Correct Answer - Option 3 : Hardy Cross
Concept:
Column Analogy Method:
- It is proposed by Hardy Cross.
- It is a method used to analyze indeterminate structures specifically fixed beams, frames, and arches.
- It is ideally suited for computing stiffness and carryover factor in beams and frames having variable cross-sections.
Note:
- It is applicable to a maximum of 3rd degree of indeterminacy.
- It is based on the mathematical similarity between the stresses developed on a column section and the moment imposed due to the fixity of support.
A fixed beam has three degrees of static indeterminacy and hence column analogy method is used to analyze the fixed beam only.
Any portal frame and box frame up to 3 degrees of indeterminacy can also be analyzed using the column analogy method.
Difference between Force & Displacement Methods
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Force Methods
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Displacement Methods
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Types of indeterminacy: Static Indeterminacy
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Types of indeterminacy: Kinematic Indeterminacy
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Governing equation: Compatibility Equations
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Governing equations: Equilibrium Equations
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Force displacement relations: Flexibility matrix
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Force displacement relations: Stiffness matrix
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Example:
1. Method of consistent deformation
2. Theorem of least work
3. Column analogy method
4. Flexibility matrix method
5. Castigliano’s Theorem- II
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Example:
1. Slope deflection method
2. Moment distribution method
3. Kani’s method
4. Stiffness matrix method
5. Castigliano’s Theorem- I
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