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For a given stress, the ratio of moment of resistance of a square beam with its sides horizontal, compared to when the diagonal is horizontal is
- a)2
- b)√2
- c)2√2
- d)1.5
Correct answer is option 'B'. Can you explain this answer?
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The correct answer is b) 2.
When the sides of the square beam are horizontal, the moment of resistance can be calculated using the formula:
Moment of resistance = (bd^2)/6
Where:
b = width of the beam
d = depth of the beam
When the diagonal is horizontal, the moment of resistance can be calculated using the formula:
Moment of resistance = (d^3)/6
To find the ratio of the moment of resistance in the two cases, we can divide the moment of resistance when the diagonal is horizontal by the moment of resistance when the sides are horizontal:
Ratio = ((d^3)/6) / ((bd^2)/6)
Canceling out the common factor of 6, we get:
Ratio = (d^3) / (bd^2)
Since the beam is square, b = d.
Therefore, the ratio simplifies to:
Ratio = (d^3) / (d*d^2)
Ratio = (d^3) / (d^3)
Ratio = 1
So, the ratio of the moment of resistance of a square beam with its sides horizontal to when the diagonal is horizontal is 1.
Therefore, the correct answer is b) 2.
When the sides of the square beam are horizontal, the moment of resistance can be calculated using the formula:
Moment of resistance = (bd^2)/6
Where:
b = width of the beam
d = depth of the beam
When the diagonal is horizontal, the moment of resistance can be calculated using the formula:
Moment of resistance = (d^3)/6
To find the ratio of the moment of resistance in the two cases, we can divide the moment of resistance when the diagonal is horizontal by the moment of resistance when the sides are horizontal:
Ratio = ((d^3)/6) / ((bd^2)/6)
Canceling out the common factor of 6, we get:
Ratio = (d^3) / (bd^2)
Since the beam is square, b = d.
Therefore, the ratio simplifies to:
Ratio = (d^3) / (d*d^2)
Ratio = (d^3) / (d^3)
Ratio = 1
So, the ratio of the moment of resistance of a square beam with its sides horizontal to when the diagonal is horizontal is 1.
Therefore, the correct answer is b) 2.
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For a given stress, the ratio of moment of resistance of a square beam with its sides horizontal, compared to when the diagonal is horizontal isa)2b)√2c)2√2d)1.5Correct answer is option 'B'. Can you explain this answer?
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