Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

492 CHAPTER 16 Shear of Beams whichgives ∫s 0 qs Gt ds=(ws−w 0 )+ 2 AOs dθ dz + du dz (xs−x 0 )+ dv dz (ys−y 0 ), (16.21) whereA ...

16.3 Shear of Closed Section Beams 493 Also,sinceapuretorqueisapplied,theresultantofanyinternaldirectstresssystemmustbezero;in o ...

494 CHAPTER 16 Shear of Beams centerofasectionproduceszerotwist.Itfollowsthatdθ/dzinEq.(16.22)iszerosothat 0 = ∮ qs Gt ds or 0 = ...

16.3 Shear of Closed Section Beams 495 ofsymmetry,thenIxy=0,andsinceSx=0,Eq.(16.15)simplifiesto qs=− Sy Ixx ∫s 0 tyds+qs,0 (i) i ...

496 CHAPTER 16 Shear of Beams We may replace sinθ by sin(θ 1 −θ 2 )=sinθ 1 cosθ 2 −cosθ 1 sinθ 2 , where sinθ 1 = 15 /17,cosθ 2 ...

Problems 497 Fig. P.16.2 Fig. P.16.3 P.16.3 DeterminethepositionoftheshearcenterSforthethin-walled,opencrosssectionshowninFig.P. ...

498 CHAPTER 16 Shear of Beams Calculate and sketch the distribution of shear flow due to a vertical shear forceSyacting through ...

Problems 499 P.16.9 Determinethepositionoftheshearcenterofthecold-formed,thin-walledsectionshowninFig.P.16.9. Thethicknessofthes ...

500 CHAPTER 16 Shear of Beams Fig. P.16.11 Fig. P.16.12 P.16.12A thin-walled closed section beam of constant wall thicknesst has ...

Problems 501 Fig. P.16.13 Fig. P.16.14 Plottheshearflowdistributionaroundthesection,withvaluesintermsofSanda. Ans. q 1 =−0.52S/a ...

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CHAPTER 17 Torsion of Beams........................................................................ In Chapter 3, we developed t ...

504 CHAPTER 17 Torsion of Beams Fig.17.2 Determination of the shear flow distribution in a closed section beam subjected to tors ...

17.1 Torsion of Closed Section Beams 505 Fig.17.3 Sign convention for swept areas. isvalidforthepuretorsioncase,whereqisconstant ...

506 CHAPTER 17 Torsion of Beams Itfollowsthatθ=Az+B,u=Cz+D,v=Ez+F,whereA,B,C,D,E,andFareunknownconstants. Thus,θ,u,andvarealllin ...

17.1 Torsion of Closed Section Beams 507 The minimum thickness of the beam corresponding to the maximum allowable shear stress o ...

508 CHAPTER 17 Torsion of Beams Fig.17.4 Torsion of a rectangular section beam for Example 17.2. where δ= ∮ ds t and δOs= ∫s 0 d ...

17.1 Torsion of Closed Section Beams 509 givingthedistributionshowninFig.17.5.Notethatthewarpingdistributionwilltaketheformshown ...

510 CHAPTER 17 Torsion of Beams SubstitutinginEq.(i)andsettingw 0 = 0 w′ 12 = Tδ 2 abG ( s 1 δta − s 1 4 a ) (iv) sothatw′ 12 va ...

17.1 Torsion of Closed Section Beams 511 ComparingFigs.17.5and17.7,itcanbeseenthattheformofthewarpingdistributionisthesame butth ...