso Sect. 2.3.1).Next,aseriesofqualitativeconceptualdesignrules,prescriptive verificationchecks,andempiricallocaldetailingrequirementsareconsideredto ensurethatthefirstthree(1)–(3)performanceobjectivesaremet.Inthisrespect, current(conventional)seismicdesignpracticesforordinarystructuresfocusonthe nocollapserequirementtoensurelifeprotectionforanominal“designseismic action”.Consequently,itisnaturaltoexpectthatthestructuralpropertiesofthe thusdesignedstructuresand,hence,theirachievedlevelofstructuralsafetyexhibit significantvariability.

Despitetheirqualitativenature,theabovedesignobjectivesillustratethecurrent consensusofwhatisconsideredtobetheacceptable(byGovernmentsandRegulatoryAgencies,butnotnecessarilybyindividualinfrastructureowners)minimum requirementsofstructuralperformanceinseismicallyproneareasandarecommonlyadopted,withminorvariations,bymostmodernseismiccodesofpractice.

Inthisrespect,EC8,inparticular,prescribesthefollowingtwofundamental requirementstobesatisfiedbyordinarystructuresconstructedinseismicregions withan adequatedegreeofreliability (clause2.1ofEC8)

(a) Nocollapserequirement

“Thestructureshallbedesignedandconstructedtowithstandthedesign seismicactiondefinedinSection3withoutlocalorglobalcollapse,thus retainingitsstructuralintegrityandaresidualloadbearingcapacityafterthe seismicevents.”

(b) Damagelimitationrequirement

“Thestructureshallbedesignedandconstructedtowithstandaseismicaction havingalargerprobabilityofoccurrencethanthedesignseismicaction, withouttheoccurrenceofdamageandtheassociatedlimitationsofuse,the costsofwhichwouldbedisproportionatelyhighincomparisonwiththecosts ofthestructureitself.”

Theabovetworequirementsareassumedtocoverthethreefirstseismicdesign objectives(1)–(3).Further,inclause2.1oftheEC8,thedesignobjective(4)isalso covered,byrequiringthatanenhanced“levelofreliability”inmeetingtheabove requirementsisachieveddependingonaclassificationofstructuresaccordingto their“importance”tocommunities.Thisincreasedlevelofreliabilityisaccomplishedbyincreasingthereturnperiodofthedesignseismicaction,thatis,by increasingtheconsidereddesignseismicloads(seealsoSect. 2.3.1.1).

1.1.5Stiffness,Strength,andDuctility:TheKeyStructural PropertiesinEarthquakeResistantDesign

Ingeneral,thefundamentalseismicdesignobjectivesdiscussedintheprevious sectionaremetby judiciallyequippingstructureswithadequateandappropriately distributed(inplanandinelevation)stiffness,strength,andductility (Villaverde 2009).Specifically:

– Anadequatelevelofstiffness forthelateralload-resistingstructuralsystemis requiredsuchthat(i)undermoderateearthquakeshaking,thestructureexhibits smalldeformationsandremainselastic(nodamagetostructuralmembers occurs),and(ii)undersevereearthquakeshaking(designseismicaction),lateral deflectionsaresufficientlysmallrenderingthecontributionofsecondorder phenomenanegligible(seefurtherSect. 2.4.3.3).Furthermore, thedistribution ofstiffnessshouldbesufficientlyuniform toavoidsignificantlocalizedstress accumulationatcriticalregionsofstructuralmembers.

– Anadequatelevelofstrength forstructuralmembersofthelateralload-resisting systemisrequired,sothatonlyinsignificant,ifany,damageisobservedunder moderateearthquakeshaking.Furthermore,the distributionofstrengthshould

besufficientlyuniform toavoidlargedifferencesbetweentheobserveddemandcapacityratiosacrossstructuralmembers(seefurtherSect. 2.4.4.1).

– Anadequatelevelofductilitycapacityisrequired (herein,“ductilitycapacity” referstotheabilityofastructuretoundergolargeinelasticdeformations withoutsignificantreductionofitsstiffnessandstrengthduringrepetitive dynamicloading-unloading-reloadingcycles).Insuchacase,localdamageat structuralmembersinducedbysevereearthquakeshaking(designseismic action)exhibitanon-brittle(ductile)behaviour,and,thus,theydonotleadto aprematureglobalstructuralinstability/collapse.Furthermore,a properdistributionofductility withinthelateralload-resistingstructuralsystemisrequiredto avoidtheformationofkinematiccollapsemechanismsundersevereearthquake shaking(seefurtherSect. 2.2.4).

