土木工程概論

IntroductiontoCivilEngineering第九章土木工程設計概述Chapter9IntroductiontoDesignofCivilEngineering土木工程概論

IntroductiontoCivilEIntroductiontoDesignofCivilEngineeringWhatisIntroductiontoDesignofCivilEngineering?Itprovidesthestudentswiththenecessarybackgroundonterminologyusedindesign.Withthischapter,entry-levelstudentsofcivilengineeringwillbetterunderstandfromtheoutsetlecturesondetailedsubjectareas.Itwillalsoprovebeneficialfornewlyqualifiedprofessionalsandotherswhowantaconciseguidetoeverydaydesignterminology.

IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringClassificationofloads:Accordingtovariationwithtime:Loadswhosemagnitudeisconstant,andnotvaryingwithtimearecalledasstaticloads,andmayvarywithtimearecalledasdynamicloads.Accordingtooccupation:Theloadswhichremainconstantinpositionarecalleddeadloads.Accordingtodistribution:Thedistributionwhereaheavyloaddistributedoverasmallareaiscalledconcentratedload.Theloadwhichareevenlydistributedoveralargeareaiscalledanuniformlydistributedload.

IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringClassificationofloadsConcentratedLoadUniformlydistributedLoadUniformlyVaryingLoadIntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringInternalforces:Conceptofstress:Conceptofstrain:IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringTypesofstressesandstrainsIntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringTRUSSBRIDGELABORATORYBridgesareessentialtoournation'sinfrastructure.Asimplebridgecanbemadebyspanningagapwithplanks.Asthegapbecomeswider,however,theplankswillbegintosagexcessivelyevenundertheweightofaperson.Ifthebridgeislongerstill,theplanksmaybreak.Whenoneoftheplanks,calledabeam,isloaded,itbendsasshownbelow.Linesaredrawnonthebeamforillustration.

IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringTRUSSBRIDGELABORATORYIntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringTRUSSBRIDGELABORATORYAclose-upviewofashortsegmentofthebeamisshownbelow.Thetoppartofthebeamisbeingsqueezed(incompression)andthebottompartofthebeamisbeingstretched(intension).Theforceinthebeamactuallychangescontinuouslyfromthetopofthebeamtothebottom.Thatmeansthatinthemiddle(toptobottom),itisneitherincompressionnortension.Theseforcesactinabendingmanneronthebeam.Thisbendingforceisreferredtoasmoment,asshowninthediagram.

IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringTRUSSBRIDGELABORATORYIntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringTRUSSBRIDGELABORATORYIfaplankbridgebreaks,itislikelytosplinterinthemiddleleavingtherestoftheplankundamaged.Thisisbecausethecenteroftheplankexperiencesmuchmoremomentthantheends,whichexperiencenone,becausetheyarefreetorotatewithoutresistance.Sothemoment,ortwistingforce,variescontinuouslyfromzeroattheleftendtoitshighestvalueinthemiddleandbacktozeroagainattherightend.Theresultisthatalthoughitissimpletobuild,aplankbridgedoesnotmakeveryefficientuseofmaterial.

IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringTRUSSBRIDGELABORATORYOnewayofmakingmoreefficientuseofwoodenbeamsistostandthemonedge.Ifyouhaveeverbeeninanunfinishedattic,youmayhavenoticedthatthefloorbeams(andtherafters)areinthisconfiguration.Thebeamsdon'tbendasmuchintheuprightorientation.Thisisbecauseofapropertycalledmomentofinertia.Thebasicprincipleofmomentofinertiafollows.

IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringTRUSSBRIDGELABORATORYAswesawbefore,thehighestcompressionandtensionoccurintheverytopandtheverybottomofthebeam,respectively.Wealsofoundoutthatthemiddleofthebeam(toptobottom)isn'tworkingveryhardatall.Sowhatwewantistohaveasmuchmaterialattheouteredgesaspossibleandhaveaslittlematerialinthemiddleaspossible.Thepicturesbelowshowsomebeamstoillustratemomentofinertia.

IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringTRUSSBRIDGELABORATORYLowMomentofInertiaUsethisforadivingboardwhichyouwanttobendalotHighMomentofInertiaUsethisforsupportbeamswhichyouwanttobestiffIntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringTRUSSBRIDGELABORATORYThetwobeamsabovearecalledI-beamsorwideflangesbecauseoftheirshape(whenlookedatonend).Theleftbeamwouldbemadeofsteelandtherightofconcrete.IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringTRUSSBRIDGELABORATORYTheseshowhowmaterialisconcentratedatthetopandbottomofthebeam.IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringTRUSSBRIDGELABORATORYThemorematerialandthefartherawayfromthecenteritis,thehigherthemomentofinertia,andhencethestrongerthebeam.Asnaturewouldhaveit,achievinggreaterdistancefromthecenterismorebeneficialthanaddingmorematerial,becausethemomentofinertiaincreasesasthesquareofthatdistance.

IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringTRUSSBRIDGELABORATORYObviously,wecannotremoveallthematerialfromthemiddleofthebeam,becausethetopandbottommustbeconnected.Thematerialinthemiddlealsokeepsthetopandbottomfromslidingwithrespecttoeachotherinwhatiscalledshear.Yetthereisamoreefficientwaytofocusmaterialatthetopandbottomandprovideresistancetoshear.

IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringTRUSSBRIDGELABORATORYThemiddlepartofthebeamdoesnotneedtobesolidandcontinuous,butcaninsteadbemadeupofthinrods.Thisisshowninthefigurebelow.

IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringTRUSSBRIDGELABORATORYThisconfigurationestablishesthebasisforwhatisknownasatruss.Atrussistheoldestandmostoftenusedmethodofmakingmoreefficientbridges,andyouwillbebuildingonetoday.Atrussisastructuremadefromstraightlinksconnectedatjoints.Thejointsarealwaysattheendsofthelinks,neverinthemiddle.

IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringTRUSSBRIDGELABORATORYThelinksarecalledmembers,andinyourcase,theyarecraftstickswithdrilledholes.Thejointsareassembledwithsmallboltsinyourcase.Ifthetermmembersmakesyouthinkofateam,youareontherighttrack.Whenaloadisappliedtoanyjoint,thememberswillsharetheload,althoughnotequally.

IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringSomeConcepts:

COMPRESSION:This,asyouwouldexpect,describesa"squeezing"actionorforceonanobject.TENSION:Theoppositeofcompression,ora"stretching"actionorforceonanobject.

IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringSTRESS:

Ameasureofforceperunitofarea,i.e.lb./in2(orpsi),kN/m2STRAIN:

Ameasureofdeformationorelongationofamaterial,itsunitsareinchperinch;itistheratioofachangeinlengthtotheoriginallengthofaspecimen.STRENGTH:

Thestressvalueatwhichasampleofmaterialfails.IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringMODULUSOFELASTICITY:

Relatesstresstostrainandvisaversa.Itistheratioofthestressonasampletotheamountofstainthatlevelofstresscauses.Itisalsotheslopeofthestraightlineportionofthestress-straincurveforaspecificmaterial.

ELASTICRANGE:

Theportionofthestress-strainrelationshipforamaterialwhereifthespecimenloadedandthenunloaded,itwillreturntoitsoriginalundeformedshape.Thestraightlineportionofthestressstraincurve.

IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringNEUTRALAXIS:

Alinewhichrunsalongthelengthofabeamwherestressandstrainareequaltozero.MOMENTOFINERTIA:

Thisisonemeasureofthestiffnessofabeam.Itrelatescrosssectionalareaandthedistancefromtheneutralaxisatwhichthemajorityoftheareaislocatedtotheeaseinwhichthebeamisbent.IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringExample:

An"I"beamhasagreatermomentofinertiathanaflatplateoftheexactsamecrosssectionalarea.CANTILEVERBEAMAbeam(amemberwhosemainactionisbending)supported,orfixed,atonlyoneend.i.e.anoverhangoradivingboardconfiguration.IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringSTABILITYANDSIMPLETRUSSESThereisanimportantcharacteristicofausefultruss:itmustbestable,whichistosaythatitshouldnotmovefreelyinanydirection.Belowaresomeconfigurationsofmembersjoinedattheends.Thefirstshownisthemostbasictriangulartruss.Theleftsupportonlyallowsconnectedmemberstorotate.Therightsupportadditionallyallowshorizontalmovement.Thisconfigurationisstable,becausethereisnomotionwhichcanfreelyoccur.

IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringSTABILITYANDSIMPLETRUSSESTwomembersconnectedatajointformahingedarch,asshownbelow.Ahingedarchmaybeaddedtoanystabletrusstoformanotherstabletruss,aslongastheangleofthearchisotherthan180o.Atrusswhichcanbeassembledinthismanneriscalledasimpletruss.IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringSTABILITYANDSIMPLETRUSSESLastly,weseethatapentagonalconfigurationisalsounstable,becauseaspointsAandBmoveapart,pointCisfreetomovedown.Whatisthesmallestnumberofmembersrequiredtomakethisstable?Inasimilarfashion,allbutthetrianglewillbeunstable,sothetriangleisbasicunitofanytrussstructure.

IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringTHELONGANDSHORTOFIT

Anotherspecialfeatureoftrussesisthatthemembersdon'tbend.Theygetpulledapart(intension)andpushedtogether(incompression),buttheydon'tbendliketheplankdoeswhenyoustandonit.Themembersstaystraightfromendtoenduntiltheybreak.Thisdoesnotmeanthebridgewillstaystraight,though.Asheavierloadsareputonthebridge,itwillstillsaginthemiddle.Thisisbecausetheindividualmembersofthetrussaregettinglonger(iftheyareintension)andshorter(iftheyareincompression).IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringABELTISN'TTHEONLYTHINGTHATBUCKLESManymaterials,intheory,havethesamestrengthwhenbeingsqueezedtogether(incompression)astheydowhenpulledapart(intension).Theproblemisthatifyoupressthetwoendsofathinmember(likearuler)together,itdoesn'tsimplystaystraightandgetshorter,butinsteaditbendsouttotheside.Thisiscalledbuckling,whichisthewaythatmosttall,skinnythingsbreakwhencompressedend-to-end.IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringHOWCANMYTRUSSFAIL?

Therearethreewaysyourtrusscanfail.Ifamemberbucklesenough,itwillbendandbreakinthedirectioninwhichthecraftstickshavealowmomentofinertia.Thismaybepreventediftheloadingframesupportspartiallybuckledmembers.Anothertypeoffailureisthatacraftstickpullsapartinthemiddleintension.Thethirdtypeoffailurepossibleisjointbreak-out.Thisiswhenthecraftstickbreaksrightwheretheboltisconnected.

IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringStudentsintheStructureslab

IntroductiontoDesignofCiviBuildingEnvelopePerformanceLaboratoryFullscalewallthermalresistanceexperimentIntroductiontoDesignofCivilEngineeringBuildingEnvelopeFullscalewaStructuresLaboratoryIntroductiontoDesignofCivilEngineeringStructuresLaboratoryIntroductEnvironmentalLaboratoryIntroductiontoDesignofCivilEngineeringEnvironmentalLaboratoryIntrodWaterResourcesLaboratoryIntroductiontoDesignofCivilEngineeringWaterIntroductiontoDesignofBuildingAerodynamicLaboratoryIntroductiontoDesignofCivilEngineeringBuildingIntroductiontoDesignAcousticsLaboratoryIntroductiontoDesignofCivilEngineeringAcousticsLaboratoryIntroductiIndoorAirQualityandVentilationLaboratoryIntroductiontoDesignofCivilEngineeringIndoorAirIntroductiontoDesiThermalEnvironmentandControlsLaboratoryIntroductiontoDesignofCivilEngineeringThermalIntroductiontoDesignComputerLaboratoriesIntroductiontoDesignofCivilEngineeringComputerIntroductiontoDesignIntroductiontoDesignofCivilEngineeringENGINEERINGRESEARCHTheroleoftheresearchengineerisachievedaftermanyyearsofstudy.Studentswishingtopursuethisfieldshouldtakecoursesthatemphasizeadvancedmathematicsandstatistics.Useofthecomputerisessential;computerlanguagessuchasFORTRANandC++aidtheresearchengineerincompletingprojects.

