Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

Problems 525

P.17.9 DeterminetherateoftwistperunittorqueofthebeamsectionshowninFig.P.16.11iftheshearmodulus
Gis25000N/mm^2 .(NotethattheshearcenterpositionhasbeencalculatedinP.16.11.)

Ans. 6.42× 10 −^8 rad/mm.

P.17.10 Figure P.17.10 shows the cross section of a thin-walled beam in the form of a channel with lipped
flanges.Thelipsareofconstantthickness1.27mmwhiletheflangesincreaselinearlyinthicknessfrom1.27mm,
wheretheymeetthelipsto2.54mmattheirjunctionswiththeweb.Thewebhasaconstantthicknessof2.54mm.
TheshearmodulusGis26700N/mm^2 throughout.

Fig. P.17.10

The beam has an enforced axis of twist RR′and is supported in such a way that warping occurs freely but
is zero at the midpoint of the web. If the beam carries a torque of 100Nm, calculate the maximum shear stress
accordingtotheSt.Venanttheoryoftorsionforthin-walledsections.Ignoreanyeffectsofstressconcentrationat
thecorners.Findalsothedistributionofwarpingalongthemiddlelineofthesection,illustratingyourresultsby
meansofasketch.

Ans. τmax=±297.4N/mm^2 ,w 1 =−5.48mm=−w 6.

w 2 =5.48mm=−w 5 ,w 3 =17.98mm=−w 4.