Theassociationofthe(minimum)seismicdesignobjectiveswiththeabovekey structuralpropertiesissummarizedinTable 1.1

Focusingonreinforcedconcrete(r/c)structures,itisnotedthatcertaingeometric and/ormaterialparametersmayaffectthevalueofmorethanoneoftheabove structuralproperties.Thus,itmaynotalwaysbepossibletomodifytheseproperties independentlyatwill.Forexample,increasingthelongitudinalreinforcement providedtoanr/cbeamwithoutchangingitscross-sectionaldimensionsincreases itsflexuralstrength(yieldingmoment)aswellasits(crackedanduncracked) flexuralstiffness.However,despitethisfact,seismiccodestypicallyallowfor usingreinforcement-independentflexuralandshearstiffnessvaluesinthe(forcebased)designandanalysisofbuildings(seeSect. 2.3.2.1).

Forseismicdesignpurposes,itisinstructivetorepresentlateralloadresisting structuralsystemsofbuildingsintermsoftotalstaticlateralload(baseshear) versustopstoreybuildinglateralswaygraphs(e.g.,Fig. 1.5).Thisrelationshipis commonlyreferredtoas capacitycurve andisanimportantproxyofthenonlinear responseofthestructure.Itisnotedthatthestoreyshearsareappliedaccordingto thecorrespondingprofileofthemodalforcesalongthedirectionofinterest.

Itisalsorecalledthattheslopeoftheinitial(pre-yielding)branchoftheseplots isproportionaltothe(lateral)stiffnessofthestructuralsystemandthepeakattained valueofthebaseshearcanbeinterpretedasthestrengthofthestructure.Further, forstaticloads,ductilityiscommonlyquantifiedastheratioutot/uy ofanominal peakelastoplasticdisplacementutot (e.g.,translation,deflection,rotation,curvature, etc.)signifyingtheinitiationofcollapse/instabilityoveranominalyielddisplacementuy signifyingtheinitiationofnonlinearmaterialbehaviour(yieldingpoint).It isnotedinpassing,thattheaboveratiomightbeinsomecasesaquitemisleading proxyoftheseismicenergyabsorption.Toillustratethisissue,letastructurebe characterizedbyultimateandyielddisplacementsutot 1 anduy 1,andanotherone byutot 2 ¼ 2utot 1 anduy 2 ¼ 2uy 1,respectively;bothstructurespresentthesame nominalductilitydespitethefactthatthelatterstructuremayobviouslyabsorb moreseismicenergyinabsoluteterms(seefurtherdiscussioninSect. 1.2.1).

Thecapacitycurve,asdefinedabove,facilitatestheinterpretationandquantificationofstiffness,strength,andductilitypropertiesofstructuresatthesystemlevel

Table1.1 Mappingofminimumdesignobjectivesforkeystructuralpropertiesfordifferent levelsofearthquakeshakingseverityfollowingthepartialprotectiontostructuraldamage philosophy(seealsoSect. 1.3.2)

Levelofearthquake shaking(return period)

Frequent/minor (~45years)

Occasional/moderate (~75years)

Rare/major“Design earthquake” (~475years)

Desirablestructural propertiesMinimumrequireddesignobjectives

Adequateanduniformly distributed stiffness

plusadequateand properlydistributed strength

plusadequateand properlydistributed ductility

Nodamage(serviceabilitylimitstate)

Fairlylimitedreadilyrepairabledamage,if required.(costlimitstate)

Extensivedamageareacceptable,without localorglobalcollapse(ultimatelimitstatelifeprotection)

Fig.1.5 Capacitycurvesofstructureswithdifferentstiffness,strength,andductilityproperties

(reflectingtheeffectofmultipledamagemechanismsatthelocallevel).Italso renderspossiblethecomparativeassessmentofdifferentstructuralsystemsatinitial seismicdesignstages.Tofurtherillustratethispoint,fourbaseshear-topstorey displacementgraphsA,B,C,andDcorrespondingtofourdifferentstructural systemsareconsideredinFig 1.5

SystemsAandBhavedifferentstiffness(i.e.,slopeinclinationoftheelastic branch)andalsodifferentstrength(VA ¼ VB),yetthesameductilityratioutot A/ uy A.SystemCisstifferandhasgreaterstrengthcomparedtosystemsAandB (FC > FA,FB),butissignificantlylessductile(i.e.,morebrittle).Finally,systemD hasthesamestiffnessassystemC,butissignificantlymoreductileand,thus,more capableofresistingseismicinputloadsexceedingthestrengthofthestructureas willbeexplainedindetailinsubsequentsections.

Ithastobenotedhereinthathorizontalearthquakegroundmotionsinduce lateralinertialloadstostructuresthatareessentiallytime-variant(dynamic)and

theirattributes(e.g.,intensity,distribution,etc.)dependonthedynamiccharacteristicsofthestructureitself(e.g.,naturalfrequencies,modeshapes,etc.).Since ordinarystructuresaremostlydesigned(and,thus,areexpected)toexhibit nonlinearinelastic behaviourunderthenominal“designseismicaction”,the seismicresponseof(yielding)structuresis,ultimately,aninherentlynonlinear dynamicproblem.

