Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

Problems 523

Calculate the maximum shear stress in the beam and sketch the distribution of twist along its length. Take
G=30000N/mm^2 andneglectaxialconstrainteffects.

Ans. τmax=24.2N/mm^2 ,θ=−0.85× 10 −^8 z^2 rad, 0≤z≤500mm,

θ=1.7× 10 −^8 ( 1450 z−z^2 / 2 )−12.33× 10 −^3 rad, 500≤z≤1000mm.

P.17.4 Thethin-walledboxsectionbeamABCDshowninFig.P.17.4isattachedateachendtosupportswhich
allowrotationoftheendsofthebeaminthelongitudinalverticalplaneofsymmetrybutpreventrotationoftheends
inverticalplanesperpendiculartothelongitudinalaxisofthebeam.Thebeamissubjectedtoauniformtorque
loadingof20Nm/mmovertheportionBCofitsspan.Calculatethemaximumshearstressinthecrosssectionof
thebeamandthedistributionofangleoftwistalongitslength,G=70000N/mm^2.

Ans. 71.4N/mm^2 ,θB=θC=0.36◦,θatmidspan=0.72◦.

Fig. P.17.4

P.17.5 FigureP.17.5showsathin-walledcantileverboxbeamhavingaconstantwidthof50mmandadepthwhich
decreaseslinearlyfrom200mmatthebuilt-inendto150mmatthefreeend.Ifthebeamissubjectedtoatorque
of1kNmatitsfreeend,plottheangleoftwistofthebeamat500mmintervalsalongitslengthanddeterminethe
maximumshearstressinthebeamsection.TakeG=25000N/mm^2.

Ans. τmax=33.3N/mm^2.

Fig. P.17.5

P.17.6 A uniform closed section beam, of the thin-walled section shown in Fig. P.17.6, is subjected to a twist-
ing couple of 4500Nm. The beam is constrained to twist about a longitudinal axis through the center C of the
semicirculararc12.Forthecurvedwall12,thethicknessis2mmandtheshearmodulusis22000N/mm^2 .Forthe
planewalls23,34,and41,thecorrespondingfiguresare1.6mmand27500N/mm^2 .(Note:Gt=constant.)