Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

432 CHAPTER 15 Bending of Open and Closed, Thin-Walled Beams Fig.15.7 Direct stress distribution in beam of Example 15.3. or tan ...

15.2 Unsymmetrical Bending 433 Fig.15.8 Anticlastic bending of a beam section. 15.2 UnsymmetricalBending........................ ...

434 CHAPTER 15 Bending of Open and Closed, Thin-Walled Beams Fig.15.9 Notation and sign convention for forces, moments, and disp ...

15.2 Unsymmetrical Bending 435 15.2.2 Resolution of Bending Moments A bending momentMapplied in any longitudinal plane parallel ...

436 CHAPTER 15 Bending of Open and Closed, Thin-Walled Beams Fig.15.12 Determination of neutral axis position and direct stress ...

15.2 Unsymmetrical Bending 437 The moment resultants of the internal direct stress distribution have the same sense as the appli ...

438 CHAPTER 15 Bending of Open and Closed, Thin-Walled Beams Further,ifeitherMyorMxiszero,then σz= Mx Ixx y or σz= My Iyy x (15. ...

15.2 Unsymmetrical Bending 439 Fig.15.13 Cross section of beam in Example 15.4. Thepositionofthecentroidofthesectionmaybefoundby ...

440 CHAPTER 15 Bending of Open and Closed, Thin-Walled Beams SinceMx=1500NmandMy=0,wehave,fromEq.(15.19), σz=1.5y−0.39x (i) inwh ...

15.3 Deflections due to Bending 441 or,whensecond-ordertermsareneglected Sy= ∂Mx ∂z Wemaycombinetheseresultsintoasingleexpressio ...

442 CHAPTER 15 Bending of Open and Closed, Thin-Walled Beams Thecomponentsuandvofζareinthenegativedirectionsofthexandyaxes,respe ...

15.3 Deflections due to Bending 443 Fig.15.16 Deflection of a cantilever beam carrying a concentrated load at its free end (Exam ...

444 CHAPTER 15 Bending of Open and Closed, Thin-Walled Beams whereC 1 isaconstantofintegrationwhichisobtainedfromtheboundarycond ...

15.3 Deflections due to Bending 445 Thebendingmoment,M,atanysectionZisgivenby M= w 2 (L−z)^2 (i) SubstitutingforMinthesecondofEq ...

446 CHAPTER 15 Bending of Open and Closed, Thin-Walled Beams Fig.15.18 Deflection of a simply supported beam carrying a uniforml ...

15.3 Deflections due to Bending 447 Sincev=0whenz=0(orsincev=0whenz=L),itfollowsthatC 2 =0andthedeflectedshapeofthe beamhastheeq ...

448 CHAPTER 15 Bending of Open and Closed, Thin-Walled Beams Fig.15.19 Deflection of a simply supported beam carrying a concentr ...

15.3 Deflections due to Bending 449 Fig.15.20 Macauley’s method for the deflection of a simply supported beam. deflectionproblem ...

450 CHAPTER 15 Bending of Open and Closed, Thin-Walled Beams and EIv= 1 8 Wz^3 − W 6 [z−a]^3 − W 6 [z− 2 a]^3 + W 3 [z− 3 a]^3 + ...

15.3 Deflections due to Bending 451 SolutionofEq.(vii)gives z=1.35a sothatthemaximumdownwarddeflectionis,fromEq.(vi), EIv= 1 8 W ...