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CIVL3310 STRUCTURAL ANALYSIS Professor CC Chang Chapter 10: Analysis of Statically Indeterminate Structures by the Force Method
Determinate or Indeterminate ? Structure Equilibrium Determinate Indeterminate Yes No
Why Indetermiante ? Advantages Smaller stresses and deflections
Why Indetermiante ? Advantages Fail safe 1995 Oklahoma City bombing
Prices Disadvantages Stresses due to support settlement
Prices Disadvantages Stresses due to temperature changes
Symmetric Structures StructureReflection Axis of symmetry Identical in geometry, supports and material properties
Anti-Symmetrical Loadings Anti-Symmetrical
Decomposition of Loadings (A) (B) = (A)/2 (C) = Reflection of (B) (B)+(C) (B)-(C) Symmetrical Anti-symmetrical sum
Decomposition of Loadings Loadings = Symmetrical + Anti-symmetric Loads + =
Decomposition of Loadings
Analysis of Symmetrical Structures Loading Anti-symmetrical Loading Symmetrical Loading Symmetrical Structure Response 1 Response 2 + Response
Symmetrical Structures under Symmetrical Loads L aa PP Moment & vertical displacement ≠ 0 Slope & axial displacement = 0 P V ≠ 0 slope = 0 M ≠ 0
Symmetrical Structures under Symmetrical Loads
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
Symmetrical Structures under Anti-symmetrical Loads
6 degrees of indeterminacy 4 degrees of indeterminacy
Analysis of Statically Indeterminate Structures Force methods This chapter Displacement methods Next two chapters
Compatibility ByBy B =0
A B P C D C D P 1 1 = +
Least Work Method Castigliano’s theory P P F U(P,F) M(P,F)
Least Work Method P FF 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
Least Work Method Virtual work principle P F PP P F M(P,F) Castigliano’s theorem Least work principle Note: F does not do any work !
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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