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4.1INVESTIGATIONOFSTRUCTURALBEHAVIORInvestigatinghowstructuresbehaveisanimportantpartofstructuraldesign:itprovidesabasisforensuringtheadequacyandsafetyofadesign,InthissectionIdiscussstructuralinvestigationingeneral.AsIdothroughoutthisbook.Ifocusonmaterialrelevanttostructuraldesigntasks.PurposeofInvestigationMoststructuresexistbecausetheyareneeded.Anyevaluationofastructurethusmustbeginwithananalysisofhoweffectivelythestructuremeetstheusagerequirements.Designersmustconsiderthefollowingthreefactors:Functionality.orthegeneralphysicalrelationshipsofthestructure'sform.detail.durability.fireresistance.deformationresistance.andsoon.Feasibility.includingcost.availabilityofmaterialsandproducts.andpracticalityofconstruction.Safety.orcapacity10resistanticipatedloads.MeansAninvestigationofafullydefinedstructureinvolvesthefollowing:1.Determinethestructure'sphysicalbeing-materials,form,scale.orientation.location.supportconditions,andinternalcharacteranddetail.2.Determinethedemandsplacedonthestructure-thatis.loads.3.Determinethestructure'sdeformationlimits.4.Determinethestructure'sloadresponse-howithandlesinternalforcesandstressesandsignificantdeformations.5.Evaluatewhetherthestructurecansafelyhandletherequiredstructuraltasks.Investigationmaytakeseveralforms.YoucanVisualizegraphicallythestructure'sdeformationunderload.Manipulatemathematicalmodels.Testthestructureorascaledmodel,measuringitsresponsestoloads.Whenprecisequantitativeevaluationsarerequired.usemathematicalmodelsbasedonreliabletheoriesordirectlymeasurephysicalresponses.Ordinarily.mathematicalmodelingprecedesanyactualconstruction-evenofatestmodel.Limitdirectmeasurementtoexperimentalstudiesortoverifyinguntestedtheoriesordesignmethods.VisualAidsInthisbook,Iemphasizegraphicalvisualization;sketchesarcinvaluablelearningandproblem-solvingaids.Threetypesofgraphicsaremostuseful:thefree-bodydiagram.theexaggeratedprofileofaload-deformedstructure.andthescaledpial.Afree-bodydiagramcombinesapictureofanisolatedphysicalclemenIwithrepresentationsofallexternalforces.Theisolatedclementmaybeawholestructureorsomepartofit.Forexample.Figure4.1ashowsanentirestructure-abeamand-eolumnrigidbent-andtheexternalforces(representedbyarrows).whichincludegravity.wind.andthereactiveresistanceofthesupports(calledthereactions).Note:Suchaforcesystemholdsthestructureinstaticequilibrium.Figure4.lbisafree-bodydiagramofasinglebeamfromthebent.Operatingonthebeamaretwoforces:itsownweightandtheinteractionbetweenthebeamendsandthecolumns10whichthebeamisallached.TheseinteractionsarenotvisibleintheIreebodydiagramofthewholebent.soonepurposeofthediagramforthebeamistoillustratetheseinteractions.Forexample.notethatthecolumnstransmittotheendsofthebeamshorizontalandverticalforcesaswellasrotationalbendingactions.Figure4.lcshowsanisolatedportionofthebeamlength.illustratingthebeam'sinternalforceactions.Operatingonthisfreebodyarcitsownweightandtheactionsofthebeamsegmentsontheoppositesidesoftheslicingplanes.sinceitistheseactionsthatholdtheremovedportioninplaceinthewholebeam.Figure4.ld.atinysegment.orparticle.ofthebeammaterialisisolated,illustratingtheinteractionsbetweenthisparticleandthoseadjacenttoit.Thisdevicehelpsdesignersvisualizestress:inthiscase.duetoitslocationinthebeam.theparticleissubjectedtoacombinationofshearandlinearcompressionstresses.Anexaggeratedprofileofaload-deformedstructurehelpsestablishthequalitativenatureoftherelationshipsbetweenforceactionsandshapechanges.Indeed.youcaninfertheformdeformationfromthetypeofforceorstress.andviceversa.FIGURE4.1Free-bodydiagrams.Forexample.Figure4.lashows{heexaggerateddeformationofthebentinFigure4.1underwindloading.Notehowyoucandeterminethenatureofbendingactionineachmemberoftheframefromthisfigure.Figure4.2bshowsthenatureofdeformationofindividualparticlesundervarioustypesofstress.FIGURE4.2StructuraldeformationThescaledplotisagraphofsomemathematicalrelationshiporrealdata.Forexample,thegraphinFigure4.3representstheformofadampedibrationofanelasticspring.Itconsistsoftheplotofthedisplacementsagainstelapsedtimet.andrepresentsthegraphoftheexpression.FIGURE4.3Graphicalplotofadampedcyclicmotion.Althoughtheequationistechnicallysufficienttodescribethephenomenon,thegraphillustratesmanyaspectsoftherelationship.suchastherateofdecayofthedisplacement.theintervalofthevibration.thespecificpositionatsomespecificelapsedtime.andsoon..4.2METHODSOFINVESTIGATIONANDDESIGNTraditionalstructuraldesigncenteredontheworkingstressmethod.amethodnowreferredtoasstressdesignorallowablestressdesign(ASD).Thismethod.whichreliesontheclassictheoriesofelasticbehavior,measuresadesign'ssafetyagainsttwolimits:anacceptablemaximumstress(calledallowableworkingstress)andatolerableextentofdeformation(deflection.stretch.erc.).Theselimitsrefertoastructure'sresponsetoserviceloads-thatis.theloadscausedbynormalusageconditions.Thestrengthme/hod,mean-while,measuresadesign'sadequacyagainstitsabsoluteloadlimit-thatis.whenthestructuremustfail.Toconvincinglyestablishstress.strain.andfailurelimits,testswereperformedextensivelyinth
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