Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

164 CHAPTER 5 Energy Methods

P.5.14 TheplanestructureshowninFig.P.5.14consistsofauniformcontinuousbeamABCpinnedtoafixture
atAandsupportedbyaframeworkofpin-jointedmembers.AllmembersotherthanABChavethesamecross-
sectionalareaA.ForABC,theareais4AandthesecondmomentofareaforbendingisAa^2 /16.Thematerialis
thesamethroughout.Find(intermsofw,A,a,andYoung’smodulusE)theverticaldisplacementofpointDunder
theverticalloadingshown.IgnoreshearingstrainsinthebeamABC.

Ans. 30232 wa^2 /3AE.

Fig. P.5.14

P.5.15 ThefuselageframeshowninFig.P.5.15consistsoftwoparts,ACBandADB,withfrictionlesspinjoints
atAandB.Thebendingstiffnessisconstantineachpart,withvalueEIforACBandxEIforADB.Findxsothat
themaximumbendingmomentinADBwillbeone-halfofthatinACB.Assumethatthedeflectionsaredueto
bendingstrainsonly.

Ans. 0.092.

Fig. P.5.15

P.5.16 A transverse frame in a circular section fuel tank is of radiusrand constant bending stiffnessEI.The
loadingontheframeconsistsofthehydrostaticpressureduetothefuelandtheverticalsupportreactionP,which
isequaltotheweightoffuelcarriedbytheframe,asshowninFig.P.5.16.