Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

524 CHAPTER 17 Torsion of Beams

Calculatetherateoftwistinrad/mm.Giveasketchillustratingthedistributionofwarpingdisplacementinthe
crosssectionandquotevaluesatpoints1and4.

Ans.dθ/dz=29.3× 10 −^6 rad/mm, w 3 =−w 4 =−0.19mm,

w 2 =−w 1 =−0.056mm.

Fig. P.17.6

P.17.7 AuniformbeamwiththedoublysymmetricalcrosssectionshowninFig.P.17.7,hashorizontalandvertical
wallsmadeofdifferentmaterialswhichhaveshearmoduliGaandGb,respectively.Ifforanymaterialtheratio
massdensity/shearmodulusisconstant,findtheratioofthewallthicknessestaandtbsothatforagiventorsional
stiffnessandgivendimensionsa,bthebeamhasminimumweightperunitspan.AssumetheBredt–Bathotheory
oftorsionisvalid.
Ifthisthicknessrequirementissatisfied,findthea/bratio(previouslyregardedasfixed),whichgivesminimum
weightforgiventorsionalstiffness.

Ans. tb/ta=Ga/Gb,b/a=1.

Fig. P.17.7 Fig. P.17.8

P.17.8 Thecold-formedsectionshowninFig.P.17.8issubjectedtoatorqueof50Nm.Calculatethemaximum
shearstressinthesectionanditsrateoftwist.G=25000N/mm^2.

Ans. τmax=220.6N/mm^2 ,dθ/dz=0.0044rad/mm.