Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

Problems 287

Problems..............................................................................................

P.8.1 ThesysteminFig.P.8.1consistsoftwobars,ABandBC,eachofbendingstiffnessEIelasticallyhinged
togetheratBbyaspringofstiffnessK(i.e.,bendingmomentappliedbyspring=K×changeinslopeacrossB).
RegardingAandCassimplepin-joints,obtainanequationforthefirstbucklingloadofthesystem.Whatare
thelowestbucklingloadswhen(a)K→∞,(b)EI→∞.NotethatBisfreetomovevertically.

Ans. μK/tanμl.

Fig. P.8.1

P.8.2 Apin-endedcolumnoflengthlandconstantflexuralstiffnessEIisreinforcedtogiveaflexuralstiffness
4 EIoveritscentralhalf(seeFig.P.8.2).

Fig. P.8.2

Considering symmetric modes of buckling only, obtain the equation whose roots yield the flexural buckling
loadsandsolveforthelowestbucklingload.

Ans. tanμl/ 8 = 1 /

√

2,P=24.2EI/l^2

P.8.3 AuniformcolumnoflengthlandbendingstiffnessEIisbuilt-inatoneendandfreeattheotherandhas
beendesignedsothatitslowestflexuralbucklingloadisP(seeFig.P.8.3).

Fig. P.8.3

Subsequently,ithastocarryanincreasedload,andforthis,itisprovidedwithalateralspringatthefreeend.
Determinethenecessaryspringstiffnessksothatthebucklingloadbecomes4P.

Ans. k= 4 Pμ/(μl−tanμl).