Intheremainderofthissection,certainpracticalimplicationsduetothe nonlineardynamicnatureoftheproblemathandarediscussedfromadesign viewpoint.Theinterestedreaderisreferredtostandardtextsinthefieldofearthquakeengineeringandstructuraldynamicsforamoreelaboratetreatmentofthe followingtopics(Chopra 2007).Itisfurthernotedinpassingthat,apartfromthe aforementionedstructuralproperties,thechoiceofthelateralload-resistingstructuralsystemalongwithcompliancewithcertainconceptualdesignrulesareof paramountimportanceinachievingthedesignobjectivesofTable 1.1 (seealso Sect. 2.1).

1.1.5.1DependencyofInputSeismicLoadsonStructuralProperties

Importantdifferencesbetweenstaticgravitationalloadsvis-a-visseismicloads consideredinthedesignofr/cbuildingsarediscussedbelow.

Withintherangeoflinearelasticstructuralbehaviour(priortoyielding):

–Thedistributionandintensityof static(gravitational)designliveloads are prescribedbystandardbuildingcodesbasedonthepurpose/usageofstructures (e.g.,standardoccupancyresidentialbuildings,heavyoccupancypublicbuildings,etc.).Theseloadsareconstantfromtheoutsetofthedesignprocessanddo notdependonthepropertiesofthestructuralload-resistingsystem. Thus, increasingthestiffnessofabuildingwouldnotalterthedesignstaticlive loading. Itwouldonlyincreasetheself-weight(deadload)ofthestructure,as stiffeningiscommonlyaccomplishedbyincreasingthedimensionsofstructural membersorbyaddingnewones.Itisfurtherremindedthat,foragivenlevelof liveloads,astifferstructuraldesigngenerallyachievesreduceddisplacements andstrainsinstructuralmembers.

–The designseismicloading dependsnotonlyonthesite-specificcharacteristicsof thedesignseismicactionasdefinedbycodesofpractice(e.g.,siteseismichazard, localsoilconditions,etc.),butalsoonthedynamic(modal)characteristicsofthe lateralload-resistingstructuralsystemofthebuildingunderdesign(e.g.,natural frequencies,modeshapes,etc.).Thesecharacteristicsdepend,inturn,onthe stiffness,mass(inertia),anddampingpropertiesofthestructureandtheirdistributionwithinthelateralload-resistingsystem. Thus,increasingthelateral stiffnessofabuildingwouldgenerally(thoughnotalways)alter(increaseor decrease)thedesignseismicloadthatthestructuremustbeabletoresist. For example,increasingthestiffnessofaratherflexiblestructuresubjectedtoagiven designseismicloadleads,mostprobably,tohigherlevelsofstressesatstructural

memberswhileithasamixedeffectonstrains.Inthisregard,twoadjacent buildingsofthesamegeometryanddeadloadbutwithdifferentlateralloadresistingstructuralsystems(e.g.,onewitharelativelyflexiblemomentresisting frame(MRF)systemvis-a-visonewithastiffercoupledMRF-shearwallsystem) subjectedtothesamestronggroundmotionwilldevelopsignificantlydifferent baseshearand,therefore,internalforcesatstructuralmembersduetotheir differentdynamiccharacteristicswithrespecttothoseoftheearthquakeground motion.

Withintherangeofnonlinearinelasticstructuralbehaviour(post-yielding):

–Static(design)gravitationalloadsappliedtoabuildingremainconstantupto localand/orglobalstructuralinstability(buildingcollapse).Althoughsecond ordereffectsmaydevelopatlargedisplacementsandvariousforcedistributions maytakeplace,staticloadsthemselvesdonotvaryduetoinelasticbehaviour.

–Theintensityanddistributionofseismicloadsappliedtostructureschange continuouslybeyondyielding.Stiffnessisgraduallyreducedbothatthemember andthesystemlevel;however,theintensityoftheseismicloadinginlightof structuralnonlinearresponsemayvarydependingontheinterplaybetweenthe (modified)structuraldynamiccharacteristicsandthefrequencycontentofseismicmotion.

Furtherdetailsontheinfluenceofinelasticstructuralbehaviourontheinput seismicloadsfromtheviewpointofearthquakeresistancedesignareprovidedinSects. 1.2.1 and 1.2.2.

1.1.5.2StructuralPropertiesInfluencingtheDesignforEarthquake Resistance

Thetotalmass(inertia)ofordinaryr/cbuildingsdependsmainlyontheouter dimensions(envelop)ofthestructureinplanandinelevationandonitsintended usage(e.g.,standardoccupancy,heavyoccupancy,etc.).Therefore,although ensuringafavourable(i.e.,uniform)massdistributionwithinthelateralloadresistingstructuralsystemofabuildingisanimportantconsiderationindesigning forearthquakeresistance(seealsoSect. 1.2.5),thetotalmassofordinaryr/c buildingsisnotapropertythatcanbesignificantlyinfluencedattheseismicdesign stage.

