Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

9.6 Failure Stress in Plates and Stiffened Panels 303

Gerard[Refs.9–12]extendedtheprecedingmethodtothepredictionoflocalfailurestressesforthe
plateelementsofthin-walledcolumns.Equation(9.11)becomes

σ ̄f

σcy

=βg

[(

gt^2

A

)(

E

σcy

) 1

2

]m

(9.12)

whereAisthecross-sectionalareaofthecolumn,βgandmareempiricalconstants,andgisthenumber
ofcutsrequiredtoreducethecrosssectiontoaseriesofflangedsectionsplusthenumberofflanges
thatwouldexistafterthecutsaremade.ExamplesofthedeterminationofgareshowninFig.9.6.
ThelocalfailurestressinlongitudinallystiffenedpanelswasdeterminedbyGerard[Refs.10,12]
usingaslightlymodifiedformofEqs.(9.11)and(9.12).Thus,forasectionofthepanelconsistingof
astiffenerandawidthofskinequaltothestiffenerspacing

σ ̄f

σcy

=βg

[

gtsktst

A

(

E

σ ̄cy

)^12 ]m

(9.13)

wheretskandtstaretheskinandstiffenerthicknesses,respectively.Aweightedyieldstressσ ̄cyisused
forapanelinwhichthematerialoftheskinandstiffenerhavedifferentyieldstresses;thus,

σ ̄cy=

σcy+σcy,sk[(t/tst)−1]

t/tst

where ̄tistheaverageorequivalentskinthicknesspreviouslydefined.Theparametergisobtainedin
asimilarmannertothatforathin-walledcolumn,exceptthatthenumberofcutsintheskinandthe

Fig.9.6

Determination of empirical constantg.