Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

Problems 167

P.5.21 FigureP.5.21showstwocantilevers,theendofonebeingverticallyabovetheotherandconnectedtoitby
aspringAB.Initiallythesystemisunstrained.AweightWplacedatAcausesaverticaldeflectionatAofδ 1 and
averticaldeflectionatBofδ 2 .Whenthespringisremoved,theweightWatAcausesadeflectionatAofδ 3 .Find
theextensionofthespringwhenitisreplacedandtheweightWistransferredtoB.

Ans. δ 2 (δ 1 −δ 2 )/(δ 3 −δ 1 ).

Fig. P.5.21

P.5.22 Abeam2400mmlongissupportedattwopointsAandBwhichare1440mmapart;pointAis360mm
fromtheleft-handendofthebeamandpointBis600mmfromtheright-handend;thevalueofEIforthebeamis
240 × 108 Nmm^2 .Findtheslopeatthesupportsduetoaloadof2000NappliedatthemidpointofAB.
Usethereciprocaltheoreminconjunctionwiththeaboveresult,tofindthedeflectionatthemidpointofAB
duetoloadsof3000Nappliedateachoftheextremeendsofthebeam.

Ans. 0.011,15.8mm.

P.5.23 FigureP.5.23showsaframepinnedtoitssupportatAandB.Theframecenter-lineisacirculararcandthe
sectionisuniform,ofbendingstiffnessEIanddepthd.Findanexpressionforthemaximumstressproducedbya
uniformtemperaturegradientthroughthedepth,thetemperaturesontheouterandinnersurfacesbeingrespectively
raisedandloweredbyamountT.ThepointsAandBareunalteredinposition.

Ans. 1.30ETα.

Fig. P.5.23

P.5.24 Auniform,semicircularfuselageframeispin-jointedtoarigidportionofthestructureandissubjected
toagiventemperaturedistributionontheinsideasshowninFig.P.5.24.Thetemperaturefallslinearlyacrossthe
sectionoftheframetozeroontheoutersurface.Findthevaluesofthereactionsatthepinjointsandshowthatthe
distributionofthebendingmomentintheframeis

M=

0.59EIαθ 0 cosψ

h