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11
#ANYOUDETERMINETHESTRENGTHOFAMEMBER
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11
#ANYOUCALCULATETHEFACTOROFSAFETYFORAMEMBER
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STRENGTHSNOTALREADYRECORDEDINTHETABLE
#ALCULATETHE&ACTOROF3AFETY
/NCEWEKNOWTHESTRENGTHOFAMEMBERANDTHEINTERNALFORCEITISACTUALLYEXPERIENCINGWECANCALCULATEITSFACTOROFSAFETY&ORTHEBOTTOMCHORDMEMBER#$THEFACTOROFSAFETYIS
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/NAN!CTUAL"RIDGE0ROJECT
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MEMBERINTHESTRUCTURECANCARRYLOADSAFELY/NANACTUAL
BRIDGEPROJECTTHEENGINEERWOULDALSOCHECKTOENSURETHATTHEDEmECTIONSAREACCEPT
ABLYSMALL!DEmECTIONISTHEDISTANCEASTRUCTUREMOVESWHENITISLOADED!BRIDGE
ALWAYSDEmECTSWHENITISLOADED/NAWELLDESIGNEDBRIDGETHESEDEmECTIONSARESO
SMALLTHATTHEYAREIMPERCEPTIBLETODRIVERSANDPEDESTRIANSCROSSINGTHESPAN)FABRIDGE
ISTOOmEXIBLETHENDRIVERSANDPEDESTRIANSWILLFEELITSMOVEMENTANDWILLPERCEIVETHE
STRUCTURETOBEUNSAFEEVENIFITSSTRENGTHENTIRELYADEQUATE4HEENGINEERISRESPONSIBLE
FORENSURINGNOTONLYTHATTHEBRIDGEISSAFEBUTALSOTHATTHEPUBLIC PERCEIVESITTOBESAFE
4HUSTHEENGINEERCAREFULLYCOMPUTESTHESTRUCTURESDEmECTIONSUNDERVARIOUSLOADING
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FROMTHEmOORBEAMS7ENOWHAVETHEANALYTICALTOOLSTOCHECKTHISASSUMPTION3INCETHEmOORBEAMSAREATTACHEDTOTHEBOTTOMCHORDSLOADINGTHEmOORBEAMSISESSENTIALLYTHESAMEASLOADINGTHEBOTTOMCHORDJOINTSOFTHETRUSS4HUSOURREVISEDSTRUCTURALMODELSHOULDHAVETHETHREE.LOADSAPPLIEDATTHEBOTTOMCHORDASSHOWNBELOW
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11
#ANYOUAPPLYTHE-ETHODOF*OINTSTOANALYZEATRUSS
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11
#ANMEMBERSWITHZEROFORCEBEREMOVED
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11
#ANYOUANALYZEADIFFERENTTRUSS
3ELECTANYTRUSSFROMTHE'ALLERYOF3TRUCTURAL!NALYSIS2ESULTS
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)NTHISLEARNINGACTIVITYWEAPPLIEDCONCEPTSFROMGEOMETRYTRIGONOMETRYALGEBRAANDPHYSICSTOCALCULATETHEINTERNALFORCESINEVERYMEMBEROFATRUSS)NDOINGSOYOUSAWHOWMATHANDSCIENCEAREAPPLIEDTOSOLVEANIMPORTANTREALWORLDPROBLEM9OUALSOSAWHOWDATAFROMLABORATORYEXPERIMENTSTHESTRENGTHTESTSWEDIDIN,EARNING!CTIVITYCANBEINTEGRATEDINTOTHESOLUTIONOFANENGINEERINGPROBLEM-OSTIMPORTANTYOULEARNEDTOUSEANIMPORTANTANALYSISTOOLCALLEDTHE-ETHODOF*OINTS4HISTECHNIQUEISNTEASY)TREQUIRESYOUTOCONSTRUCTANDSOLVEEQUILIBRIUMEQUATIONSLOTSOFTHEMWHILEPAYINGCAREFULATTENTIONTOTHEMAGNITUDESANDDIRECTIONSOFFORCES7OULDNTITBEGREATIFWECOULDUSETHECOMPUTERTODOTHISWORKFORUS7ELLWECAN)N,EARNING!CTIVITYWEWILLUSETHE7EST0OINT"RIDGE$ESIGNERSOFTWARETOANALYZEANDEVALUATEATRUSSBRIDGE