Further,theintensityofthedampingforces,commonlyassumedtobevelocity proportional(viscousdampingmodel),dependsonthestructuralmaterialofchoice forthelateralload-resistingsystem.Incode-compliantseismicdesignofr/c structures,a5%ofcriticalviscousdampingratioforallmodesofvibrationis theusualassumption.Therefore,similartothecaseofthetotalstructuralmass,the intensityofdampingforcesresistingtheseismicallyinducedvibratorymotionof structuresisnotaparameterthatcanbecontrolledattheseismicdesignstage, unlesssupplementaldampingisintroducedbymeansofspecialenergydissipation

1.1PartialProtectionAgainstStructuralDamageastheUnderlyingDesign

devices.However,theuseofsuchdevicesfallswithinthenon-conventionaldesign approachesforearthquakeresistance,andassuch,itisnotaddressedinthisbook. Inthisrespect,stiffness,strength,andductilityofstructuralmembersarethe mainstructuralpropertiesleveragingtheearthquakeresistantdesignofordinaryr/c buildingstructures(LindeburgandMcMullin 2014).Tosummarize:

– stiffness, mass,and(viscous) damping propertiesdeterminethenaturalfrequenciesofvibrationoflinearstructures(priortoyielding),which,inturn,determine theintensityofthedesignseismicinputloads.

–fordesignpurposes, strength isassumedtocoincidewiththeelasticlimitof structuralbehaviourabovewhichthestructuresuffers permanent plasticstrains and,thus,structuraldamage.Suchdamageoccurslocallyatspecificcritical regionsofstructuralmemberswheretheflexuralcapacityofthesectionis exceeded,thusformingaseriesof“plastichinges”.Similarly,theshearcapacity ofasection(orabeam-columnjoint)mayalsobeexceededleadingto unfavourablemodesofbrittlefailure.However,specialcapacitydesignrules areenforcedindesigntominimizetheprobabilityofthelatterfailuremodes whichwillbefurtherdiscussedinSect. 1.2.6.Largepartsoftheinputseismic (kinetic)energycanbeabsorbedatplastichingesviahysteretic(inelastic) mechanismsprovidedthatsufficient ductilebehaviour isexhibited.Thatis,no prematurefailuretakesplaceduringstronggroundshakingeitherlocally,at plastichinges,orgloballyleadingtostructuralcollapse.

– ductility orductilebehaviourcanbeviewedasameanstodissipatetheinput seismicenergythroughinelastic/hystereticmechanismsofstructuralbehaviour. Thesemechanismsareactivatedbyallowingthestructuretoyieldinacontrolled manner(i.e.,withoutleadingtoglobalinstability/collapse)and,thus,by allowingtheoccurrenceofstructuraldamageunderthedesignseismicaction. Conveniently,thelatterconsiderationisinalignmentwiththeadoptionofpartial protectionagainststructuraldamagephilosophyofearthquakeresistantdesign. Infact,itistheductilitycapacitypropertyofstructuresthatrendersthepartial protectionagainststructuraldamagephilosophypracticallypossibleandhistoricallyacceptable.

1.1.5.3TheRoleofDuctilityinSeismicDesign

Theroleofductility,thatis,theabilityofthelateralload-resistingstructuralsystem toexhibitlargeplasticstrainswithnosignificantstiffnessandstrengthdegradation duringalargenumberofrepetitivedynamicloadingcycles,bothatthesystemand thecomponentlevel,iscrucialindesigningforearthquakeresistance(Fardis etal. 2005;Elghazouli 2009;Bischetal. 2012).

Specifically,incaseastructureisdesignedtoresistthedesignseismicactionby developinginelastic/hystereticenergydissipationmechanisms(i.e.,byallowingfor structuraldamagetooccur–partialprotectionagainststructuraldamageforthe designearthquake),ensuringadequateandreliableductilebehaviour(ductility

capacity)viaappropriatelocaldetailingandconceptualdesignconsiderationsisof paramountimportance (Booth 2012).

Ontheantipode,inthecaseofastructuredesignedtoresistthedesignseismic actionthroughlinearbehaviouronastrength-baseddesign(fullprotectionagainst structuraldamageforthedesignearthquake),nospecialmeasuresforductile behaviourareneededtoresistthedesignearthquake.Thismayevenbethecase forearthquakeshakinglevelsbeyondthedesignseismicactionsinceacertainlevel of inherent ductilitycapacityisalwaysexistentinr/cstructuresduetointernal sectionmechanismsabletoabsorbseismicenergy.Apparently,forsignificantly higherlevelsofseismicforce,boththeinherentandtheadditionalductility, providedthroughcapacitydesignandappropriatedetailing,shallbemobilized, hencethelatterisdeemednecessarytominimizetheprobabilityofcollapse(see alsoSect. 1.2.6).

