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

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Presentation on theme: "CIVL3310 STRUCTURAL ANALYSIS Professor CC Chang Chapter 10: Analysis of Statically Indeterminate Structures by the Force Method."— Presentation transcript:

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

2 Determinate or Indeterminate ? Structure Equilibrium Determinate Indeterminate Yes 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 StructureReflection Axis of symmetry Identical in geometry, supports and material properties

9 Symmetrical Structures

10

11 Symmetrical Loadings

12

13 Anti-Symmetrical Loadings Anti-Symmetrical

14 Anti-Symmetrical Loadings

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

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

17 Decomposition of Loadings

18

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

20 Symmetrical Structures under Symmetrical Loads L aa PP Moment & vertical displacement ≠ 0 Slope & axial displacement = 0 P V ≠ 0 slope = 0 M ≠ 0

21 Symmetrical Structures under Symmetrical Loads

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

23 Symmetrical Structures under Anti-symmetrical Loads

24 Analysis

25 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 ByBy  B =0

29 Compatibility

30

31

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

33

34 Settlement

35 Compatibility Settlement

36 Least Work Method Castigliano’s theory P   P F U(P,F) M(P,F)

37 Least Work Method P FF F 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 P F PP  P  F M(P,F) Castigliano’s theorem Least work principle Note: F does not do any work !

39 Least Work Method P1P1 FnFn F2F2 F1F1 PmPm P2P2 Strain energy Forces that do not do work Forces that do work


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