Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

320 CHAPTER 9 Thin Plates

andapproximatevaluesofFcandFtarefound,givingbetterestimatesforσcfandσtf.Theprocedure

wasthenrepeateduntiltherequiredaccuracywasobtained.

References

[1] Gerard,G.,IntroductiontoStructuralStabilityTheory,McGraw-Hill,1962.
[2] Murray,N.W.,IntroductiontotheTheoryofThin-walledStructures,OxfordEngineeringScienceSeries,1984.
[3] Argyris,andDunne,HandbookofAeronauticsNo.1:StructuralPrinciplesandData,4thedition,TheRoyal
AeronauticalSociety,1952.
[4] Bleich,F.,BucklingStrengthofMetalStructures,McGraw-Hill,1952.
[5] Gerard,G.,andBecker,H.,HandbookofStructuralStability,Pt.I,BucklingofFlatPlates,NACATech.Note
3781,1957.
[6] Rivello,R.M.,TheoryandAnalysisofFlightStructures,McGraw-Hill,1969.
[7] Stowell,E.Z.,CompressiveStrengthofFlanges,NACATech.Note1323,1947.
[8] Mayers,J.,andBudiansky,B.,AnalysisofBehaviourofSimplySupportedFlatPlatesCompressedBeyond
theBucklingLoadinthePlasticRange,NACATech.Note3368,1955.
[9] Gerard, G., and Becker, H.,Handbook of Structural Stability, Pt. IV, Failure of Plates and Composite
Elements,NACATech.Note3784,1957.
[10] Gerard, G.,Handbook of Structural Stability, Pt. V, Compressive Strength of Flat Stiffened Panels,NACA
Tech.Note3785,1957.
[11] Gerard, G., and Becker, H.,Handbook of Structural Stability, Pt. VII, Strength of Thin Wing Construction,
NACATech.NoteD-162,1959.
[12] Gerard,G.,Thecripplingstrengthofcompressionelements,J.Aeron.Sci.,25(1),37–52,1958.
[13] Kuhn,P.,StressesinAircraftandShellStructures,McGraw-Hill,1956.
[14] Megson,T.H.G.,StructuralandStressAnalysis,2ndedition,Elsevier,2005.
[15] Evans,H.R.,Porter,D.M.,andRockey,K.C.Thecollapsebehaviourofplategirderssubjectedtoshearand
bending,Proc.Int.Assn.BridgeandStruct.Eng.P-18/78,1–20.

Problems..............................................................................................

P.9.1 Athinsquareplateofsideaandthicknesstissimplysupportedalongeachedgeandhasaslightinitial

curvature,givingitaninitialdeflectedshape.

w 0 =δsin

πx

a

sin

πy

a

If the plate is subjected to a uniform compressive stressσin thex-direction (see Fig. P.9.1), find an expression

fortheelasticdeflectionwnormaltotheplate.Showalsothatthedeflectionatthemidpointoftheplatecanbe

presentedintheformofaSouthwellplotandillustrateyouranswerwithasuitablesketch.

Ans. w=[σtδ/( 4 π^2 D/a^2 −σt)]sinπaxsinπay

P.9.2 A uniform flat plate of thicknessthas a widthbin theydirection and lengthlin thexdirection (see

Fig. P.9.2). The edges parallel to thexaxis are clamped, and those parallel to theyaxis are simply supported.

Auniformcompressivestressσisappliedinthexdirectionalongtheedgesparalleltotheyaxis.Usinganenergy