Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

308 CHAPTER 9 Thin Plates

compressiveloadPinastiffenerisgivenby

P=σytb

whichbecomes,fromEq.(9.22),

P=

Wb

d

tanα (9.23)

IftheloadPissufficientlyhigh,thestiffenerswillbuckle.Testsindicatethattheybuckleascolumns
ofequivalentlength

or

le=d/

√

4 − 2 b/d forb<1.5d

le=d forb>1.5d

}

(9.24)

Inadditiontocausingcompressioninthestiffeners,thedirectstressσyproducesbendingofthebeam
flangesbetweenthestiffeners,asshowninFig.9.11.Eachflangeactsasacontinuousbeamcarryinga
uniformlydistributedloadofintensityσyt.Themaximumbendingmomentinacontinuousbeamwith
endsfixedagainstrotationoccursatasupportandiswL^2 /12,inwhichwistheloadintensityandLis
thebeamspan.Inthiscase,therefore,themaximumbendingmomentMmaxoccursatastiffenerandis
givenby

Mmax=

σytb^2

12

or,substitutingforσyfromEq.(9.22),

Mmax=

Wb^2 tanα

12 d

(9.25)

MidwaybetweenthestiffenersthisbendingmomentreducestoWb^2 tanα/ 24 d.
Theangleαadjustsitselfsuchthatthetotalstrainenergyofthebeamisaminimum.Ifitisassumed
thattheflangesandstiffenersarerigid,thenthestrainenergycomprisestheshearstrainenergyofthe
webonlyandα= 45 ◦.Inpractice,bothflangesandstiffenersdeformsothatαissomewhatlessthan

Fig.9.11

Bending of flanges due to web stress.