Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

9.7Tension Field Beams 311

InEqs.(9.28)and(9.29),itisimplicitlyassumedthatastiffenerisfullyeffectiveinresistingaxial
load. This will be the case if the centroid of area of the stiffener lies in the plane of the beam web.
Suchasituationariseswhenthestiffenerconsistsoftwomemberssymmetricallyarrangedonopposite
sidesoftheweb.Inthecasewherethewebisstiffenedbyasinglememberattachedtooneside,the
compressiveloadPisoffsetfromthestiffeneraxis,therebyproducingbendinginadditiontoaxialload.
Forastiffenerhavingitscentroidadistanceefromthecenteroftheweb,thecombinedbendingand
axialcompressivestress,σc,atadistanceefromthestiffenercentroidis

σc=

P

AS

+

Pe^2

ASr^2

inwhichristheradiusofgyrationofthestiffenercrosssectionaboutitsneutralaxis.(Note:second
momentofareaI=Ar^2 .)Then,

σc=

P

AS

[

1 +

(e

r

) 2 ]

or

σc=

P

ASe

where

ASe=

AS

1 +(e/r)^2

(9.30)

andistermedtheeffectivestiffenerarea[Ref.1].

9.7.2 Incomplete Diagonal Tension

Inmodernaircraftstructures,beamshavingextremelythinwebsarerare.Theyretain,afterbuckling,
someoftheirabilitytosupportloadssothatevennearfailuretheyareinastateofstresssomewhere
between that of pure diagonal tension and the prebuckling stress. Such a beam is described as an
incompletediagonaltensionfieldbeamandmaybeanalyzedbysemiempiricaltheoryasfollows.
Itisassumedthatthenominalwebshearτ(=S/td)maybedividedintoa“trueshear”component
τSandadiagonaltensioncomponentτDTbywriting

τDT=kτ, τS=( 1 −k)τ (9.31)

wherek,thediagonal tension factor, is a measure of the degree to which the diagonal tension is
developed. A completely unbuckled web hask=0, whereask=1 for a web in complete diagonal
tension. The value ofkcorresponding to a web having a critical shear stressτCRisgivenbythe
empiricalexpression

k=tanh

(

0.5log

τ

τCR

)

(9.32)