Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

Problems 321

Fig. P.9.1 Fig. P.9.2

method,findanapproximateexpressionforthemagnitudeofthestressσwhichcausestheplatetobuckle,assuming

thatthedeflectedshapeoftheplateisgivenby

w=a 11 sin

mπx

l

sin^2
πy
b
Fortheparticularcasel= 2 b,findthenumberofhalf-wavesmcorrespondingtothelowestcriticalstress,expressing
theresulttothenearestinteger.Determinealsothelowestcriticalstress.
Ans. m=3,σCR=6E/( 1 −v^2 )^2
P.9.3 Apanel,comprisingflatsheetanduniformlyspacedZ-sectionstringers,apartofwhosecrosssectionis
showninFig.P.9.3,istobeinvestigatedforstrengthunderuniformcompressiveloadsinastructureinwhichitis
tobestabilizedbyframesadistancelapart,lbeingappreciablygreaterthanthespacingb.
(a) Statemodesoffailureyouwouldconsiderandhowyouwoulddetermineappropriatelimitingstresses.
(b) Describeasuitabletesttoverifyyourcalculations,givingparticularsofthespecimen,themannerofsupport,
andthemeasurementsyouwouldtake.Thelattershouldenableyoutoverifytheassumptionsmade,aswell
astoobtaintheloadsupported.

Fig. P.9.3

P.9.4 PartofacompressionpanelofinternalconstructionisshowninFig.P.9.4.Theequivalentpin-centerlength

ofthepanelis500mm.ThematerialhasaYoung’smodulusof70000N/mm^2 ,anditselasticitymaybetakenas

fallingcatastrophicallywhenacompressivestressof300N/mm^2 isreached.Takingcoefficientsof3.62forbuckling

ofaplatewithsimplysupportedsidesandof0.385withonesidesimplysupportedandonefree,determine(a)the

loadpermmwidthofpanelwheninitialbucklingmaybeexpectedand(b)theloadpermmforultimatefailure.

Treatthematerialasthinforcalculatingsectionconstants,andassumethatafterinitialbuckling,thestressinthe

plateincreasesparabolicallyfromitscriticalvalueinthecenterofsections.