CHAPTER 8 Columns...................................................................................
A large proportion of an aircraft’s structure comprises thin webs stiffened by slender longerons or
stringers. Both are susceptible to failure by buckling at a buckling stress or critical stress, which is
frequently below the limit of proportionality and seldom appreciably above the yield stress of the
material. Clearly, for this type of structure, buckling is the most critical mode of failure so that the
prediction of buckling loads of columns, thin plates, and stiffened panels is extremely important in
aircraftdesign.Inthischapter,weconsiderthebucklingfailureofallthesestructuralelementsandalso
theflexural–torsionalfailureofthin-walledopentubesoflowtorsionalrigidity.
Twotypesofstructuralinstabilityarise:primaryandsecondary.Theformerinvolvesthecomplete
element, there being no change in cross-sectional area, while the wavelength of the buckle is of the
sameorderasthelengthoftheelement.Generally,solidandthick-walledcolumnsexperiencethistype
offailure.Inthelattermode,changesincross-sectionalareaoccurandthewavelengthofthebuckleis
oftheorderofthecross-sectionaldimensionsoftheelement.Thin-walledcolumnsandstiffenedplates
mayfailinthismanner.
8.1 EulerBucklingofColumns.........................................................................
Thefirstsignificantcontributiontothetheoryofthebucklingofcolumnswasmadeasearlyas1744
byEuler.Hisclassicalapproachisstillvalid,andlikelytoremainso,forslendercolumnspossessing
avarietyofendrestraints.OurinitialdiscussionisthereforeapresentationoftheEulertheoryforthe
smallelasticdeflectionofperfectcolumns.However,weinvestigate,first,thenatureofbucklingand
thedifferencebetweentheoryandpractice.
Itiscommonexperiencethatifanincreasingaxialcompressiveloadisappliedtoaslendercolumn,
thereisavalueoftheloadatwhichthecolumnwillsuddenlyboworbuckleinsomeunpredetermined
direction.Thisloadispatentlythebucklingloadofthecolumnorsomethingveryclosetothebuckling
load. Clearly, this displacement implies a degree of asymmetry in the plane of the buckle caused by
geometrical and/or material imperfections of the column and its load. However, in our theoretical
stipulation of a perfect column in which the load is applied precisely along the perfectly straight
centroidal axis, there is perfect symmetry so that, theoretically, there can be no sudden bowing or
buckling.Therefore,werequireaprecisedefinitionofbucklingload,whichmaybeusedinouranalysis
oftheperfectcolumn.
Copyright©2010,T.H.G.Megson. PublishedbyElsevierLtd. Allrightsreserved.
DOI:10.1016/B978-1-85617-932-4.00008-7 253