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Flexibility matrix is always:-
- a)symmetric
- b)non-symmetric
- c)anti-symmetric
- d)depends upon loads applied
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Flexibility matrix is always:-a)symmetricb)non-symmetricc)anti-symmetr...
Answer: a
Explanation: Flexibility matrixes are always symmetric as a consequence of Betti’s law.
Explanation: Flexibility matrixes are always symmetric as a consequence of Betti’s law.
Most Upvoted Answer
Flexibility matrix is always:-a)symmetricb)non-symmetricc)anti-symmetr...
Flexibility matrix is always symmetric
Explanation:
The flexibility matrix is a mathematical representation of the structural behavior of a system under applied loads. It relates the displacements at various points in the structure to the applied forces or moments. The matrix is square and symmetric in nature, which means that the entries above and below the main diagonal are the same.
Explanation:
1. What is a flexibility matrix?
The flexibility matrix is a mathematical tool used in structural analysis to determine the displacements and forces in a structure. It relates the applied loads (forces or moments) to the resulting displacements at various points in the structure. The flexibility matrix is denoted by [F], and it is a square matrix with dimensions equal to the number of degrees of freedom in the structure.
2. Symmetry of the flexibility matrix
The flexibility matrix is always symmetric, which means that the entries above and below the main diagonal are the same. This symmetry arises from the fundamental principle of equilibrium and the reciprocity of displacements and forces in a structure. When a force is applied at one point in a structure, it induces a displacement at that point and a reaction force at other points in the structure. The flexibility matrix captures this relationship and ensures that the displacements and forces are balanced throughout the structure.
3. Significance of symmetry
The symmetry of the flexibility matrix has several important implications:
- Efficiency: The symmetry reduces the number of independent entries in the matrix, making it more efficient to calculate and store. This is particularly important for large and complex structures.
- Consistency: The symmetry ensures that the flexibility matrix is consistent with the equilibrium equations and the physical behavior of the structure. It reflects the fact that displacements and forces are interrelated and cannot exist in isolation.
- Compatibility: The symmetry allows for the analysis of complex structural systems by dividing them into smaller substructures. The flexibility matrices of the substructures can then be combined to obtain the overall flexibility matrix of the entire system.
4. Conclusion
In summary, the flexibility matrix is always symmetric due to the fundamental principles of equilibrium and reciprocity in structural analysis. This symmetry ensures the consistency, efficiency, and compatibility of the matrix, making it a powerful tool for analyzing the behavior of structures under applied loads.
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Flexibility matrix is always:-a)symmetricb)non-symmetricc)anti-symmetricd)depends upon loads appliedCorrect answer is option 'A'. Can you explain this answer?
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Flexibility matrix is always:-a)symmetricb)non-symmetricc)anti-symmetricd)depends upon loads appliedCorrect answer is option 'A'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Flexibility matrix is always:-a)symmetricb)non-symmetricc)anti-symmetricd)depends upon loads appliedCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Flexibility matrix is always:-a)symmetricb)non-symmetricc)anti-symmetricd)depends upon loads appliedCorrect answer is option 'A'. Can you explain this answer?.
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