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Two beams of equal cross-section area are subjected to equal bending moment. If one beam has square cross-section and the other has circular section, then
- a)Both beams will be equally strong
- b)Circular section beam will be stronger
- c)Square section beam will be stronger
- d)The strength of the beam will depend on the nature of loading
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Two beams of equal cross-section area are subjected to equal bending ...
If, for the same applied moment, stresses generated are less, then the beam can be said as stronger.
View all questions of this test
Given, Asquare = Acircular
Stress generated in circular section,
⇒ Stress in square cross-section < stress="" in="" circular="" />
Hence, the square beam is stronger.
Most Upvoted Answer
Two beams of equal cross-section area are subjected to equal bending ...
Explanation:
When a beam is subjected to bending moment, the maximum stress occurs at the outermost fibers of the beam. The ability of a beam to resist bending stresses is directly related to the distribution of material away from the neutral axis.
1. Moment of Inertia:
The moment of inertia of a cross-section is a measure of its ability to resist bending. For a square cross-section, the moment of inertia is given by I = (a^4)/12, where 'a' is the side length of the square. For a circular cross-section, the moment of inertia is given by I = πd^4/64, where 'd' is the diameter of the circle.
2. Relationship between Moment of Inertia and Strength:
The moment of inertia is directly proportional to the strength of the beam. A larger moment of inertia indicates a greater ability to resist bending stresses. Therefore, the beam with a larger moment of inertia will be stronger.
3. Comparison:
In the case of a square cross-section, the moment of inertia is proportional to a^4. In the case of a circular cross-section, the moment of inertia is proportional to d^4. Since both beams have equal cross-sectional area, the side length of the square (a) and the diameter of the circle (d) will be related as follows:
a^2 = (πd^2)/4
Taking the fourth power of both sides:
(a^2)^4 = ((πd^2)/4)^4
a^8 = (π^4/256)d^8
Since the moment of inertia is proportional to a^4 and d^4, we can conclude that the moment of inertia of the square cross-section is greater than that of the circular cross-section:
I(square) = (a^4)/12 > (d^4)π/64 = I(circle)
Therefore, the square section beam will be stronger than the circular section beam.
Conclusion:
The strength of the beam is determined by the moment of inertia of its cross-section. In this case, the square section beam has a larger moment of inertia compared to the circular section beam, making it stronger. Therefore, the correct answer is option 'C' - The square section beam will be stronger.
When a beam is subjected to bending moment, the maximum stress occurs at the outermost fibers of the beam. The ability of a beam to resist bending stresses is directly related to the distribution of material away from the neutral axis.
1. Moment of Inertia:
The moment of inertia of a cross-section is a measure of its ability to resist bending. For a square cross-section, the moment of inertia is given by I = (a^4)/12, where 'a' is the side length of the square. For a circular cross-section, the moment of inertia is given by I = πd^4/64, where 'd' is the diameter of the circle.
2. Relationship between Moment of Inertia and Strength:
The moment of inertia is directly proportional to the strength of the beam. A larger moment of inertia indicates a greater ability to resist bending stresses. Therefore, the beam with a larger moment of inertia will be stronger.
3. Comparison:
In the case of a square cross-section, the moment of inertia is proportional to a^4. In the case of a circular cross-section, the moment of inertia is proportional to d^4. Since both beams have equal cross-sectional area, the side length of the square (a) and the diameter of the circle (d) will be related as follows:
a^2 = (πd^2)/4
Taking the fourth power of both sides:
(a^2)^4 = ((πd^2)/4)^4
a^8 = (π^4/256)d^8
Since the moment of inertia is proportional to a^4 and d^4, we can conclude that the moment of inertia of the square cross-section is greater than that of the circular cross-section:
I(square) = (a^4)/12 > (d^4)π/64 = I(circle)
Therefore, the square section beam will be stronger than the circular section beam.
Conclusion:
The strength of the beam is determined by the moment of inertia of its cross-section. In this case, the square section beam has a larger moment of inertia compared to the circular section beam, making it stronger. Therefore, the correct answer is option 'C' - The square section beam will be stronger.
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Two beams of equal cross-section area are subjected to equal bending moment. If one beam has square cross-section and the other has circular section, thena) Both beams will be equally strongb) Circular section beam will be strongerc) Square section beam will be strongerd) The strength of the beam will depend on the nature of loadingCorrect answer is option 'C'. Can you explain this answer?
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Two beams of equal cross-section area are subjected to equal bending moment. If one beam has square cross-section and the other has circular section, thena) Both beams will be equally strongb) Circular section beam will be strongerc) Square section beam will be strongerd) The strength of the beam will depend on the nature of loadingCorrect answer is option 'C'. 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 equal cross-section area are subjected to equal bending moment. If one beam has square cross-section and the other has circular section, thena) Both beams will be equally strongb) Circular section beam will be strongerc) Square section beam will be strongerd) The strength of the beam will depend on the nature of loadingCorrect answer is option 'C'. 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 equal cross-section area are subjected to equal bending moment. If one beam has square cross-section and the other has circular section, thena) Both beams will be equally strongb) Circular section beam will be strongerc) Square section beam will be strongerd) The strength of the beam will depend on the nature of loadingCorrect answer is option 'C'. Can you explain this answer?.
Two beams of equal cross-section area are subjected to equal bending moment. If one beam has square cross-section and the other has circular section, thena) Both beams will be equally strongb) Circular section beam will be strongerc) Square section beam will be strongerd) The strength of the beam will depend on the nature of loadingCorrect answer is option 'C'. 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 equal cross-section area are subjected to equal bending moment. If one beam has square cross-section and the other has circular section, thena) Both beams will be equally strongb) Circular section beam will be strongerc) Square section beam will be strongerd) The strength of the beam will depend on the nature of loadingCorrect answer is option 'C'. 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 equal cross-section area are subjected to equal bending moment. If one beam has square cross-section and the other has circular section, thena) Both beams will be equally strongb) Circular section beam will be strongerc) Square section beam will be strongerd) The strength of the beam will depend on the nature of loadingCorrect answer is option 'C'. Can you explain this answer?.
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Two beams of equal cross-section area are subjected to equal bending moment. If one beam has square cross-section and the other has circular section, thena) Both beams will be equally strongb) Circular section beam will be strongerc) Square section beam will be strongerd) The strength of the beam will depend on the nature of loadingCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for Two beams of equal cross-section area are subjected to equal bending moment. If one beam has square cross-section and the other has circular section, thena) Both beams will be equally strongb) Circular section beam will be strongerc) Square section beam will be strongerd) The strength of the beam will depend on the nature of loadingCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of Two beams of equal cross-section area are subjected to equal bending moment. If one beam has square cross-section and the other has circular section, thena) Both beams will be equally strongb) Circular section beam will be strongerc) Square section beam will be strongerd) The strength of the beam will depend on the nature of loadingCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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