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CIVL3310 STRUCTURAL ANALYSIS

Chapter 10: Analysis of Statically Indeterminate Structures by the Force Method. CIVL3310 STRUCTURAL ANALYSIS. Professor CC Chang. Determinate or Indeterminate ?. Determinate. Equilibrium. Indeterminate. Yes. Structure. No. Why Indetermiante ?. Advantages.

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CIVL3310 STRUCTURAL ANALYSIS

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  1. Chapter 10: Analysis of Statically Indeterminate Structures by the Force Method CIVL3310 STRUCTURAL ANALYSIS Professor CC Chang

  2. Determinate or Indeterminate ? Determinate Equilibrium Indeterminate Yes Structure No

  3. Why Indetermiante ? • Advantages Smaller stresses and deflections

  4. Why Indetermiante ? • Advantages Fail safe 1995 Oklahoma City bombing

  5. Prices • Disadvantages Stresses due to support settlement

  6. Prices • Disadvantages Stresses due to temperature changes

  7. Symmetric Structures Axis of symmetry Structure Reflection Identical in geometry, supports and material properties

  8. Symmetrical Structures

  9. Symmetrical Structures

  10. Symmetrical Loadings

  11. Symmetrical Loadings

  12. Anti-Symmetrical Loadings

  13. Anti-Symmetrical Loadings

  14. Decomposition of Loadings sum (A) (B) = (A)/2 (C) = Reflection of (B) (B)+(C) Symmetrical (B)-(C) Anti-symmetrical

  15. Decomposition of Loadings + = • Loadings = Symmetrical + Anti-symmetric Loads

  16. Decomposition of Loadings

  17. Decomposition of Loadings

  18. Analysis of Symmetrical Structures Loading Symmetrical Loading Anti-symmetrical Loading Symmetrical Structure Response Response 1 Response 2 +

  19. Symmetrical Structures under Symmetrical Loads a a P P L P Moment & vertical displacement ≠ 0 Slope & axial displacement = 0 slope = 0 M ≠ 0 V ≠ 0

  20. Symmetrical Structures under Symmetrical Loads

  21. Symmetrical Structures under Anti-symmetrical Loads a a Slope ≠ 0 Moment & vertical displacement = 0 P L/2 L/2 P P Slope ≠ 0 M = 0 V = 0

  22. Symmetrical Structures under Anti-symmetrical Loads

  23. Analysis

  24. Analysis 6 degrees of indeterminacy 4 degrees of indeterminacy 4 degrees of indeterminacy

  25. Analysis

  26. Analysis of Statically Indeterminate Structures • Force methods • This chapter • Displacement methods • Next two chapters

  27. Compatibility DB=0 By

  28. Compatibility

  29. Compatibility

  30. Compatibility

  31. Compatibility P P 1 1 C C D D = A B +

  32. Compatibility

  33. Compatibility • Settlement

  34. Compatibility • Settlement

  35. Least Work Method D=? P F M(P,F) U(P,F) • Castigliano’s theory P D

  36. Least Work Method DF F M(P,F) U(P,F) P Obtain F

  37. Least Work Method F DP M(P,F) Castigliano’s theorem Least work principle • Virtual work principle +dP P +dF Note: F does not do any work !

  38. Least Work Method P1 Pm P2 Fn F2 F1 Strain energy Forces that do work Forces that do not do work

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