Studentscanstartearlyasastudentassistantforaprofessorintheundergraduatemajor.

IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringENGINEERINGRESEARCH

Mostoftheskillsnecessarytoworkinthefield,however,willcomewithresearchcompletedingraduatestudies.Mostcollegesanduniversitiesdonotofferaresearchsub-disciplineintheCivilEngineeringmajor.Studentsshouldchoosecourseswhichtheywishtospecializein.

IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringSTRUCTURALENGINEERING

Allstructures,regardlessoftheirfunction,aresubjectedtoforcescausedbythenaturalenvironment(suchaswindandearthquakes)andbyman(suchascargoandautomobiletraffic),andtheymustbedesignedtowithstandtheseforces.Thesestructurescanbeasvariedasbuildings,bridges,pipelines,machinery,automobilesandspacecraft.IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringSTRUCTURALENGINEERINGThejobofthestructuralengineeristocreatethesenewdesignsortoevaluateandimprovetheloadresistancecapabilitiesofexistingstructureswhichmayhavebeendamagedduringanearthquake.Inordertoaccomplishthisthestructuralengineermustbeknowledgeableaboutthebehaviorofdeformablebodies,aboutthesources,magnitudesandprobabilityofoccurrenceofappliedloads,aboutmaterialproperties,designphilosophiesandgovernmentaldesigncodes,andaboutcomputerprogrammingandusage.

IntroductiontoDesignofCiviExplainthetermsstressandstrain.StateHook’sLaw.Whyisafactorofsafetyprovidedforadesign?Whatismeantbyworkingstress?Define(i)Poisson’sratio(ii)hydrostaticpressureand(iii)volumetricstrain.IntroductiontoDesignofCivilEngineeringReviewQuestionsExplainthetermsstressands土木工程概論

IntroductiontoCivilEngineering第九章土木工程設計概述Chapter9IntroductiontoDesignofCivilEngineering土木工程概論

IntroductiontoCivilEIntroductiontoDesignofCivilEngineeringWhatisIntroductiontoDesignofCivilEngineering?Itprovidesthestudentswiththenecessarybackgroundonterminologyusedindesign.Withthischapter,entry-levelstudentsofcivilengineeringwillbetterunderstandfromtheoutsetlecturesondetailedsubjectareas.Itwillalsoprovebeneficialfornewlyqualifiedprofessionalsandotherswhowantaconciseguidetoeverydaydesignterminology.

IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringClassificationofloads:Accordingtovariationwithtime:Loadswhosemagnitudeisconstant,andnotvaryingwithtimearecalledasstaticloads,andmayvarywithtimearecalledasdynamicloads.Accordingtooccupation:Theloadswhichremainconstantinpositionarecalleddeadloads.Accordingtodistribution:Thedistributionwhereaheavyloaddistributedoverasmallareaiscalledconcentratedload.Theloadwhichareevenlydistributedoveralargeareaiscalledanuniformlydistributedload.

IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringClassificationofloadsConcentratedLoadUniformlydistributedLoadUniformlyVaryingLoadIntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringInternalforces:Conceptofstress:Conceptofstrain:IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringTypesofstressesandstrainsIntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringTRUSSBRIDGELABORATORYBridgesareessentialtoournation'sinfrastructure.Asimplebridgecanbemadebyspanningagapwithplanks.Asthegapbecomeswider,however,theplankswillbegintosagexcessivelyevenundertheweightofaperson.Ifthebridgeislongerstill,theplanksmaybreak.Whenoneoftheplanks,calledabeam,isloaded,itbendsasshownbelow.Linesaredrawnonthebeamforillustration.

IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringTRUSSBRIDGELABORATORYIntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringTRUSSBRIDGELABORATORYAclose-upviewofashortsegmentofthebeamisshownbelow.Thetoppartofthebeamisbeingsqueezed(incompression)andthebottompartofthebeamisbeingstretched(intension).Theforceinthebeamactuallychangescontinuouslyfromthetopofthebeamtothebottom.Thatmeansthatinthemiddle(toptobottom),itisneitherincompressionnortension.Theseforcesactinabendingmanneronthebeam.Thisbendingforceisreferredtoasmoment,asshowninthediagram.

IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringTRUSSBRIDGELABORATORYIntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringTRUSSBRIDGELABORATORYIfaplankbridgebreaks,itislikelytosplinterinthemiddleleavingtherestoftheplankundamaged.Thisisbecausethecenteroftheplankexperiencesmuchmoremomentthantheends,whichexperiencenone,becausetheyarefreetorotatewithoutresistance.Sothemoment,ortwistingforce,variescontinuouslyfromzeroattheleftendtoitshighestvalueinthemiddleandbacktozeroagainattherightend.Theresultisthatalthoughitissimpletobuild,aplankbridgedoesnotmakeveryefficientuseofmaterial.

IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringTRUSSBRIDGELABORATORYOnewayofmakingmoreefficientuseofwoodenbeamsistostandthemonedge.Ifyouhaveeverbeeninanunfinishedattic,youmayhavenoticedthatthefloorbeams(andtherafters)areinthisconfiguration.Thebeamsdon'tbendasmuchintheuprightorientation.Thisisbecauseofapropertycalledmomentofinertia.Thebasicprincipleofmomentofinertiafollows.

IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringTRUSSBRIDGELABORATORYAswesawbefore,thehighestcompressionandtensionoccurintheverytopandtheverybottomofthebeam,respectively.Wealsofoundoutthatthemiddleofthebeam(toptobottom)isn'tworkingveryhardatall.Sowhatwewantistohaveasmuchmaterialattheouteredgesaspossibleandhaveaslittlematerialinthemiddleaspossible.Thepicturesbelowshowsomebeamstoillustratemomentofinertia.

IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringTRUSSBRIDGELABORATORYLowMomentofInertiaUsethisforadivingboardwhichyouwanttobendalotHighMomentofInertiaUsethisforsupportbeamswhichyouwanttobestiffIntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringTRUSSBRIDGELABORATORYThetwobeamsabovearecalledI-beamsorwideflangesbecauseoftheirshape(whenlookedatonend).Theleftbeamwouldbemadeofsteelandtherightofconcrete.IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringTRUSSBRIDGELABORATORYTheseshowhowmaterialisconcentratedatthetopandbottomofthebeam.IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringTRUSSBRIDGELABORATORYThemorematerialandthefartherawayfromthecenteritis,thehigherthemomentofinertia,andhencethestrongerthebeam.Asnaturewouldhaveit,achievinggreaterdistancefromthecenterismorebeneficialthanaddingmorematerial,becausethemomentofinertiaincreasesasthesquareofthatdistance.

IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringTRUSSBRIDGELABORATORYObviously,wecannotremoveallthematerialfromthemiddleofthebeam,becausethetopandbottommustbeconnected.Thematerialinthemiddlealsokeepsthetopandbottomfromslidingwithrespecttoeachotherinwhatiscalledshear.Yetthereisamoreefficientwaytofocusmaterialatthetopandbottomandprovideresistancetoshear.

IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringTRUSSBRIDGELABORATORYThemiddlepartofthebeamdoesnotneedtobesolidandcontinuous,butcaninsteadbemadeupofthinrods.Thisisshowninthefigurebelow.

IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringTRUSSBRIDGELABORATORYThisconfigurationestablishesthebasisforwhatisknownasatruss.Atrussistheoldestandmostoftenusedmethodofmakingmoreefficientbridges,andyouwillbebuildingonetoday.Atrussisastructuremadefromstraightlinksconnectedatjoints.Thejointsarealwaysattheendsofthelinks,neverinthemiddle.

IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringTRUSSBRIDGELABORATORYThelinksarecalledmembers,andinyourcase,theyarecraftstickswithdrilledholes.Thejointsareassembledwithsmallboltsinyourcase.Ifthetermmembersmakesyouthinkofateam,youareontherighttrack.Whenaloadisappliedtoanyjoint,thememberswillsharetheload,althoughnotequally.

IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringSomeConcepts:

COMPRESSION:This,asyouwouldexpect,describesa"squeezing"actionorforceonanobject.TENSION:Theoppositeofcompression,ora"stretching"actionorforceonanobject.

IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringSTRESS:

Ameasureofforceperunitofarea,i.e.lb./in2(orpsi),kN/m2STRAIN:

Ameasureofdeformationorelongationofamaterial,itsunitsareinchperinch;itistheratioofachangeinlengthtotheoriginallengthofaspecimen.STRENGTH:

Thestressvalueatwhichasampleofmaterialfails.IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringMODULUSOFELASTICITY:

Relatesstresstostrainandvisaversa.Itistheratioofthestressonasampletotheamountofstainthatlevelofstresscauses.Itisalsotheslopeofthestraightlineportionofthestress-straincurveforaspecificmaterial.

ELASTICRANGE:

Theportionofthestress-strainrelationshipforamaterialwhereifthespecimenloadedandthenunloaded,itwillreturntoitsoriginalundeformedshape.Thestraightlineportionofthestressstraincurve.

IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringNEUTRALAXIS:

Alinewhichrunsalongthelengthofabeamwherestressandstrainareequaltozero.MOMENTOFINERTIA:

Thisisonemeasureofthestiffnessofabeam.Itrelatescrosssectionalareaandthedistancefromtheneutralaxisatwhichthemajorityoftheareaislocatedtotheeaseinwhichthebeamisbent.IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringExample:

An"I"beamhasagreatermomentofinertiathanaflatplateoftheexactsamecrosssectionalarea.CANTILEVERBEAMAbeam(amemberwhosemainactionisbending)supported,orfixed,atonlyoneend.i.e.anoverhangoradivingboardconfiguration.IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringSTABILITYANDSIMPLETRUSSESThereisanimportantcharacteristicofausefultruss:itmustbestable,whichistosaythatitshouldnotmovefreelyinanydirection.Belowaresomeconfigurationsofmembersjoinedattheends.Thefirstshownisthemostbasictriangulartruss.Theleftsupportonlyallowsconnectedmemberstorotate.Therightsupportadditionallyallowshorizontalmovement.Thisconfigurationisstable,becausethereisnomotionwhichcanfreelyoccur.

IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringSTABILITYANDSIMPLETRUSSESTwomembersconnectedatajointformahingedarch,asshownbelow.Ahingedarchmaybeaddedtoanystabletrusstoformanotherstabletruss,aslongastheangleofthearchisotherthan180o.Atrusswhichcanbeassembledinthismanneriscalledasimpletruss.IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringSTABILITYANDSIMPLETRUSSESLastly,weseethatapentagonalconfigurationisalsounstable,becauseaspointsAandBmoveapart,pointCisfreetomovedown.Whatisthesmallestnumberofmembersrequiredtomakethisstable?Inasimilarfashion,allbutthetrianglewillbeunstable,sothetriangleisbasicunitofanytrussstructure.

IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringTHELONGANDSHORTOFIT

Anotherspecialfeatureoftrussesisthatthemembersdon'tbend.Theygetpulledapart(intension)andpushedtogether(incompression),buttheydon'tbendliketheplankdoeswhenyoustandonit.Themembersstaystraightfromendtoenduntiltheybreak.Thisdoesnotmeanthebridgewillstaystraight,though.Asheavierloadsareputonthebridge,itwillstillsaginthemiddle.Thisisbecausetheindividualmembersofthetrussaregettinglonger(iftheyareintension)andshorter(iftheyareincompression).IntroductiontoDesignofCiviIntroductiontoDesignofCivilEngineeringABELTISN'TTHEONLYTHI