ABSTRACT
Inastructuralanalysis,whentheequilibriumandkinematicrelationshipsare writtenwithrespecttotheundeformed(ororiginal)geometryofthestructure,the analysisisreferredtoasafirst-orderanalysis.Ontheotherhand,whenthe equilibriumandkinematicrelationshipsarewrittenwithrespecttothedeformed geometryofthestructure,theanalysisisreferredtoasasecond-orderanalysis. Second-orderanalysisisalwaysnecessaryforthestabilityconsiderationof structures.Whenastructurebecomesunstableunderasystemofforces,itoften assumesaconfigurationwhichdeviatesquitenoticeablyfromitsundeformed configuration.Infact,inabifurcationanalysis,thecriticalloadisobtainedasthe eigenvalueofthecharacteristicequationofthegoverningdifferentialequation writtenwithrespecttothedeformedconfigurationofthestructure.Inaloaddeflectionanalysis,thenonlinearload-deflectioncurvecanbetracedonlyifthe changeofgeometryofthestructureistakenintoaccount.
