Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

522 CHAPTER 17 Torsion of Beams

Thebeamissubjectedtoauniformlydistributedtorqueof20Nm/mmalongitslength.Calculatethemaximum
shearstressaccordingtotheBred–Bathotheoryoftorsion.Calculatealso,andsketch,thedistributionoftwistalong
thelengthofthecantilever,assumingthataxialconstrainteffectsarenegligible.

Ans. τmax=83.3N/mm^2 ,θ=8.14× 10 −^9

(

2500 z−

z^2

2

)

rad.

P.17.2 Asinglecell,thin-walledbeamwiththedoubletrapezoidalcrosssectionshowninFig.P.17.2,issubjected
toaconstanttorqueT=90500NmandisconstrainedtotwistaboutanaxisthroughthepointR.Assumingthatthe
shearstressesaredistributedaccordingtotheBredt–Bathotheoryoftorsion,calculatethedistributionofwarping
aroundthecrosssection.
Illustrateyouranswerclearlybymeansofasketchandinserttheprincipalvaluesofthewarpingdisplacements.
TheshearmodulusG=27500N/mm^2 andisconstantthroughout.
Ans. w 1 =−w 6 =−0.53mm,w 2 =−w 5 =0.05mm,w 3 =−w 4 =0.38mm.
Lineardistribution.

Fig. P.17.2

P.17.3 Auniformthin-walledbeamiscircularincrosssectionandhasaconstantthicknessof2.5mm.Thebeamis
2000mmlong,carryingendtorquesof450Nmand,inthesamesense,adistributedtorqueloadingof1.0Nm/mm.
TheloadsarereactedbyequalcouplesRatsections500mmdistantfromeachend(Fig.P.17.3).

Fig. P.17.3