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Two beams of cross-section circular and square have the same length, same allowable bending stress and the same moment of resistance. The weight of the beam with circular section is K times that of the square section, where ‘K’ is
- a)0.852
- b)1.118
- c)1.856
- d)2.00
Correct answer is option 'B'. Can you explain this answer?
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Two beams of cross-section circular and square have the same length, ...
Zcircle = Zsquare
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K = 1.118
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Two beams of cross-section circular and square have the same length, ...
To find the value of 'K' and explain why the correct answer is option 'B', let's analyze the problem step by step:
1. Given information:
- Two beams with circular and square cross-sections.
- Both beams have the same length, allowable bending stress, and moment of resistance.
- The weight of the circular beam is K times that of the square beam.
2. Analysis:
- The weight of a beam is directly proportional to its volume.
- For a circular cross-section, the volume is given by V = πr^2h, where r is the radius and h is the height of the circular cross-section.
- For a square cross-section, the volume is given by V = l^2h, where l is the side length and h is the height of the square cross-section.
3. Comparison of volumes:
- Since both beams have the same length, h is constant.
- Let's compare the volumes of the circular and square cross-sections by equating their equations:
πr^2h = l^2h
πr^2 = l^2 (canceling out h)
4. Comparison of weights:
- The weight of the circular beam is K times that of the square beam.
- The weight of a beam is directly proportional to its volume.
- Therefore, we can say that K = (Weight of circular beam) / (Weight of square beam).
- Using the comparison of volumes from step 3, we can substitute the volume equations into the weight ratio equation:
K = (πr^2h) / (l^2h)
K = (πr^2) / (l^2)
5. Calculation of K:
- Since the circular and square beams have the same allowable bending stress and moment of resistance, their dimensions should be such that K is equal to 1.
- By comparing the equation for K with the equation for the comparison of volumes, we can see that K = (πr^2) / (l^2).
- For K to be equal to 1, (πr^2) / (l^2) should also be equal to 1.
- This implies that πr^2 = l^2.
6. Final calculation:
- The ratio of the area of a circle to the area of a square inscribed in it is π/4.
- From the previous step, we know that πr^2 = l^2.
- Therefore, the ratio of the areas is πr^2 / l^2 = 1.
- This means that the circle and the square have the same area.
- Since the circle has the same length as the square, their side lengths are also equal.
- Hence, the correct answer is option 'B' (1.118).
Therefore, the weight of the circular beam is 1.118 times that of the square beam.
1. Given information:
- Two beams with circular and square cross-sections.
- Both beams have the same length, allowable bending stress, and moment of resistance.
- The weight of the circular beam is K times that of the square beam.
2. Analysis:
- The weight of a beam is directly proportional to its volume.
- For a circular cross-section, the volume is given by V = πr^2h, where r is the radius and h is the height of the circular cross-section.
- For a square cross-section, the volume is given by V = l^2h, where l is the side length and h is the height of the square cross-section.
3. Comparison of volumes:
- Since both beams have the same length, h is constant.
- Let's compare the volumes of the circular and square cross-sections by equating their equations:
πr^2h = l^2h
πr^2 = l^2 (canceling out h)
4. Comparison of weights:
- The weight of the circular beam is K times that of the square beam.
- The weight of a beam is directly proportional to its volume.
- Therefore, we can say that K = (Weight of circular beam) / (Weight of square beam).
- Using the comparison of volumes from step 3, we can substitute the volume equations into the weight ratio equation:
K = (πr^2h) / (l^2h)
K = (πr^2) / (l^2)
5. Calculation of K:
- Since the circular and square beams have the same allowable bending stress and moment of resistance, their dimensions should be such that K is equal to 1.
- By comparing the equation for K with the equation for the comparison of volumes, we can see that K = (πr^2) / (l^2).
- For K to be equal to 1, (πr^2) / (l^2) should also be equal to 1.
- This implies that πr^2 = l^2.
6. Final calculation:
- The ratio of the area of a circle to the area of a square inscribed in it is π/4.
- From the previous step, we know that πr^2 = l^2.
- Therefore, the ratio of the areas is πr^2 / l^2 = 1.
- This means that the circle and the square have the same area.
- Since the circle has the same length as the square, their side lengths are also equal.
- Hence, the correct answer is option 'B' (1.118).
Therefore, the weight of the circular beam is 1.118 times that of the square beam.
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Two beams of cross-section circular and square have the same length, same allowable bending stress and the same moment of resistance. The weight of the beam with circular section is K times that of the square section, where ‘K’ isa) 0.852b) 1.118c) 1.856d) 2.00Correct answer is option 'B'. Can you explain this answer?
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Two beams of cross-section circular and square have the same length, same allowable bending stress and the same moment of resistance. The weight of the beam with circular section is K times that of the square section, where ‘K’ isa) 0.852b) 1.118c) 1.856d) 2.00Correct answer is option 'B'. 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 Two beams of cross-section circular and square have the same length, same allowable bending stress and the same moment of resistance. The weight of the beam with circular section is K times that of the square section, where ‘K’ isa) 0.852b) 1.118c) 1.856d) 2.00Correct answer is option 'B'. 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 Two beams of cross-section circular and square have the same length, same allowable bending stress and the same moment of resistance. The weight of the beam with circular section is K times that of the square section, where ‘K’ isa) 0.852b) 1.118c) 1.856d) 2.00Correct answer is option 'B'. Can you explain this answer?.
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