1.1.5.4TheUseofReduced“Effective”StiffnessPropertiesforR/C

Structures

Inthecaseofr/cstructures,partialprotectionagainststructuraldamageentailsthat significantconcretecrackingoccursatcertainregionsofstructuralmembers(local structuraldamage).Thus,themechanicalpropertiesofstructuralmembers,and especiallytheirstiffness(inflexure,shear,tension/compressionandtorsion),deterioratecomparedtothecaseofan“intact”structurewith“uncracked”members. Thedeterminationofthislevelofdeteriorationanditsinfluenceonthestructural memberstiffnessvaluestobeusedinseismicanalysisinordertoachieverealistic resultsisanactiveareaofresearch.Currentcodesofpracticearetakinginto accountthisinfluenceinundertaking“equivalentlinear”typesofanalysesby consideringreduced(“effective”)flexuralandshearstiffnesspropertiesatstructural memberscomparedtotheuncrackedvalues(seealsoSect. 2.3.2.1)

1.2ImplementationofthePartialProtectionAgainst StructuralDamageSeismicDesignPhilosophy inCurrentCodesofPractice

Thethreefundamentalseismicdesignobjectives(1)–(3)ofSect. 1.1.4 correspond tothreedifferentlevelsofseismicactionassociatedwith“frequent/minor”,“occasional/moderate”,and“rare/major”earthquakeevents.Accordingly,onewould expectthedesignofordinarystructurestoinvolveverificationchecksusingthree separatesetsofstructuralanalysisresultscorrespondingtotheaboveseismicaction levels.Sucharigorousdesignpracticewouldrequireexplicitquantificationofthree distinctlevelsoftheseismicactionateachsitealongwithundertakingthree separatestructuralanalysesof,perhaps,differenttype(linearelastic,nonlinear).

Further,itwouldalsorequiretheprescriptionofappropriatedesignverification checksandcorrespondingpermissiblecriteriaforeachoftheseseismicaction levels.

However,thecurrentconsensusisthatsuchanexplicitthree-seismic-actionleveldesignprocedurewouldbetoocumbersomeandnotreadilyapplicablein practice.Thus,withtheexceptionofveryfewcurrentcodesofpractice(e.g.,the Japanesecode,(Midorikawaetal. 2003)),code-compliantseismicdesignofordinarystructuresinvolvesoneanalysisforasingle-seismic-action-level(“design seismicaction”)correspondingtothe“nocollapse”requirement.Thebulkof designverificationchecks,typicallyconcernedwiththeultimatestrengthofstructuralmembers,isperformedforthissinglestructuralanalysisruntoensurethatthe lifesafetyrequirementismet.

Further,special“capacitydesign”rulesareprescribedtoachieveasufficient levelofglobalductilebehaviour(seeSects. 1.2.5 and 1.2.6),alongwithlocal detailingprovisionstoensurelocalductilitycapacityatcriticalregionsofstructural members.Itisimplicitlyassumedthatcapacitydesignprovisionsensurethe no-collapserequirementforhigher-than-the-nominal-“designseismicaction”-level earthquakegroundmotionswithoutperforminganyadditionalquantitative assessment.

Finally,certainverificationcheckscorrespondingtothe“damagelimitation” requirementarealsoundertakeninvolvingstructuraldeflectionsandrelativedeformations.Thesestructuralresponsequantitiesaredeterminedwithoutperforming structuralanalysisforanadditionalinputseismicactionlevellower-than-thenominal-“designseismicaction”.Instead,empiricalreductionfactorsareapplied tonumericalresultsobtainedfromtheanalysisforthedesignseismicactionlevelto implicitlyaccountforthefactthatdamagelimitationrequirementscorrespondtoa “moderate”earthquakeevent.Inthisrespect,theabovecode-compliantseismic designframework,whichiscloselyfollowedbyEC8amongotherinternational seismiccodes,maynotbecharacterizedasa“full-fledged”two-seismic-actionleveldesignprocedure.However,itdoesconstitutea“quasi” two-tierseismic designprocedure,asitincludesverificationchecksfortwodifferentlevelsofthe seismicaction(Fardisetal. 2005;Fardis 2009).

Itisfurthernotedthat aforce-baseddesignapproach iscommonlyadoptedin conjunctionwiththeaboveframework.Consequently,theverificationchecksfor thenocollapserequirementdonotinvolveanexplicitquantitativeassessmentfor structuraldamageassumedtooccurunderthedesignseismicaction(Fardis 2009). Forthecaseofreinforcedconcrete(r/c)buildings,structuraldamageentailsthe formationoflocalised“plastichinges”atcertain“criticalregions”ofr/cstructural members.Conveniently,thedesignverificationchecksspecifiedbytheherein describeddesignframeworkdonotrequiredeterminingthetotalnumberofplastic hinges,theirsequenceofoccurrence,andtheiroveralldistributionwithinthe structure.Further,noassessmentoftheseverityofinelasticdeformationsateach plastichingeismandated.

