Inthispaper,thenonlinearconjugatemapbasedontheconjugateRackwitz-FiesslerandHasofer-Lind(CHL-RF)methodisusedtoevaluatethereliabilityusingfirstorderreliabilitymethodoftheembeddednanocompositebeam,whichismadefrompolymerreinforcedwithcarbonnanotubs(CNTs).ThestructureissimulatedwithTimoshenkobeammodel.TheMori-Tanakamethodisappliedforobtainingtheeffectivepropertiesofnanocompositebeam.Thesurroundingelasticmediumisconsideredbyspringandshearconstants.UtilisingenergymethodandHamilton'sprincipal,thegoverningequationsareobtained.Usingananalyticalmethod,thebucklingperformancefunctionofstructureisobtained.Theinfluencesofthebasicrandomvariablesincludingthelengthtothicknessratioofbeam(L/h),springconstantandshearconstantoffoundationwithrespecttothevolumefractionofCNTsareinvestigatedonthereliabilityindexofthenanocompositebeamsubjectedtoaxialforceof20GPa.Theresultsindicatedthatthefailureprobabilitiesofthestudiedthenanocompositebeamarethesensitivetothelengthtothicknessofbeam(L/h)andspringconstantoffoundationvariables.
