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Two beams, one having a square cross-section and another circular cross-section, are subjected to the same amount of bending moment. If the cross-sectional area as well as the material of both the beams are the same, then
1. Both the beams will experience the same amount of deformation
2. The circular beam experience more extreme flexural stress than the square one
Which of the above is/are correct?
- a)1 only
- b)2 only
- c)Both 1 and 2
- d)Neither 1 nor 2
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Two beams, one having a square cross-section and another circular cro...
Area = a2 = A, material is same this means that E is the same.
Assuming same span length and loading beam having larger moment of inertia will have smaller deflection.
⇒ δrec < />cir
⇒ Statement 1 is wrong (Flexural strength)max = Mymax / 1 For the same bending moment, a beam having larger ymax / 1 will experience large flexural stress.
⇒ Circular section experience more flexural stress.
Most Upvoted Answer
Two beams, one having a square cross-section and another circular cro...
Explanation:
When a beam is subjected to bending, it experiences a combination of tensile and compressive stresses. The amount of deformation and the distribution of stress within the beam depend on its cross-sectional shape.
1. Both the beams will experience the same amount of deformation:
This statement is incorrect. The deformation of a beam under bending depends on its moment of inertia. The moment of inertia is a measure of how the mass is distributed around an axis. For a given cross-sectional area, the moment of inertia is different for a square and a circular cross-section.
The moment of inertia for a square cross-section is given by the formula I = (b^4)/12, where b is the side length of the square. The moment of inertia for a circular cross-section is given by the formula I = πr^4/4, where r is the radius of the circle.
Since the moment of inertia is different for the two cross-sectional shapes, the amount of deformation experienced by the beams will also be different. The beam with the circular cross-section will experience less deformation compared to the beam with the square cross-section.
2. The circular beam experiences more extreme flexural stress than the square one:
This statement is correct. Flexural stress is the stress that develops within a beam when it is subjected to bending. It is given by the formula σ = M*c/I, where M is the bending moment, c is the distance from the neutral axis to the outermost fiber of the beam, and I is the moment of inertia.
For a given bending moment and cross-sectional area, the moment of inertia is smaller for a circular cross-section compared to a square cross-section. This means that the flexural stress experienced by the circular beam will be larger than that experienced by the square beam.
This can be further understood by considering the distribution of stress within the beams. The stress is maximum at the outermost fibers of the beam. In a square cross-section, the outermost fibers are located farther away from the neutral axis compared to a circular cross-section. Therefore, the square beam experiences less extreme flexural stress compared to the circular beam.
Conclusion:
In conclusion, both beams will not experience the same amount of deformation. The circular beam will experience more extreme flexural stress compared to the square beam. Therefore, option 'B' is the correct answer.
When a beam is subjected to bending, it experiences a combination of tensile and compressive stresses. The amount of deformation and the distribution of stress within the beam depend on its cross-sectional shape.
1. Both the beams will experience the same amount of deformation:
This statement is incorrect. The deformation of a beam under bending depends on its moment of inertia. The moment of inertia is a measure of how the mass is distributed around an axis. For a given cross-sectional area, the moment of inertia is different for a square and a circular cross-section.
The moment of inertia for a square cross-section is given by the formula I = (b^4)/12, where b is the side length of the square. The moment of inertia for a circular cross-section is given by the formula I = πr^4/4, where r is the radius of the circle.
Since the moment of inertia is different for the two cross-sectional shapes, the amount of deformation experienced by the beams will also be different. The beam with the circular cross-section will experience less deformation compared to the beam with the square cross-section.
2. The circular beam experiences more extreme flexural stress than the square one:
This statement is correct. Flexural stress is the stress that develops within a beam when it is subjected to bending. It is given by the formula σ = M*c/I, where M is the bending moment, c is the distance from the neutral axis to the outermost fiber of the beam, and I is the moment of inertia.
For a given bending moment and cross-sectional area, the moment of inertia is smaller for a circular cross-section compared to a square cross-section. This means that the flexural stress experienced by the circular beam will be larger than that experienced by the square beam.
This can be further understood by considering the distribution of stress within the beams. The stress is maximum at the outermost fibers of the beam. In a square cross-section, the outermost fibers are located farther away from the neutral axis compared to a circular cross-section. Therefore, the square beam experiences less extreme flexural stress compared to the circular beam.
Conclusion:
In conclusion, both beams will not experience the same amount of deformation. The circular beam will experience more extreme flexural stress compared to the square beam. Therefore, option 'B' is the correct answer.
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Two beams, one having a square cross-section and another circular cross-section, are subjected to the same amount of bending moment. If the cross-sectional area as well as the material of both the beams are the same, then1. Both the beams will experience the same amount of deformation2. The circular beam experience more extreme flexural stress than the square oneWhich of the above is/are correct?a) 1 onlyb) 2 onlyc) Both 1 and 2d) Neither 1 nor 2Correct answer is option 'B'. Can you explain this answer?
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Two beams, one having a square cross-section and another circular cross-section, are subjected to the same amount of bending moment. If the cross-sectional area as well as the material of both the beams are the same, then1. Both the beams will experience the same amount of deformation2. The circular beam experience more extreme flexural stress than the square oneWhich of the above is/are correct?a) 1 onlyb) 2 onlyc) Both 1 and 2d) Neither 1 nor 2Correct 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, one having a square cross-section and another circular cross-section, are subjected to the same amount of bending moment. If the cross-sectional area as well as the material of both the beams are the same, then1. Both the beams will experience the same amount of deformation2. The circular beam experience more extreme flexural stress than the square oneWhich of the above is/are correct?a) 1 onlyb) 2 onlyc) Both 1 and 2d) Neither 1 nor 2Correct 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, one having a square cross-section and another circular cross-section, are subjected to the same amount of bending moment. If the cross-sectional area as well as the material of both the beams are the same, then1. Both the beams will experience the same amount of deformation2. The circular beam experience more extreme flexural stress than the square oneWhich of the above is/are correct?a) 1 onlyb) 2 onlyc) Both 1 and 2d) Neither 1 nor 2Correct answer is option 'B'. Can you explain this answer?.
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