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

2. Determinate or Indeterminate ?
Yes
Structure
Equilibrium 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. Indeterminate Structures

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

9. Symmetrical Structures

10. Symmetrical Structures

11. Symmetrical Loadings

12. Symmetrical Loadings

13. Anti-Symmetrical Loadings

14. Anti-Symmetrical Loadings

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

16. Decomposition of Loadings
Loadings = Symmetrical + Anti-symmetric Loads + =

17. Decomposition of Loadings

18. Decomposition of Loadings

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

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

21. Symmetrical Structures under Symmetrical Loads

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

23. Symmetrical Structures under Anti-symmetrical Loads

24. Analysis

25. Analysis 6 degrees of indeterminacy 4 degrees of indeterminacy

26. Analysis

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

28. Compatibility
DB=0 By

29. Compatibility

30. Compatibility

31. Compatibility

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

33. Compatibility

34. Compatibility
Settlement

35. Compatibility
Settlement

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

37. Least Work Method DF F P M(P,F) U(P,F) Obtain F
The magnitude of redundant force must be such that
the strain energy stored in the structure is a minimum

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

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