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A square beam laid flat is then rotated in such a way that one of its diagonal becomes horizontal. How is its moment capacity affected?
- a)Increase in 41.4%
- b)Increase in 29.27%
- c)Decrease in 29.27%
- d)Decrease in 41.4%
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A square beam laid flat is then rotated in such a way that one of its...
Moment capacity of a beam is given by MR = σy × Z
View all questions of this test
For a particular beam σy is constant
∴ MR ∝ Z
When beam is laid flat, then
∴ Moment capacity increases by 41.4%.
Most Upvoted Answer
A square beam laid flat is then rotated in such a way that one of its...
Effect of rotation of square beam on moment capacity
Heading: Introduction
When a square beam is laid flat and rotated in such a way that one of its diagonals becomes horizontal, its moment capacity is affected. This effect can be calculated using mathematical formulas.
Heading: Calculation of moment capacity
The moment capacity of a square beam can be calculated using the formula M = fy(Zx + Zy)/gammaM, where M is the moment capacity, fy is the yield strength of the beam, Zx is the plastic section modulus about the x-axis, Zy is the plastic section modulus about the y-axis, and gammaM is the safety factor.
Heading: Calculation of plastic section moduli
The plastic section moduli Zx and Zy can be calculated using the formulas Zx = bh^2/6 and Zy = hb^2/6, where b and h are the width and height of the beam.
Heading: Effect of rotation on plastic section moduli
When the square beam is rotated in such a way that one of its diagonals becomes horizontal, its width and height change. The new width and height can be calculated using the formulas b' = h/sqrt(2) and h' = b/sqrt(2), where b' and h' are the new width and height.
Heading: Calculation of new plastic section moduli
Using the new width and height, the new plastic section moduli Zx' and Zy' can be calculated using the formulas Zx' = b'h'^2/6 and Zy' = h'b'^2/6.
Heading: Calculation of new moment capacity
Using the new plastic section moduli, the new moment capacity M' can be calculated using the formula M' = fy(Zx' + Zy')/gammaM.
Heading: Comparison of moment capacities
The ratio of the new moment capacity to the original moment capacity can be calculated as M'/M = (Zx' + Zy')/(Zx + Zy). Substituting the values, we get M'/M = (2 + sqrt(2))/2. This is approximately equal to 1.414, which represents an increase in moment capacity of 41.4%.
Conclusion
When a square beam is rotated in such a way that one of its diagonals becomes horizontal, its moment capacity increases by 41.4%.
Heading: Introduction
When a square beam is laid flat and rotated in such a way that one of its diagonals becomes horizontal, its moment capacity is affected. This effect can be calculated using mathematical formulas.
Heading: Calculation of moment capacity
The moment capacity of a square beam can be calculated using the formula M = fy(Zx + Zy)/gammaM, where M is the moment capacity, fy is the yield strength of the beam, Zx is the plastic section modulus about the x-axis, Zy is the plastic section modulus about the y-axis, and gammaM is the safety factor.
Heading: Calculation of plastic section moduli
The plastic section moduli Zx and Zy can be calculated using the formulas Zx = bh^2/6 and Zy = hb^2/6, where b and h are the width and height of the beam.
Heading: Effect of rotation on plastic section moduli
When the square beam is rotated in such a way that one of its diagonals becomes horizontal, its width and height change. The new width and height can be calculated using the formulas b' = h/sqrt(2) and h' = b/sqrt(2), where b' and h' are the new width and height.
Heading: Calculation of new plastic section moduli
Using the new width and height, the new plastic section moduli Zx' and Zy' can be calculated using the formulas Zx' = b'h'^2/6 and Zy' = h'b'^2/6.
Heading: Calculation of new moment capacity
Using the new plastic section moduli, the new moment capacity M' can be calculated using the formula M' = fy(Zx' + Zy')/gammaM.
Heading: Comparison of moment capacities
The ratio of the new moment capacity to the original moment capacity can be calculated as M'/M = (Zx' + Zy')/(Zx + Zy). Substituting the values, we get M'/M = (2 + sqrt(2))/2. This is approximately equal to 1.414, which represents an increase in moment capacity of 41.4%.
Conclusion
When a square beam is rotated in such a way that one of its diagonals becomes horizontal, its moment capacity increases by 41.4%.
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A square beam laid flat is then rotated in such a way that one of its diagonal becomes horizontal. How is its moment capacity affected?a) Increase in 41.4%b) Increase in 29.27%c) Decrease in 29.27%d) Decrease in 41.4%Correct answer is option 'A'. Can you explain this answer?
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A square beam laid flat is then rotated in such a way that one of its diagonal becomes horizontal. How is its moment capacity affected?a) Increase in 41.4%b) Increase in 29.27%c) Decrease in 29.27%d) Decrease in 41.4%Correct answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A square beam laid flat is then rotated in such a way that one of its diagonal becomes horizontal. How is its moment capacity affected?a) Increase in 41.4%b) Increase in 29.27%c) Decrease in 29.27%d) Decrease in 41.4%Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A square beam laid flat is then rotated in such a way that one of its diagonal becomes horizontal. How is its moment capacity affected?a) Increase in 41.4%b) Increase in 29.27%c) Decrease in 29.27%d) Decrease in 41.4%Correct answer is option 'A'. Can you explain this answer?.
A square beam laid flat is then rotated in such a way that one of its diagonal becomes horizontal. How is its moment capacity affected?a) Increase in 41.4%b) Increase in 29.27%c) Decrease in 29.27%d) Decrease in 41.4%Correct answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A square beam laid flat is then rotated in such a way that one of its diagonal becomes horizontal. How is its moment capacity affected?a) Increase in 41.4%b) Increase in 29.27%c) Decrease in 29.27%d) Decrease in 41.4%Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A square beam laid flat is then rotated in such a way that one of its diagonal becomes horizontal. How is its moment capacity affected?a) Increase in 41.4%b) Increase in 29.27%c) Decrease in 29.27%d) Decrease in 41.4%Correct answer is option 'A'. Can you explain this answer?.
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A square beam laid flat is then rotated in such a way that one of its diagonal becomes horizontal. How is its moment capacity affected?a) Increase in 41.4%b) Increase in 29.27%c) Decrease in 29.27%d) Decrease in 41.4%Correct answer is option 'A'. Can you explain this answer?, a detailed solution for A square beam laid flat is then rotated in such a way that one of its diagonal becomes horizontal. How is its moment capacity affected?a) Increase in 41.4%b) Increase in 29.27%c) Decrease in 29.27%d) Decrease in 41.4%Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of A square beam laid flat is then rotated in such a way that one of its diagonal becomes horizontal. How is its moment capacity affected?a) Increase in 41.4%b) Increase in 29.27%c) Decrease in 29.27%d) Decrease in 41.4%Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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