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Structural Analysis of Sweptback Wings: Bending Moments and Stress States in Boeing 757

This lecture focuses on the structural layout and analysis of sweptback wings, specifically using the Boeing 757 as a case study. It explores various components, including the fuselage beams, rib structures, and wingbox elements. The concepts of structural idealization, assumptions concerning load distribution, and the analysis of bending moments and shear flows are discussed. Attention is given to the complexity of the wingbox stress state, evaluated through the lens of Papkovich's theorem. The aim is to ascertain the distribution of forces and moments within the wing's root triangle beams.

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Structural Analysis of Sweptback Wings: Bending Moments and Stress States in Boeing 757

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  1. Lecture #10 Stress state of sweptback wing

  2. STRUCTURAL LAYOUT OF SWEPTBACK WINGS Boeing 757 2

  3. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 3

  4. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 4

  5. STRUCTURAL LAYOUT OF SWEPTBACK WINGS 5

  6. STRUCTURAL IDEALIZATION 6

  7. STRUCTURAL IDEALIZATION 7

  8. STRUCTURAL LAYOUT OF SWEPTBACK WING 1 – front fuse-lage beam; 2 – rear fuse-lage beam; 3 – fuselage rib; 4 – front spar continuation; 5 – root rib; 6 – front spar; 7 – ribs; 8 – rear spar; 9 – wingbox; 10 – end rib. 8

  9. STRUCTURAL IDEALIZATION 9

  10. DESIGN MODEL OF SWEPTBACK WING 10

  11. ASSUMPTIONS AND SIMPLIFICATIONS a) deformations are linear; b) displacements are small; c) wingbox has absolutely rigid cross section; d) the axial loads are carried only by spar caps; e) spar webs and skins carry only shear loads; f) the elements of the root triangle ABC and the fuselage structure (RR, FR, FSC, FFB, RFB) are planar beams, they are finitely rigid in their planes and absolutely flexible outside them; g) upper and lower skins of the root triangle do not carry any loads; h) the fuselage structure composed of beams FR, FFB, RFB is a spatial statically determinate system. 11

  12. STRUCTURAL IDEALIZATION 12

  13. AIM OF THE PROJECT The aim is to find the distribution of bending moments in root triangle beams. Other data (normal forces, shear flows) could not be used since it is obtained using very robust idealization. Actually, the wingbox is studied just to take its rigidity into account. 13

  14. ANALYSIS OF THE MODEL Kinematical analysis: 14

  15. ANALYSIS OF THE MODEL 15

  16. ANALYSIS OF THE MODEL Matrix for statical analysis: 16

  17. ANALYSIS OF THE MODEL Conclusion: The system is twice statically indeterminate. The force method will be used as one being optimal for systems with small degree of statical indeterminacy. 17

  18. FLOWCHART OF SOLUTION USING FORCE METHOD 18

  19. BASIC SYSTEM 19

  20. EQUIVALENT SYSTEM 20

  21. BASIC SYSTEM IN LOADED STATE 21

  22. FORCES IN LOADED STATE 22

  23. STRESS STATE OF WINGBOX – NORMAL FORCES The stress state of wingbox is a problem inside a problem, twice statically indeterminate. In contrast to general problem, it is solved using Papkovich’ theorem. 23

  24. STRESS STATE OF WINGBOX – SHEAR FLOWS 24

  25. LOADS ACTING ON ROOT TRIANGLE BEAMS 25

  26. STRESS STATE OF ROOT TRIANGLE BEAMS 26

  27. BASIC SYSTEM IN 1ST UNIT STATE 27

  28. FORCES IN 1ST UNIT STATE 28

  29. FORCES IN 1ST UNIT STATE 29

  30. LOADING OF ROOT TRIANGLE IN 1ST UNIT STATE 30

  31. MOMENTS IN ROOT TRIANGLE IN 1ST UNIT STATE 31

  32. TABLE FOR MOMENTS IN DIFFERENT STATES 32

  33. SYSTEM OF CANONICAL EQUATIONS We have twice statically indeterminate problem: 33

  34. TABLE FOR MOMENTS IN DIFFERENT STATES Each of coefficients has three terms; last term is from bending moments: 34

  35. EXAMPLE FOR A TOTAL STRESS STATE

  36. NEXT LECTURE EXAM #2 36 All materials of our course are available at k102.khai.edu

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