Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

16.3 Shear of Closed Section Beams 493

Also,sinceapuretorqueisapplied,theresultantofanyinternaldirectstresssystemmustbezero;in
otherwords,itisself-equilibrating.Thus,

Resultantaxialload=

∮

σtds

whereσisthedirectstressatanypointinthecrosssection.Then,fromtheaboveassumption

0 =

∮

wtds

or

0 =

∮

(ws−w 0 )tds

sothat

w 0 =

∮

wstds

∮

tds

(16.26)

16.3.2 Shear Center

TheshearcenterofaclosedsectionbeamislocatedinasimilarmannertothatdescribedinSection16.2.1
foropensectionbeams.Therefore,todeterminethecoordinateξS(referredtoanyconvenientpointin
thecrosssection)oftheshearcenterSoftheclosedsectionbeamshowninFig.16.12,weapplyan
arbitraryshearloadSythroughS,calculatethedistributionofshearflowqsduetoSy,andthenequate
internalandexternalmoments.However,adifficultyarisesinobtainingqs,0,since,atthisstage,itis
impossibletoequateinternalandexternalmomentstoproduceanequationsimilartoEq.(16.17),as
thepositionofSy,isunknown.Wethereforeusetheconditionthatashearloadactingthroughtheshear

Fig.16.12

Shear center of a closed section beam.