Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

432 CHAPTER 15 Bending of Open and Closed, Thin-Walled Beams

Fig.15.7

Direct stress distribution in beam of Example 15.3.

or

tanα=

MyIxx

MxIyy

sinceyispositiveandxispositiveforapositivevalueofα.Weshalldefineinaslightlydifferentway
inSection15.2.4forbeamsofunsymmetricalsection.

15.1.3 Anticlastic Bending

IntherectangularbeamsectionshowninFig.15.8(a),thedirectstressdistributionduetoanegative
bending moment applied in a vertical plane varies from compression in the upper half of the beam
totensioninthelowerhalf(Fig.15.8(b)).However,duetothePoissoneffect,thecompressivestress
producesalateralelongationoftheupperfibersofthebeamsection,whilethetensilestressproducesa
lateralcontractionofthelower.Thesectiondoesnotthereforeremainrectangularbutdistortsasshown
inFig.15.8(c);theeffectisknownasanticlasticbending.
Anticlasticbendingisofinterestintheanalysisofthin-walledboxbeamsinwhichthecrosssections
aremaintainedbystiffeningribs.Thepreventionofanticlasticdistortioninduceslocalvariationsinstress
distributionsinthewebsandcoversoftheboxbeamandalsointhestiffeningribs.