296 CHAPTER 9 Thin Plates
Fig.9.2
Buckling coefficientkfor simply supported plates.
In general, the critical stress for a uniform rectangular plate, with various edge supports and loaded
byconstantorlinearlyvaryingin-planedirectforces(Nx,Ny)orconstantshearforces(Nxy)alongits
edges,isgivenbyEq.(9.6).Thevalueofkremainsafunctionofa/bbutalsodependsonthetypeof
loadingandedgesupport.Solutionsforsuchproblemshavebeenobtainedbysolvingtheappropriate
differential equation or by using the approximate (Rayleigh–Ritz) energy method. Values ofkfor a
variety of loading and support conditions areshown in Fig. 9.3. In Fig. 9.3(c), wherekbecomes the
shearbucklingcoefficient,bisalwaysthesmallerdimensionoftheplate.
We see from Fig. 9.3 thatkis very nearly constant fora/b>3. This fact is particularly useful in
aircraftstructureswherelongitudinalstiffenersareusedtodividetheskinintonarrowpanels(having
smallvaluesofb),therebyincreasingthebucklingstressoftheskin.
9.2 InelasticBucklingofPlates.........................................................................
Forplateshavingsmallvaluesofb/t,thecriticalstressmayexceedtheelasticlimitofthematerialof
theplate.Insuchasituation,Eq.(9.6)isnolongerapplicable,since,aswesawinthecaseofcolumns,E
becomesdependentonstress,asdoesPoisson’sratioν.Theseeffectsareusuallyincludedinaplasticity
correctionfactorηsothatEq.(9.6)becomes
σCR=ηkπ^2 E
12 ( 1 −ν^2 )(
t
b