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**CIVL3310 STRUCTURAL ANALYSIS**

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

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**Determinate or Indeterminate ?**

Yes Structure Equilibrium No

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Why Indetermiante ? Advantages Smaller stresses and deflections

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Why Indetermiante ? Advantages Fail safe 1995 Oklahoma City bombing

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Prices Disadvantages Stresses due to support settlement

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Prices Disadvantages Stresses due to temperature changes

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**Indeterminate Structures**

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**Symmetric Structures Structure Reflection Axis of symmetry**

Identical in geometry, supports and material properties

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**Symmetrical Structures**

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**Symmetrical Structures**

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Symmetrical Loadings

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Symmetrical Loadings

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**Anti-Symmetrical Loadings**

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**Anti-Symmetrical Loadings**

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**Decomposition of Loadings**

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

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**Decomposition of Loadings**

Loadings = Symmetrical + Anti-symmetric Loads + =

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**Decomposition of Loadings**

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**Decomposition of Loadings**

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**Analysis of Symmetrical Structures**

Loading Symmetrical Loading Anti-symmetrical Loading Symmetrical Structure Response Response 1 Response 2 +

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**Symmetrical Structures under Symmetrical Loads**

P P a L a P Moment & vertical displacement ≠ 0 Slope & axial displacement = 0 slope = 0 M ≠ 0 V ≠ 0

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**Symmetrical Structures under Symmetrical Loads**

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**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

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**Symmetrical Structures under Anti-symmetrical Loads**

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Analysis

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**Analysis 6 degrees of indeterminacy 4 degrees of indeterminacy**

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Analysis

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**Analysis of Statically Indeterminate Structures**

Force methods This chapter Displacement methods Next two chapters

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Compatibility DB=0 By

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Compatibility

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Compatibility

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Compatibility

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

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Compatibility

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Compatibility Settlement

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Compatibility Settlement

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

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**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

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**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 !

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**Least Work Method Strain energy F1 F2 Fn P1 P2 Pm Forces that do work**

Forces that do not do work

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