Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

472 CHAPTER 15 Bending of Open and Closed, Thin-walled Beams Fig. P.15.1 P.15.2 Athin-walled,cantileverbeamofunsymmetricalcrosss ...

Problems 473 Fig. P.15.3 ThewallthicknesstcanbetakenasverysmallincomparisonwithdincalculatingthesectionalpropertiesIxx, Ixy,ands ...

474 CHAPTER 15 Bending of Open and Closed, Thin-walled Beams Fig. P.15.5 Fig. P.15.6 P.15.7 Athin-walledcantileverhasaconstantcr ...

Problems 475 Ans. α=51.9◦,σz,max=101N/mm^2. Fig. P.15.8 P.15.9 A uniform beam is simply supported over a span of 6m. It carries ...

476 CHAPTER 15 Bending of Open and Closed, Thin-walled Beams Ans. v=− 1 EI ( 125 6 z^3 −50[z−1]^2 + 50 12 [z−2]^4 − 50 12 [z−4]^ ...

Problems 477 Ans. (a)3wlIxy/8Ixx; (b)wl^4 /8EIxx. Fig. P.15.14 P.15.15Auniformbeamofarbitrary,unsymmetricalcrosssectionandlength ...

478 CHAPTER 15 Bending of Open and Closed, Thin-walled Beams P.15.17ThebeamsectionshowninFig.P.15.17issubjectedtoatemperaturecha ...

CHAPTER 16 Shear of Beams.......................................................................... InChapter15,wedevelopedtheth ...

480 CHAPTER 16 Shear of Beams Fig.16.1 (a) General stress system on element of a closed or open section beam; (b) direct stress ...

16.1 General Stress, Strain, and Displacement Relationships 481 Fig.16.2 Axial, tangential, and normal components of displacemen ...

482 CHAPTER 16 Shear of Beams Inadditiontotheassumptionsspecifiedintheearlierpartofthissection,wefurtherassumethatduring any dis ...

16.2 Shear of Open Section Beams 483 and ∂vt ∂z =p dθ dz −xRsinψ dθ dz +yRcosψ dθ dz (16.9) AlsofromEq.(16.7) ∂vt ∂z =p dθ dz + ...

484 CHAPTER 16 Shear of Beams UsingtherelationshipsofEqs.(15.23)and(15.24)—thatis,∂My/∂z=Sx,andsoon—thisexpression becomes ∂σz ∂ ...

16.2 Shear of Open Section Beams 485 Fig.16.6 Shear loaded Z-section of Example 16.1. Thesecondmomentsofareaofthesectionhaveprev ...

486 CHAPTER 16 Shear of Beams Fig.16.7 Shear flow distribution in Z-section of Example 16.1. WenoteinEq.(iv)thattheshearflowisno ...

16.2 Shear of Open Section Beams 487 Fig.16.8 Shear center position for type of open section beam shown. Fig.16.9 Determination ...

488 CHAPTER 16 Shear of Beams SubstitutingforIxxinEq.(i),wehave qs= − 12 Sy h^3 ( 1 + 6 b/h) ∫s 0 yds (ii) Theamountofcomputatio ...

16.3 Shear of Closed Section Beams 489 Fig.16.10 Shear of closed section beams. satwhichthevalueofshearflowisknown.Considerthecl ...

490 CHAPTER 16 Shear of Beams Fig.16.11 (a) Determination ofqs,0; (b) equivalent loading on “open” section beam. We obtainqbby s ...

16.3 Shear of Closed Section Beams 491 If the moment center is chosen to coincide with the lines of action ofSxandSy, then Eq. ( ...