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Two beams, one of circular cross section and the other of square cross section, have equal areas of cross section. If subjected to bending, then
- a)Circular cross section is more economical
- b)Square cross section is more economical
- c)Both sections are equally economical
- d)Both sections are equally stiff
Correct answer is option 'A'. Can you explain this answer?
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Two beams, one of circular cross section and the other of square cross...
Economic Design of Beams with Different Cross Sections
Introduction:
In beam design, the aim is to select the most economical cross-sectional shape that can resist the applied loads without failing. The economy of the beam is determined by the cost of materials and the ease of fabrication. In this regard, two cross-sectional shapes, the circular and the square, are compared to identify the most economical one.
Comparison of Circular and Square Cross Sections:
Assuming that both the circular and the square cross-sectional beams have equal areas, the comparison of the two shapes is done as follows:
1. Moment of Inertia:
The moment of inertia is a measure of a beam's stiffness. For a given cross-sectional area, a larger moment of inertia indicates greater stiffness. The moment of inertia of a circular beam is π/4 times the diameter to the power of 4. The moment of inertia of a square beam is b times h to the power of 3 divided by 12, where b is the width and h is the height of the beam. Therefore, for the same area, the moment of inertia of a square beam is greater than that of a circular beam. This means that the square beam is stiffer than the circular beam.
2. Bending Stress:
The bending stress is the stress developed in a beam due to the applied moment. It is given by the formula M*y/I, where M is the bending moment, y is the distance from the neutral axis, and I is the moment of inertia. Since the square beam has a larger moment of inertia, it will have a lower bending stress than the circular beam for the same applied moment. This means that the square beam is stronger than the circular beam.
3. Material Cost:
The cost of a beam is dependent on the cost of the material used. Assuming that the cost of materials is the same for both beams, the square beam will be more economical than the circular beam. This is because the square beam is stronger than the circular beam and can resist higher loads. Hence, less material is required to achieve the same strength, resulting in a lower cost.
Conclusion:
In conclusion, the square cross-sectional beam is the most economical choice when compared to the circular cross-sectional beam. This is because it has a larger moment of inertia, lower bending stress, and lower material cost.
Introduction:
In beam design, the aim is to select the most economical cross-sectional shape that can resist the applied loads without failing. The economy of the beam is determined by the cost of materials and the ease of fabrication. In this regard, two cross-sectional shapes, the circular and the square, are compared to identify the most economical one.
Comparison of Circular and Square Cross Sections:
Assuming that both the circular and the square cross-sectional beams have equal areas, the comparison of the two shapes is done as follows:
1. Moment of Inertia:
The moment of inertia is a measure of a beam's stiffness. For a given cross-sectional area, a larger moment of inertia indicates greater stiffness. The moment of inertia of a circular beam is π/4 times the diameter to the power of 4. The moment of inertia of a square beam is b times h to the power of 3 divided by 12, where b is the width and h is the height of the beam. Therefore, for the same area, the moment of inertia of a square beam is greater than that of a circular beam. This means that the square beam is stiffer than the circular beam.
2. Bending Stress:
The bending stress is the stress developed in a beam due to the applied moment. It is given by the formula M*y/I, where M is the bending moment, y is the distance from the neutral axis, and I is the moment of inertia. Since the square beam has a larger moment of inertia, it will have a lower bending stress than the circular beam for the same applied moment. This means that the square beam is stronger than the circular beam.
3. Material Cost:
The cost of a beam is dependent on the cost of the material used. Assuming that the cost of materials is the same for both beams, the square beam will be more economical than the circular beam. This is because the square beam is stronger than the circular beam and can resist higher loads. Hence, less material is required to achieve the same strength, resulting in a lower cost.
Conclusion:
In conclusion, the square cross-sectional beam is the most economical choice when compared to the circular cross-sectional beam. This is because it has a larger moment of inertia, lower bending stress, and lower material cost.
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Two beams, one of circular cross section and the other of square cross...
Option (a)
Bending k liye rectangular/square best rhta h.... shear k liye circular section best rhta h
Bending k liye rectangular/square best rhta h.... shear k liye circular section best rhta h
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Two beams, one of circular cross section and the other of square cross section, have equal areas of cross section. If subjected to bending, thena)Circular cross section is more economicalb)Square cross section is more economicalc)Both sections are equally economicald)Both sections are equally stiffCorrect answer is option 'A'. Can you explain this answer?
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Two beams, one of circular cross section and the other of square cross section, have equal areas of cross section. If subjected to bending, thena)Circular cross section is more economicalb)Square cross section is more economicalc)Both sections are equally economicald)Both sections are equally stiffCorrect answer is option 'A'. 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 Two beams, one of circular cross section and the other of square cross section, have equal areas of cross section. If subjected to bending, thena)Circular cross section is more economicalb)Square cross section is more economicalc)Both sections are equally economicald)Both sections are equally stiffCorrect answer is option 'A'. 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 Two beams, one of circular cross section and the other of square cross section, have equal areas of cross section. If subjected to bending, thena)Circular cross section is more economicalb)Square cross section is more economicalc)Both sections are equally economicald)Both sections are equally stiffCorrect answer is option 'A'. Can you explain this answer?.
Two beams, one of circular cross section and the other of square cross section, have equal areas of cross section. If subjected to bending, thena)Circular cross section is more economicalb)Square cross section is more economicalc)Both sections are equally economicald)Both sections are equally stiffCorrect answer is option 'A'. 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 Two beams, one of circular cross section and the other of square cross section, have equal areas of cross section. If subjected to bending, thena)Circular cross section is more economicalb)Square cross section is more economicalc)Both sections are equally economicald)Both sections are equally stiffCorrect answer is option 'A'. 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 Two beams, one of circular cross section and the other of square cross section, have equal areas of cross section. If subjected to bending, thena)Circular cross section is more economicalb)Square cross section is more economicalc)Both sections are equally economicald)Both sections are equally stiffCorrect answer is option 'A'. Can you explain this answer?.
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Two beams, one of circular cross section and the other of square cross section, have equal areas of cross section. If subjected to bending, thena)Circular cross section is more economicalb)Square cross section is more economicalc)Both sections are equally economicald)Both sections are equally stiffCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for Two beams, one of circular cross section and the other of square cross section, have equal areas of cross section. If subjected to bending, thena)Circular cross section is more economicalb)Square cross section is more economicalc)Both sections are equally economicald)Both sections are equally stiffCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of Two beams, one of circular cross section and the other of square cross section, have equal areas of cross section. If subjected to bending, thena)Circular cross section is more economicalb)Square cross section is more economicalc)Both sections are equally economicald)Both sections are equally stiffCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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