Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

9.5 Instability of Stiffened Panels 301

actingasacolumnisle,thentheEulercriticalstressis

σCR,E=

π^2 E

(le/r)^2

asinEq.(8.8).Inadditiontothecolumnbucklingmode,individualplateelementscomprisingthepanel
crosssectionmaybuckleaslongplates.ThebucklingstressisthengivenbyEq.(9.7),thatis,

σCR=

ηkπ^2 E

12 ( 1 −ν^2 )

(

t

b

) 2

where the values ofk,t,andbdepend on the particular portion of the panel being investigated. For
example,theportionofskinbetweenstiffenersmaybuckleasaplatesimplysupportedonallfoursides.
Thus,fora/b>3,k=4fromFig.9.3(a),and,assumingthatbucklingtakesplaceintheelasticrange,

σCR=

4 π^2 E

12 ( 1 −ν^2 )

(

tsk

bsk

) 2

A further possibility is that the stiffeners may buckle as long plates simply supported on three sides
withoneedgefree.Thus,

σCR=

0.43π^2 E

12 ( 1 −ν^2 )

(

tst

bst

) 2

Clearly,theminimumvalueoftheprecedingcriticalstressesisthecriticalstressforthepaneltakenas
awhole.
Thecompressiveloadisappliedtothepaneloveritscompletecrosssection.Torelatethisloadto
anappliedcompressivestressσAactingoneachelementofthecrosssection,wedividetheloadper
unitwidth,sayNx,byanequivalentskinthickness ̄t,hence

σA=

Nx

t

where

t=

Ast

bsk

+tsk

andAstisthestiffenerarea.
The preceding remarks are concerned with the primary instability of stiffened panels. Values of
localbucklingstresshavebeendeterminedbyBoughan,Baab,andGallaherforidealizedweb,Z-,and
T-stiffenedpanels.TheresultsarereproducedbyRivello[Ref.6]togetherwiththeassumedgeometries.
Furthertypesofinstabilityfoundinstiffenedpanelsoccurwherethestiffenersarerivetedorspot
weldedtotheskin.Suchstructuresmaybesusceptibletointerrivetbuckling,inwhichtheskinbuckles
between rivets with a wavelength equal to the rivet pitch, orwrinkling, where the stiffener forms an
elasticlinesupportfortheskin.Inthelattermode,thewavelengthofthebuckleisgreaterthantherivet
pitch,andseparationofskinandstiffenerdoesnotoccur.Methodsofestimatingtheappropriatecritical
stressesaregiveninthestudyofRivelloandtheHandbookofAeronautics[Ref.3].