Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

17.2 Torsion of Open Section Beams 515

Fig.17.10

(a) Shear lines in a thin-walled open section beam subjected to torsion; (b) approximation of elemental shear
lines to those in a thin rectangular strip.

Theshearstressdistributionandthemaximumshearstressaresometimesmoreconvenientlyexpressed
intermsoftheappliedtorque.Therefore,substitutingfordθ/dzinEqs.(17.9)and(17.10)gives

τzs=

2 n

J

T, τzs,max=±

tT

J

(17.13)

We assume in open beam torsion analysis that the cross section is maintained by the system of
closelyspaceddiaphragmsdescribedinSection16.1andthatthebeamisofuniformsection.Clearly,
inthisproblem,theshearstressesvaryacrossthethicknessofthebeamwall,whereasotherstresses,
suchasaxialconstraintstressesareassumedconstantacrossthethickness.

17.2.1 Warping of the Cross Section

WesawinSection3.4thatathinrectangularstripsufferswarpingacrossitsthicknesswhensubjectedto
torsion.Inthesameway,athin-walledopensectionbeamwillwarpacrossitsthickness.Thiswarping,
wt,maybededucedbycomparingFig.17.10(b)withFig.3.10andusingEq.(3.32),thus,

wt=ns

dθ

dz

(17.14)