solve truss

7/29/2019 solve truss

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CONDITIONSANDENSURESTHATTHESECOMPUTEDDEmECTIONSCOMPLYWITHTHEAPPROPRIATE

DESIGNCODES

"OTTOM#HORD,OADING

4HEANALYSISABOVEWASBASEDONANUMBEROFASSUMPTIONS0ERHAPSTHEMOSTIMPORTANTOFTHESEWASOURASSUMPTIONTHATPLACINGTHELOADONTHETOPCHORDOFTHETRUSSISMORESEVERETHANSUSPENDINGTHELOAD

FROMTHEmOORBEAMS7ENOWHAVETHEANALYTICALTOOLSTOCHECKTHISASSUMPTION3INCETHEmOORBEAMSAREATTACHEDTOTHEBOTTOMCHORDSLOADINGTHEmOORBEAMSISESSENTIALLYTHESAMEASLOADINGTHEBOTTOMCHORDJOINTSOFTHETRUSS4HUSOURREVISEDSTRUCTURALMODELSHOULDHAVETHETHREE.LOADSAPPLIEDATTHEBOTTOMCHORDASSHOWNBELOW

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11

#ANYOUAPPLYTHE-ETHODOF*OINTSTOANALYZEATRUSS

5SETHE-ETHODOF*OINTSTOANALYZETHE0RATTTRUSSWITHBOTTOMCHORD

LOADING0ROVETHATTHERESULTSINTHETABLEABOVEARECORRECT

.OTETHATMOVINGTHELOADSFROMTHETOPCHORDTOTHEBOTTOMCHORDCAUSEDTHEINTERNALFORCESTOCHANGEONLYIN-EMBERS#*%,AND$+)NALLTHREECASESTHEFORCESGOTSMALLER4HEFORCESINTHEMOSTHEAVILYLOADEDMEMBERSTHETOPANDBOTTOMCHORDSANDTHEENDPOSTSREMAINEDUNCHANGEDTHUSTHEOVERALLFACTOROFSAFETYOFTHESTRUCTUREREMAINSUNCHANGED7ECANCONCLUDETHATUSINGTHETOPCHORDLOADINGIN,EARNING!CTIVITYANDINOURINITIALSTRUCTURALANALYSISWASENTIRELYAPPROPRIATE4HEBOTTOMCHORDLOADINGISMOREREALISTICBECAUSEREALBRIDGESCARRYTRAFlCLOADSONTHEIRmOORBEAMSHOWEVERTHETOPCHORDLOADINGISMUCHEASIERTODOANDPRODUCESNEARLYIDENTICALSTRUCTURALANALYSISRESULTS

11

#ANMEMBERSWITHZEROFORCEBEREMOVED

)NTHEANALYSISABOVE-EMBERS")&-AND$+HAVEZEROINTERNAL

FORCE)TWOULDSEEMTHATTHETRUSSDOESNOTNEEDTHESEMEMBERSTO

CARRYLOADANDWEMIGHTSIMPLYREMOVETHEMFROMTHESTRUCTURETO

SAVEMATERIAL$OYOUTHINKTHESEZEROFORCEMEMBERSCANSAFELYBE

REMOVEDFROMTHETRUSS

11

#ANYOUANALYZEADIFFERENTTRUSS

3ELECTANYTRUSSFROMTHE'ALLERYOF3TRUCTURAL!NALYSIS2ESULTS

!PPENDIX"ANDCALCULATETHEINTERNALFORCESINALLOFITSMEMBERS

#ONCLUSION

)NTHISLEARNINGACTIVITYWEAPPLIEDCONCEPTSFROMGEOMETRYTRIGONOMETRYALGEBRAANDPHYSICSTOCALCULATETHEINTERNALFORCESINEVERYMEMBEROFATRUSS)NDOINGSOYOUSAWHOWMATHANDSCIENCEAREAPPLIEDTOSOLVEANIMPORTANTREALWORLDPROBLEM9OUALSOSAWHOWDATAFROMLABORATORYEXPERIMENTSTHESTRENGTHTESTSWEDIDIN,EARNING!CTIVITYCANBEINTEGRATEDINTOTHESOLUTIONOFANENGINEERINGPROBLEM-OSTIMPORTANTYOULEARNEDTOUSEANIMPORTANTANALYSISTOOLCALLEDTHE-ETHODOF*OINTS4HISTECHNIQUEISNTEASY)TREQUIRESYOUTOCONSTRUCTANDSOLVEEQUILIBRIUMEQUATIONSLOTSOFTHEMWHILEPAYINGCAREFULATTENTIONTOTHEMAGNITUDESANDDIRECTIONSOFFORCES7OULDNTITBEGREATIFWECOULDUSETHECOMPUTERTODOTHISWORKFORUS7ELLWECAN)N,EARNING!CTIVITYWEWILLUSETHE7EST0OINT"RIDGE$ESIGNERSOFTWARETOANALYZEANDEVALUATEATRUSSBRIDGE





#ANYOUDETERMINETHESTRENGTHOFTHEVERTICALSANDENDPOSTS4ODETERMINETHECOMPRESSIVESTRENGTHOFTHEVERTICALSANDENDPOSTSWEWILLUSETHESTRENGTHVSLENGTHGRAPHWEDEVELOPEDIN,EARNING!CTIVITY4HEVERTICALSAREMMXMMTUBESANDEACHHASALENGTHOFCENTIMETERS4HUSTHECOMPRESSIVESTRENGTHOFTHEVERTICALTUBESISNEWTONSASINDICATEDBELOW

$ETERMININGTHECOMPRESSIVESTRENGTHOFAMMXMMTUBETHATISCMLONG

4HEENDPOSTSAREMMXMMTUBES3INCETHEYAREDIAGONALMEMBERSWEMUSTCALCULATETHEIRLENGTHUSINGTHE0YTHAGOREAN4HEOREM

!STHEGRAPHBELOWINDICATESAMMXMMTUBEWITHALENGTHOFCENTIMETERSHASACOMPRESSIVESTRENGTHOFNEWTONS

,ENGTHCM

# O M P R E S S I V E 3 T R E N G T H N E W T O N S

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$ETERMININGTHECOMPRESSIVESTRENGTHOFAMMXMMTUBETHATISCMLONG





#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

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