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#ANYOUDETERMINETHESTRENGTHOFTHEVERTICALSANDENDPOSTS4ODETERMINETHECOMPRESSIVESTRENGTHOFTHEVERTICALSANDENDPOSTSWEWILLUSETHESTRENGTHVSLENGTHGRAPHWEDEVELOPEDIN,EARNING!CTIVITY4HEVERTICALSAREMMXMMTUBESANDEACHHASALENGTHOFCENTIMETERS4HUSTHECOMPRESSIVESTRENGTHOFTHEVERTICALTUBESISNEWTONSASINDICATEDBELOW
$ETERMININGTHECOMPRESSIVESTRENGTHOFAMMXMMTUBETHATISCMLONG
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$ETERMININGTHECOMPRESSIVESTRENGTHOFAMMXMMTUBETHATISCMLONG
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#ANYOUAPPLYTHE-ETHODOF*OINTSTOANALYZEATRUSS4OANALYZETHETRUSSWITHBOTTOMCHORDLOADINGFOLLOWEXACTLYTHESAMEPROCEDUREASYOUDIDFORTHETRUSSWITHTOPCHORDLOADING9OUWILLlNDTHATTHECALCULATIONOFREACTIONSANDTHEANALYSESOF*OINTS!"AND)AREEXACTLY THESAMEASFORTHETOPCHORDLOADING3TARTINGAT*OINT#HOWEVERTHETWOSOLUTIONSDIFFER4HETRUSSWITHBOTTOMCHORDLOADINGHASAN.LOADAT*OINT#ASSHOWNINTHEFREEBODYDIAGRAM!SARESULTTHEXDIRECTIONEQUILIBRIUMEQUATIONREMAINSTHESAMEBUTTHEYDIRECTIONEQUILIBRIUMEQUATIONCHANGES
.EXTWEANALYZE*OINT*)NTHISCASETHEABSENCEOFANEXTERNALLOADATTHEJOINTCAUSESTHEYDIRECTIONEQUILIBRIUMEQUATIONTOCHANGE
&INALLYWEANALYZE*OINT+TODETERMINE& $+
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#ANMEMBERSWITHZEROFORCEBEREMOVED-EMBERS")AND&-COULDBEREMOVEDFROMOURMODELOFTHE'RANT2OAD"RIDGEWITHNOADVERSECONSEQUENCESHOWEVERTHEYCOULDNOTBESAFELYREMOVEDFROMTHEACTUALHIGHWAYBRIDGE)NTHEACTUALBRIDGE-EMBERS")AND&-SERVEANIMPORTANTSTRUCTURALFUNCTIONTHEYSUPPORTTHEmOORBEAMSATTACHEDTOTHETRUSSAT*OINTS"AND&4HESEmOORBEAMSHELPTOSUPPORTTHEBRIDGEDECKANDTRANSMITVEHICULARLOADSFROMTHEDECKTOTHEMAINTRUSSES4HUSINTHEACTUALBRIDGE-EMBERS")AND&-AREINTENSIONANDAREESSENTIALTOTHESTRUCTURESLOADCARRYINGABILITY
-EMBER$+COULDNOTBESAFELYREMOVEDFROMEITHERTHEMODELORTHEACTUALBRIDGE7ITHOUT-EMBER$+ WEWOULDHAVEJUSTONECONTINUOUSMEMBERFROM*OINT*TO*OINT,THEREWOULDBENOREASONFORAJOINTAT+4HISNEWMEMBERLETSCALLIT-EMBER*,WOULDBETWICEASLONGAS-EMBER*+OR-EMBER+,!SARESULT-EMBER*,WOULDBEMUCHWEAKERINCOMPRESSIONTHAN*+OR+,2ECALLFROM,EARNING!CTIVITYTHATCOMPRESSIONSTRENGTHDECREASESSUBSTANTIALLYWITHINCREASINGLENGTH4OKEEP-EMBER*,FROMBUCKLINGACONSIDERABLYLARGERTUBEWOULDBEREQUIRED4HUSEVENTHOUGH-EMBER$+HASNOINTERNALFORCEITEFFECTIVELYSTRENGTHENSTHESTRUCTUREBYDIVIDING-EMBER*,INTOTWOSHORTERSTRONGERCOMPRESSIONMEMBERS
)TISALSOWORTHNOTINGTHATINANACTUALBRIDGETHEINTERNALFORCEIN-EMBER$+WOULDNOTBEZERO)T WOULDACTUALLYCARRYPARTOFTHESELFWEIGHTOF-EMBERS*+AND+,RESULTINGINASMALLCOMPRESSIVEINTERNALFORCE)NOURANALYSISTHEINTERNALFORCEIN-EMBER$+ISZEROONLYBECAUSEWEASSUMEDTHESELFWEIGHTTOBEZERO
#ANYOUANALYZEAMORECOMPLEXTRUSS4HE'ALLERYOF3TRUCTURAL!NALYSIS2ESULTS!PPENDIX"PROVIDESTHECALCULATEDINTERNALMEMBERFORCESFORAWIDEVARIETYOFCOMMONTRUSSCONlGURATIONS