Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

162 CHAPTER 5 Energy Methods

P.5.10 TheplaneframeABCDofFig.P.5.10consistsofthreestraightmemberswithrigidjointsatBandC,freely
hingedtorigidsupportsatAandD.TheflexuralrigidityofABandCDistwicethatofBC.Adistributedloadis
appliedtoAB,varyinglinearlyinintensityfromzeroatAtowperunitlengthatB.
Determinethedistributionofbendingmomentintheframe,illustratingyourresultswithasketchshowingthe
principalvalues.

Ans. MB= 7 wl^2 /45,MC= 8 wl^2 /45, cubicdistributiononAB,linearonBCandCD.

Fig. P.5.10

P.5.11 AbracketBACiscomposedofacirculartubeAB,whosesecondmomentofareais1.5I,andabeamAC,
whose second moment of area isIand which has negligible resistance to torsion. The two members are rigidly
connectedtogetheratAandbuiltintoarigidabutmentatBandC,asshowninFig.P.5.11.AloadPisappliedat
Ainadirectionnormaltotheplaneofthefigure.
DeterminethefractionoftheloadwhichissupportedatC.Bothmembersareofthesamematerialforwhich
G=0.38E.

Ans. 0.72P.

Fig. P.5.11