Insummary, theforce-baseddesignapproachforearthquakeresistancecommonlyadoptedbymostofthecurrentseismiccodesreliesonperforminglinear

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Then Drakestail traveled on a bit farther until he came to his friend, the river, lying and glistening in the sunshine.

“Where do you go this fine morning, Friend Drakestail?” asked the river.

“To the king, for he owes me money,” said Drakestail.

“I will travel with you,” said the river.

“You would soon tire if you ran so far, my friend,” said Drakestail. “Come along with me this way.” He opened his wee bill very wide, and down his wee little throat went the little river.

Then Drakestail traveled and traveled until he came to the king’s house. Now Drakestail thought that the king would meet him at the gate, so he called out very loudly:

“Honk! Honk! Drakestail waits at the gate.”

But the king did not come out to meet him. Who should appear at the gate but the king’s cook, and the cook took Drakestail by his two little legs and flung him into the poultry yard. The other fowls, who were ill-bred birds, ran up to Drakestail and bit him, and jeered at his large tail. It would have gone very badly with Drakestail, but he called to his friend, the fox:

“Reynard, Reynard, come out to the earth, Or Drakestail’s life is of little worth.”

So the fox came out, and he ate up all the ill-bred fowls in the king’s poultry yard. But still Drakestail was badly off. He heard the king’s cook putting the broth pot over the fire.

“Ladder, ladder, come out to the wall,

Drakestail does not wish to be broth at all,”

he cried. So the ladder came out and leaned against the wall, and Drakestail climbed over in safety But the king’s cook saw Drakestail and set out after him. He caught poor Drakestail and clapped him into the broth pot, and hung him over the fire.

“River, my sweetheart, put out this hot fire, The flames that would cook me rise higher and higher,”

cried Drakestail. So the river put out the fire with a great noise and sputtering, which the king heard. And the king came running to the kitchen.

“Good morning to you, King,” said Drakestail, hopping out of the broth pot, and making a very low bow, “are you through with my money, which you have kept for a year and a day?”

“That I am, Drakestail,” said the king. “You shall have it at once.”

So the king gave Drakestail the money that he owed him, and Drakestail waddled home again to tell of all his travels.

THE GREEDY CAT.

Once upon a time there lived a cat and a mouse, and they thought they would ask each other to dinner, turn and turn about. First it was the cat’s turn to ask the mouse, and he set his table and invited her, but he did not have much to eat; only a dry crust of bread and some water. But the mouse, who was very polite, ate it and thanked the cat.

When it was the mouse’s turn to give a dinner, she spread a fine feast, platters of fish, and saucers of milk, and joints of meat. Then she baked a large cake with sugar on the top for the cat, and for herself she made a very tiny cake with no frosting.

The cat came to the mouse’s dinner, and he ate the fish and the meat, and lapped the milk, and ate the cake. Then he looked around in a greedy way, and he said:

“What a very light dinner. Have you nothing more in the house to eat, mouse?”

“Here is my cake,” said the mouse, who was not at all greedy.

So the cat ate the mouse’s cake, and then he looked about again in a greedy way, and he said:

“Have you anything more to eat, mouse?”

“Nothing, kind sir,” said the mouse, “unless you eat me.”

She thought the cat would never be so greedy as that, but he opened his mouth wide, and down his throat went the mouse.

Then the greedy cat walked out of the mouse’s house and down the road, swinging his tail, for he felt very fine.

On his way he met an old woman. Now the old woman had been peeping in at the window, and she had seen what that greedy cat had done.

“You greedy cat,” she said, “to eat your friend, the mouse.”

“Greedy, indeed,” said the cat, “I have a mind to eat you.”

Then he opened his mouth very wide, and down his throat went the old woman.

Then on down the road went the cat, swinging his tail, and feeling finer than ever. As he went he met an old man taking his load of apples to market. The old man was beating his donkey to make it go faster.

“Scat, scat, pussy,” said the man, “my donkey will tread on you.”

“Tread on me, indeed,” said the cat, shaking his fat sides, “I have eaten my friend the mouse, I have eaten an old woman. What is to hinder my eating you?”

So the greedy cat opened his mouth very wide, and down his throat went the man and his donkey.

Then he walked along in the middle of the road again. After a while he spied a great cloud of dust, and he heard a great tramping of feet. It was the king riding in his chariot, and behind him marched all his soldiers and his elephants.

“Scat, scat, pussy,” said the king, “my elephants might step on you.”

“Step on me, indeed,” said the cat, “I have eaten my friend the mouse, I have eaten an old woman, I have eaten an old man and a donkey. What is to hinder my eating a king and a few elephants?”

So the cat opened his mouth wide, and down his throat went the king and the soldiers and all the elephants.

Then the cat started on again, but more slowly. He was really not hungry any more. As he traveled he met two land crabs, scuttling along in the dust.

