Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

17.1 Torsion of Closed Section Beams 509

givingthedistributionshowninFig.17.5.Notethatthewarpingdistributionwilltaketheformshown
inFig.17.5aslongasTispositiveandb/tb>a/ta.Ifeitheroftheseconditionsisreversed,w 1 andw 3
willbecomenegativeandw 2 andw 4 positive.Inthecasewhenb/tb=a/ta,thewarpingiszeroatall
pointsinthecrosssection.
Supposenowthattheoriginforsischosenarbitrarilyat,say,point1.Then,fromFig.17.6,δOsin
thewall12=s 1 /taandAOs=^12 s 1 b/ 2 =s 1 b/4,andbotharepositive.

Fig.17.5

Warping distribution in the rectangular section beam of Example 17.2.

Fig.17.6

Arbitrary origin fors.