Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

314 CHAPTER 9 Thin Plates

Also,theshearforceSatanysectionofthebeamis,fromFig.9.14,

S=W−(FT+FB)sinβ

or,substitutingforFTandFBfromEqs.(9.42)and(9.43),

S=W

(

1 −

2 z

d

tanβ

)

(9.45)

9.7.3 Postbuckling Behavior

Sections 9.7.1 and 9.7.2 are concerned with beams in which the thin webs buckle to form tension
fields; the beam flanges are then regarded as being subjected to bending action as in Fig. 9.11. It is
possible,ifthebeamflangesarerelativelylight,forfailureduetoyieldingtooccurinthebeamflanges
after the web has buckled so that plastic hinges form and a failure mechanism of the type shown in
Fig.9.15exists.ThispostbucklingbehaviorwasinvestigatedbyEvansetal.[Ref.14],whodeveloped
a design method for beams subjected to bending and shear. It is their method of analysis which is
presentedhere.
SupposethatthepanelAXBZinFig.9.15hascollapsedduetoashearloadSandabendingmoment
M; plastic hinges have formed at W, X, Y, and Z. In the initial stages of loading, the web remains
perfectlyflatuntilitreachesitscriticalstresses:τcrinshearandσcrbinbending.Thevaluesofthese

Fig.9.15

Collapse mechanism of a panel of a tension field beam.