“Scat, scat, pussy,” squeaked the crabs.

“I have eaten my friend the mouse,” said the cat, “I have eaten an old woman, and a man and a donkey, and a king and all his soldiers and all his elephants. What is to hinder my eating you, too?”

Then the cat opened his mouth wide, and down his throat went the two crabs.

But the crabs began to look about them there in the dark. There were the soldiers trying to form in fours, but there was not room. The elephants were stepping on each other’s toes. The old woman was scolding, and in a corner sat the poor little mouse, her paws and ears all drooping.

“We must go to work,” said the crabs.

Then they began snipping and snipping with their sharp little claws. Soon there was a hole large enough, and they crept out.

Then out came the king and his soldiers and all his elephants. Out came the old woman scolding her cat. Out came the man and his donkey. Last of all, out came the little mouse with one little cake under her arm, for one cake was all that she had wanted.

But the greedy cat had to spend all the rest of the day sewing up the hole in his coat.

THE THREE BILLY GOATS GRUFF.

Once upon a time there were three Billy Goats, and one was a very large Goat, and one was a middle-sized Goat, and one was a tiny Goat, but the three had the very same name, which was Gruff.

One morning the three Billy Goats started away from home, for they had decided to go far, far to a hillside where there was a quantity of green grass, and they might eat of it and make themselves fat.

Now, on the way to the hillside there ran a brook, and over the brook was a bridge, and under the bridge lived a Troll with eyes as large as saucers, and a nose as long as a poker. And this Troll was fond of eating Billy Goats.

First of all came the youngest Billy Goat Gruff to cross over the bridge. Trip trap, trip trap, his little feet pattered upon the boards.

“Who is that tripping over my bridge?” called up the Troll in a surly voice.

“Oh, it’s only I, the tiniest Billy Goat Gruff, going over to the hillside to make myself fat,” the Goat called back in a wee small voice.

“I am going to gobble you up, Billy Goat Gruff,” said the Troll.

“Oh, no, pray do not take me,” said the tiniest Billy Goat Gruff; “I am too little, that I am. Wait until the second Billy Goat Gruff comes along. He is ever so much bigger than I.”

“Well, be off with you,” said the Troll.

Then came the middle-sized Billy Goat Gruff, to cross the bridge. Trip trap, trip trap, his middle-sized feet pattered upon the boards.

“Who is that tripping over my bridge?” called up the Troll.

“Oh, it’s only I, the middle-sized Billy Goat Gruff, going over to the hillside to make myself fat,” the Goat called back in a middle-sized voice.

“I am coming to gobble you up, Billy Goat Gruff,” said the Troll.

“Oh, no, pray do not take me,” said the middle-sized Billy Goat Gruff; “I am a little larger than the tiniest Billy Goat, but I am not large enough to make a mouthful for you. Of that I am quite sure.”

“Well, be off with you,” said the Troll.

Then, last of all, came the great Billy Goat Gruff, to cross over the bridge.

Trip trap, trip trap, his great feet tramped across the boards.

“Who is that tramping over my bridge?” called up the Troll.

“It is I, the great Billy Goat Gruff, going over to the hillside to make myself fat,” the Goat called back in a great voice.

“I am coming to gobble you up, Billy Goat Gruff,” said the Troll.

“Come along,” said the great Billy Goat Gruff.

So the Troll, whose eyes were as large as saucers and his nose as long as a poker, came hurrying up to the top of the bridge,—but, ah, this is what happened to him.

The Goat tossed the Troll so high with his horns.

There on the bridge stood the great Billy Goat Gruff with his feet firmly planted on the boards and his head lowered, and as soon as the Troll came near—rush, scamper—the Goat tossed the Troll so high with his horns that no one has ever seen a Troll under a bridge from that day to this.

Then the great Billy Goat Gruff went on to the hillside, and the three Billy Goats ate, and ate, and made themselves so fat that they could scarcely walk home again.

THE HOBYAHS.

Once upon a time there lived a little old man and a little old woman in a house all made of hemp stalks. And they had a little dog named Turpie who always barked when any one came near the house.

One night when the little old man and the little old woman were fast asleep, creep, creep, through the woods came the Hobyahs, skipping along on the tips of their toes.

“Tear down the hemp stalks. Eat up the little old man, and carry away the little old woman,” cried the Hobyahs.

Then little dog Turpie ran out, barking loudly, and he frightened the Hobyahs so that they ran away home again. But the little old man woke from his dreams, and he said:

“Little dog Turpie barks so loudly that I can neither slumber nor sleep. In the morning I will take off his tail.”

So when it came morning, the little old man took off little dog Turpie’s tail to cure him of barking.

The second night along came the Hobyahs, creep, creep through the woods, skipping along on the tips of their toes, and they cried:

“Tear down the hemp stalks. Eat the little old man, and carry away the little old woman.”

