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Lecture #4 Methods of Structural Analysis Trusses and frames. Statically determinate trusses

Explore methods of structural analysis: trusses, frames, static determinacy, FEA, differential equations solution using FEM, basic solid mechanics equations, and more. Learn about truss structures in aviation, differences between trusses and frames, and analytical tools for solving problems. Discover key principles and supplementary tools to enhance your understanding of structural mechanics. Find additional resources and references for further study. Prepare for a detailed lecture on static determinacy and advanced analysis methods. All course materials provided on the department website.

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Lecture #4 Methods of Structural Analysis Trusses and frames. Statically determinate trusses

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  1. Lecture #4 Methods of Structural Analysis Trusses and frames. Statically determinate trusses

  2. FLOWCHART OF STRUCTURAL ANALYSIS 2

  3. FLOWCHART OF STRUCTURAL ANALYSIS 3

  4. FLOWCHART OF STRUCTURAL ANALYSIS 4

  5. FLOWCHART OF STRUCTURAL ANALYSIS 5

  6. METHODS OF STRUCTURAL ANALYSIS 6

  7. ANALYTICAL METHODS OF STRUCTURAL ANALYSIS • Widely used nowadays: • methods of Mechanics of Materials; • methods for statically indeterminate structures: • method of forces; • method of displacements; • beam theory for thin-walled structures; • method of reduction coefficients. • Rarely used nowadays (mostly due to the progress of numerical methods): • methods based on Calculus of Variations; • methods of Theory of Elasticity. 7

  8. NUMERICAL METHODS OF STRUCTURAL ANALYSIS Most widely used nowadays is Finite Element Method (FEM). The structural analysis using FEM is called finite element analysis (FEA). Generally, FEM is just a method to solve differential equations. The physical background of FEM is the same as in analytical methods. 8

  9. CLASSIFICATION OF STRUCTURAL ANALYSIS PROBLEMS 9

  10. BASIC EQUATIONS OF SOLID MECHANICS 10

  11. BASIC EQUATIONS OF SOLID MECHANICS 11

  12. BASIC EQUATIONS OF SOLID MECHANICS 12

  13. BASIC EQUATIONS OF SOLID MECHANICS 13

  14. BASIC EQUATIONS OF SOLID MECHANICS From analytical point of view, every design model can be expressed as a set of three basic equations with corresponding boundary conditions. 14

  15. WAYS TO SOLVE A SOLID MECHANICSPROBLEM 15

  16. MAIN METHODS COVERED IN SECOND SEMESTER For statically determinate structures 16

  17. USE OF TRUSS STRUCTURES IN AVIATION Junkers F.13, Germany, 1920 17

  18. USE OF TRUSS STRUCTURES IN AVIATION truss spar beam spar FFVS, Sweden, 1942 18

  19. USE OF TRUSS STRUCTURES IN AVIATION Concorde, Europe, 1969 truss spar beam spar 19

  20. USE OF TRUSS STRUCTURES IN AVIATION Concorde, Europe, 1969 20

  21. USE OF TRUSS STRUCTURES IN AVIATION A300, Europe, 1972 21

  22. USE OF TRUSS STRUCTURES IN AVIATION Zenith CH701, 1986 motor mount frame 22

  23. DIFFERENCE BETWEEN TRUSSES AND FRAMES 23

  24. DIFFERENCE BETWEEN TRUSSES AND FRAMES Connection by riveting, moment-resistant 24

  25. DIFFERENCE BETWEEN TRUSSES AND FRAMES Connection by welding, moment-resistant 25

  26. TOPIC OF THE LECTURE • Methods of forces calculation: • Method of joints • Method of sections • Method of substitution of members • Supplementary tools: • Zero-force member identification • Principle of superposition • Use of symmetry 26

  27. CONCLUSIONS 27

  28. WHERE TO FIND MORE INFORMATION? Method of joints and method of sections are covered in A. Kassimali. Structural Analysis. 2009, Chapters 4.5 and 4.6 Nice video on method of joints http://www.youtube.com/watch?v=-qms9xt3sbQ Nice video on method of sections http://www.youtube.com/watch?v=Yn-9voH1gZ4 Principle of superposition and method of substitution of members are covered in A. Williams. Structural Analysis In Theory and Practice. 2009, Chapters 1.7, 2.4 … Internet is boundless … 28

  29. TOPIC OF THE NEXT LECTURE Static determinacy. Methods of analysis All materials of our course are available at department website k102.khai.edu 1. Go to the page “Библиотека” 2. Press “Structural Mechanics (lecturer Vakulenko S.V.)” 29

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