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For stable structures, one of the important properties of flexibility and stiffness matrices is that the element on the main diagonal
(i) of a stiffness matrix must be negative.
(ii) of a stiffness matrix must be positive
(iii) of a flexibility matrix must be positive
(iv) of a flexibility matrix must be negative
  • a)
    (i) and (iii)
  • b)
    (i) and (iv)
  • c)
    (ii) and (iii)
  • d)
    (ii) and (iv)
Correct answer is option 'C'. Can you explain this answer?
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For stable structures, one of the important properties of flexibility ...
Flexibility and stiffness matrix:
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For stable structures, one of the important properties of flexibility ...
The correct answer is option 'C' - (ii) and (iii) of a stiffness matrix must be positive.

Explanation:
- In structural analysis, the stiffness matrix and flexibility matrix are important tools used to analyze the behavior of structures.
- The stiffness matrix relates the applied loads to the resulting displacements, while the flexibility matrix relates the applied displacements to the resulting forces.
- Both matrices are square matrices with the same dimensions, and the element on the main diagonal of each matrix represents the stiffness or flexibility of each degree of freedom of the structure.
- For stable structures, the stiffness matrix must have positive values on the main diagonal (ii), and the flexibility matrix must also have positive values on the main diagonal (iii).
- This is because the stiffness and flexibility of a structure represent its resistance to deformation and its ability to accommodate displacements, respectively.
- Positive values indicate that the structure is capable of resisting external loads and maintaining its shape and stability.
- Negative values would imply that the structure is unstable and prone to collapse, as it would indicate that the applied loads or displacements are causing the structure to deform in an undesired manner.
- Therefore, both the stiffness and flexibility matrices should have positive values on the main diagonal to ensure the stability and integrity of the structure.
- Option 'C' is the correct answer as it includes both statements (ii) and (iii) which are true for stable structures.
- The other options do not include the correct combination of statements regarding the stiffness and flexibility matrices.
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For stable structures, one of the important properties of flexibility and stiffness matrices is that the element on the main diagonal(i) of a stiffness matrix must be negative.(ii) of a stiffness matrix must be positive(iii) of a flexibility matrix must be positive(iv) of a flexibility matrix must be negativea)(i) and (iii)b)(i) and (iv)c)(ii) and (iii)d)(ii) and (iv)Correct answer is option 'C'. Can you explain this answer?
Question Description
For stable structures, one of the important properties of flexibility and stiffness matrices is that the element on the main diagonal(i) of a stiffness matrix must be negative.(ii) of a stiffness matrix must be positive(iii) of a flexibility matrix must be positive(iv) of a flexibility matrix must be negativea)(i) and (iii)b)(i) and (iv)c)(ii) and (iii)d)(ii) and (iv)Correct answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about For stable structures, one of the important properties of flexibility and stiffness matrices is that the element on the main diagonal(i) of a stiffness matrix must be negative.(ii) of a stiffness matrix must be positive(iii) of a flexibility matrix must be positive(iv) of a flexibility matrix must be negativea)(i) and (iii)b)(i) and (iv)c)(ii) and (iii)d)(ii) and (iv)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For stable structures, one of the important properties of flexibility and stiffness matrices is that the element on the main diagonal(i) of a stiffness matrix must be negative.(ii) of a stiffness matrix must be positive(iii) of a flexibility matrix must be positive(iv) of a flexibility matrix must be negativea)(i) and (iii)b)(i) and (iv)c)(ii) and (iii)d)(ii) and (iv)Correct answer is option 'C'. Can you explain this answer?.
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