Then the little dog Turpie ran out again, barking so loudly that he frightened the Hobyahs, and they ran away home again.

But the little old man tossed in his sleep, and he said:

“Little dog Turpie barks so loudly that I can neither slumber nor sleep. In the morning I will take off his legs.”

So when it came morning, the little old man took off Turpie’s legs to cure him of barking.

The third night the Hobyahs came again, skipping along on the tips of their toes, and they called out:

“Tear down the hemp stalks. Eat up the little old man, and carry away the little old woman.”

Then little dog Turpie barked very loudly, and he frightened the Hobyahs so that they ran away home again.

But the little old man heard Turpie, and he sat up in bed, and he said:

“Little dog Turpie barks so loudly that I can neither slumber nor sleep. In the morning I will take off his head.”

So when it came morning, the little old man took off Turpie’s head, and then Turpie could not bark any more.

That night the Hobyahs came again, skip- ping along on the tips of their toes, and they called out:

“Tear down the hemp stalks. Eat the little old man, and carry off the little old woman.”

Now, since little dog Turpie could not bark any more, there was no one to frighten the Hobyahs away. They tore down the hemp stalks, they took the little old woman away in their bag, but the little old man they could not get, for he hid himself under the bed.

Then the Hobyahs hung the bag which held the little old woman up in their house, and they poked it with their fingers, and they cried:

“Look you! Look you!”

But when it came daylight, they went to sleep, for Hobyahs, you know, sleep all day.

The little old man was very sorry when he found that the little old woman was gone. He knew then what a good little dog Turpie had been to guard the house at night, so he brought Turpie’s tail, and his legs, and his head, and gave them back to him again.

Then Turpie went sniffing and snuffing along to find the little old woman, and soon came to the Hobyahs’ house. He heard the little old woman crying in the bag, and he saw that the Hobyahs were all fast asleep. So he went inside.

Then he cut open the bag with his sharp teeth, and the little old woman hopped out and ran home; but Turpie got inside the bag to hide.

When it came night, the Hobyahs woke up, and they went to the bag, and they poked it with their long fingers, crying:

“Look you! Look you!”

But out of the bag jumped little dog Turpie, and he ate every one of the Hobyahs. And that is why there are not any Hobyahs now.

THE KID WHO WOULD NOT GO.

Once upon a time I was walking across London Bridge, and I found a penny. So I bought a little kid. But the kid would not go. And I saw by the moonlight it was long past midnight. It was time kid and I were home an hour and a half ago.

Then I met a staff, and to the staff I said:

“Staff, staff, drive kid. I see by the moonlight it is long past midnight. It is time kid and I were home an hour and a half ago.”

But the staff would not drive kid.

Then I met a hatchet, and to the hatchet I said:

“Hatchet, chop staff, staff will not drive kid. I see by the moonlight it is long past midnight. It is time kid and I were home an hour and a half ago.”

But the hatchet would not chop staff.

Then I met a torch, and to the torch I said:

“Torch, burn hatchet, hatchet will not chop staff, staff will not drive kid. I see by the moonlight it is long past midnight. It is time kid and I were home an hour and a half ago.”

But the torch would not burn the hatchet.

Then I met the wind, and to the wind I said:

“Wind, put out torch, torch will not burn hatchet, hatchet will not chop staff, staff will not drive kid. I see by the moonlight it is long past midnight. It is time kid and I were home an hour and a half ago.”

But the wind would not put out the fire.

Then I met a tree, and to the tree I said:

“Tree, stop wind, wind will not put out torch, torch will not burn staff, staff will not drive kid. I see by the moonlight it is long past midnight. It is time kid and I were home an hour and a half ago.”

But the tree would not.

Then I met a wee mouse, and to the mouse I said:

“Mouse, gnaw tree, tree will not stop wind, wind will not put out torch, torch will not burn staff, staff will not drive kid. I see by the moonlight it is long past midnight. It is time kid and I were home an hour and a half ago.”

Then the wee, wee mouse began to gnaw the tree, the tree began to stop the wind, the wind began to put out the torch, the torch began to burn the staff, the staff began to drive the kid, and the kid began to go.

See by the moonlight it is almost midnight. But kid and I were home an hour and a half ago.

THE ROBIN’S CHRISTMAS SONG.

Once upon a time there was an old gray Pussy and she was down by the waterside when the trees and ground were white with snow. And there she saw a wee, wee Robin Redbreast hopping upon a branch, so Pussy said to him:

“Where are you going, Robin Redbreast, this frosty Yuletide weather?”

Then the wee, wee Robin said to the Pussy, “I am going to the King to sing him a song this good Yule morning.”

And the gray Pussy replied, “Go not yet. Come here, Robin Redbreast, and I will let you see the bonny white necklace I wear around my neck.”

But the wee, wee Robin said, “No, no, gray Pussy You may show the bonny white necklace that you wear around your neck to the little mice, but not to me.”

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