Buckling loads of variable cross sections

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1、THESISELASTICBUCKLINGLOADSOFSLENDERCOLUMNSWITHVARIABLECROSSSECTIONBYTHENEWMARKMETHODSubmittedbyCharlesE.RileyDepartmentofCivilEngineeringInpartialfulfillmentoftherequirementsfortheDegreeofMasterofScienceColoradoStateUniversityFortCollins,ColoradoSummer2003C

2、OLORADOSTATEUNIVERSITYMay20,2003WEHEREBYRECOMMENDTHATTHETHESISPREPAREDUNDEROURSUPERVISIONBYCHARLESRILEYENTITLEDELASTICBUCKLINGLOADSOFSLENDERCOLUMNSBYTHENEWMARKMETHODBEACCEPTEDASFULLFILINGINPARTREQUIREMENTSFORTHEDEGREEOFMASTEROFSCIENCE.CommitteeonGraduateWor

3、k(Pleaseprintnameundersignature)AdviserDepartmentHead/DirectoriiABSTRACTOFTHESISELASTICBUCKLINGLOADSOFSLENDERCOLUMNSWITHVARIABLECROSSSECTIONBYTHENEWMARKMETHODDeterminingthecriticalbucklingloadforcolumnswithvariablecrosssectionpresentsauniquedesignproblemfor

4、engineers.Exactsolutionsforcertaincolumngeometriesandendconditionsexist,butnoconcisedesignequationshavebeenpresentedthatcoverthebroadrangeofpotentialcolumnconfigurations.Thisthesisprovidesanexhaustiveliteraturereviewtoputtheresearchpresentedhereincontextand

5、pointthewaytowardsfurtherresearch.ThisthesisutilizestheExcelspreadsheetenvironmentwiththeNewmarkiterativeproceduretoperformbucklinganalysesondeterminate(pinned-pinnedandfixed-free)andone-degreeindeterminate(fixed-pinnedandfixed-guided)columns.Thecriticalbuc

6、klingloadsofcolumnswithvariationofthemomentofinertiabetweenpowersofoneandfour,correspondingtolineartaperingofcommoncrosssectionshapes,arecalculatedtoahighdegreeofaccuracyandpresentedintheformofdesigncurvesandclosed-formequationsbasedoncurvefitting.Theproces

7、sofdevelopingtheNewmarknumericalmethodwithintheExcelspreadsheetenvironmentispresentedindetailtoprovideapowerfultoolforengineerstousewhendesigninguniquecolumnsthathavenoavailablesolution.Aroundcolumnwithparabolicvariationofitsdiameterandcrucifixcolumnwithlin

8、earvariationfromitsiiiendstothemiddleareexaminedtodemonstratethecapabilitiesoftheNewmarkmethodinthisregard.CharlesE.RileyDepartmentofCivilEngineeringColoradoStateUniversityFortCollins,CO80523Summer2003