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For a linear elastic frame, if the stiffness matrix is doubled with respect to the existing stiffness matrix, the deflection of the resulting frame will be
- a)twice the existing value
- b)half the existing value
- c)the same as existing value
- d)indeterminate value
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
For a linear elastic frame, if the stiffness matrix is doubled with re...
Stiffness (k) is defined as the force per unit deflection.
K = P/δ
⇒ δ = P/K
If stiffness matrix is doubled
i.e. K’ = 2K
then,
δ = P/K'
δ = P/2K
δ = (1/2)P/K
δ’ = δ/2.
Therefore, if the stiffness matrix is doubled with respect to the existing stiffness matrix, the deflection of the resulting frame will be half the existing value.
Most Upvoted Answer
For a linear elastic frame, if the stiffness matrix is doubled with re...
Explanation:
To understand why the deflection of the resulting frame will be half the existing value when the stiffness matrix is doubled, we need to consider the relationship between the stiffness matrix and the deflection of a linear elastic frame.
Stiffness Matrix:
The stiffness matrix represents the stiffness of the frame, which is a measure of its resistance to deformation under an applied load. It is a mathematical representation of the relationship between the applied loads and the corresponding displacements.
Deflection:
Deflection refers to the bending or displacement of the frame under an applied load. It is influenced by various factors, including the stiffness of the frame.
Relationship between Stiffness Matrix and Deflection:
In a linear elastic frame, the relationship between the stiffness matrix and the deflection can be expressed as follows:
D = K^-1 * F
Where:
D is the vector of displacements,
K is the stiffness matrix,
F is the vector of applied loads.
Effect of Doubling the Stiffness Matrix:
When the stiffness matrix is doubled, the equation for deflection becomes:
D_new = (2K)^-1 * F
Simplifying the equation, we have:
D_new = 0.5 * K^-1 * F
Comparing this equation with the original equation, it is clear that the deflection of the resulting frame (D_new) is half the value of the deflection of the existing frame (D).
Reasoning:
Doubling the stiffness matrix effectively increases the stiffness of the frame. A stiffer frame will resist deformation to a greater extent, resulting in smaller deflections. Therefore, when the stiffness matrix is doubled, the deflection of the resulting frame will be half the existing value.
Conclusion:
In conclusion, when the stiffness matrix of a linear elastic frame is doubled, the deflection of the resulting frame will be half the existing value. This is because doubling the stiffness matrix increases the stiffness of the frame, leading to smaller deflections under the same applied loads.
To understand why the deflection of the resulting frame will be half the existing value when the stiffness matrix is doubled, we need to consider the relationship between the stiffness matrix and the deflection of a linear elastic frame.
Stiffness Matrix:
The stiffness matrix represents the stiffness of the frame, which is a measure of its resistance to deformation under an applied load. It is a mathematical representation of the relationship between the applied loads and the corresponding displacements.
Deflection:
Deflection refers to the bending or displacement of the frame under an applied load. It is influenced by various factors, including the stiffness of the frame.
Relationship between Stiffness Matrix and Deflection:
In a linear elastic frame, the relationship between the stiffness matrix and the deflection can be expressed as follows:
D = K^-1 * F
Where:
D is the vector of displacements,
K is the stiffness matrix,
F is the vector of applied loads.
Effect of Doubling the Stiffness Matrix:
When the stiffness matrix is doubled, the equation for deflection becomes:
D_new = (2K)^-1 * F
Simplifying the equation, we have:
D_new = 0.5 * K^-1 * F
Comparing this equation with the original equation, it is clear that the deflection of the resulting frame (D_new) is half the value of the deflection of the existing frame (D).
Reasoning:
Doubling the stiffness matrix effectively increases the stiffness of the frame. A stiffer frame will resist deformation to a greater extent, resulting in smaller deflections. Therefore, when the stiffness matrix is doubled, the deflection of the resulting frame will be half the existing value.
Conclusion:
In conclusion, when the stiffness matrix of a linear elastic frame is doubled, the deflection of the resulting frame will be half the existing value. This is because doubling the stiffness matrix increases the stiffness of the frame, leading to smaller deflections under the same applied loads.
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For a linear elastic frame, if the stiffness matrix is doubled with respect to the existing stiffness matrix, the deflection of the resulting frame will bea)twice the existing valueb)half the existing valuec)the same as existing valued)indeterminate valueCorrect answer is option 'B'. 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 For a linear elastic frame, if the stiffness matrix is doubled with respect to the existing stiffness matrix, the deflection of the resulting frame will bea)twice the existing valueb)half the existing valuec)the same as existing valued)indeterminate valueCorrect answer is option 'B'. 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 For a linear elastic frame, if the stiffness matrix is doubled with respect to the existing stiffness matrix, the deflection of the resulting frame will bea)twice the existing valueb)half the existing valuec)the same as existing valued)indeterminate valueCorrect answer is option 'B'. Can you explain this answer?.
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