Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

Problems 165

Fig. P.5.16

Takingintoaccountonlystrainsduetobending,calculatethedistributionofbendingmomentaroundtheframe
intermsoftheforceP,theframeradiusr,andtheangleθ.

Ans. M=Pr(0.160−0.080cosθ−0.159θsinθ)

P.5.17 TheframeshowninFig.P.5.17consistsofasemicirculararc,centerB,radiusa,ofconstantflexuralrigidity
EIjointedrigidlytoabeamofconstantflexuralrigidity2EI.Theframeissubjectedtoanoutwardloadingasshown
arisingfromaninternalpressurep 0.
FindthebendingmomentatpointsA,B,andCandlocateanypointsofcontraflexure.
Aisthemidpointofthearc.Neglectdeformationsoftheframeduetoshearandnormalforces.
Ans. MA=−0.057p 0 a^2 ,MB=−0.292p 0 a^2 ,MC=0.208p 0 a^2.
Pointsofcontraflexure:inAC,at51.7◦fromhorizontal;inBC,0.764afromB.

Fig. P.5.17

P.5.18 TherectangularframeshowninFig.P.5.18consistsoftwohorizontalmembers123and456rigidlyjoined
tothreeverticalmembers16,25,and34.AllfivemembershavethesamebendingstiffnessEI.

Fig. P.5.18