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A cantilever beam of rectangular cross-section is 1 m deep and 0.6 m thick. If the beam were to be 0.6 m deep and 1 m thick then the beam would
- a)be weakened 0.5 times
- b)be weakened 0.6 times
- c)be strengthened 0.6 times
- d)have the same strength as the original beam because the cross-sectional area remains the same
Correct answer is option 'C'. Can you explain this answer?
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Explanation:
To understand why the beam would be strengthened 0.6 times, we need to consider the moment of inertia of the beam.
The moment of inertia (I) of a rectangular cross-section beam is given by the equation:
I = (b * h^3) / 12
Where b is the breadth or thickness of the beam, and h is the depth of the beam.
Original Beam:
In the original beam, the breadth (b) is 0.6 m and the depth (h) is 1 m. Therefore, the moment of inertia (I1) can be calculated as:
I1 = (0.6 * 1^3) / 12 = 0.05 m^4
Modified Beam:
In the modified beam, the breadth (b) is 1 m and the depth (h) is 0.6 m. Therefore, the moment of inertia (I2) can be calculated as:
I2 = (1 * 0.6^3) / 12 = 0.036 m^4
Comparison:
To compare the strengths of the two beams, we can compare their moments of inertia. A higher moment of inertia indicates a stronger beam.
The ratio of the moment of inertia of the modified beam (I2) to the moment of inertia of the original beam (I1) can be calculated as:
Ratio = I2 / I1 = 0.036 / 0.05 = 0.72
Therefore, the modified beam is 0.72 times as strong as the original beam.
Conclusion:
Since the modified beam has a higher moment of inertia, it is stronger than the original beam. Thus, the correct answer is option 'C': the beam would be strengthened 0.6 times.
To understand why the beam would be strengthened 0.6 times, we need to consider the moment of inertia of the beam.
The moment of inertia (I) of a rectangular cross-section beam is given by the equation:
I = (b * h^3) / 12
Where b is the breadth or thickness of the beam, and h is the depth of the beam.
Original Beam:
In the original beam, the breadth (b) is 0.6 m and the depth (h) is 1 m. Therefore, the moment of inertia (I1) can be calculated as:
I1 = (0.6 * 1^3) / 12 = 0.05 m^4
Modified Beam:
In the modified beam, the breadth (b) is 1 m and the depth (h) is 0.6 m. Therefore, the moment of inertia (I2) can be calculated as:
I2 = (1 * 0.6^3) / 12 = 0.036 m^4
Comparison:
To compare the strengths of the two beams, we can compare their moments of inertia. A higher moment of inertia indicates a stronger beam.
The ratio of the moment of inertia of the modified beam (I2) to the moment of inertia of the original beam (I1) can be calculated as:
Ratio = I2 / I1 = 0.036 / 0.05 = 0.72
Therefore, the modified beam is 0.72 times as strong as the original beam.
Conclusion:
Since the modified beam has a higher moment of inertia, it is stronger than the original beam. Thus, the correct answer is option 'C': the beam would be strengthened 0.6 times.
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A cantilever beam of rectangular cross-section is 1 m deep and 0.6 m thick. If the beam were to be 0.6 m deep and 1 m thick then the beam woulda)be weakened 0.5 timesb)be weakened 0.6 timesc)be strengthened 0.6 timesd)have the same strength as the original beam because the cross-sectional area remains the sameCorrect answer is option 'C'. Can you explain this answer?
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A cantilever beam of rectangular cross-section is 1 m deep and 0.6 m thick. If the beam were to be 0.6 m deep and 1 m thick then the beam woulda)be weakened 0.5 timesb)be weakened 0.6 timesc)be strengthened 0.6 timesd)have the same strength as the original beam because the cross-sectional area remains the sameCorrect 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 A cantilever beam of rectangular cross-section is 1 m deep and 0.6 m thick. If the beam were to be 0.6 m deep and 1 m thick then the beam woulda)be weakened 0.5 timesb)be weakened 0.6 timesc)be strengthened 0.6 timesd)have the same strength as the original beam because the cross-sectional area remains the sameCorrect 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 A cantilever beam of rectangular cross-section is 1 m deep and 0.6 m thick. If the beam were to be 0.6 m deep and 1 m thick then the beam woulda)be weakened 0.5 timesb)be weakened 0.6 timesc)be strengthened 0.6 timesd)have the same strength as the original beam because the cross-sectional area remains the sameCorrect answer is option 'C'. Can you explain this answer?.
A cantilever beam of rectangular cross-section is 1 m deep and 0.6 m thick. If the beam were to be 0.6 m deep and 1 m thick then the beam woulda)be weakened 0.5 timesb)be weakened 0.6 timesc)be strengthened 0.6 timesd)have the same strength as the original beam because the cross-sectional area remains the sameCorrect 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 A cantilever beam of rectangular cross-section is 1 m deep and 0.6 m thick. If the beam were to be 0.6 m deep and 1 m thick then the beam woulda)be weakened 0.5 timesb)be weakened 0.6 timesc)be strengthened 0.6 timesd)have the same strength as the original beam because the cross-sectional area remains the sameCorrect 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 A cantilever beam of rectangular cross-section is 1 m deep and 0.6 m thick. If the beam were to be 0.6 m deep and 1 m thick then the beam woulda)be weakened 0.5 timesb)be weakened 0.6 timesc)be strengthened 0.6 timesd)have the same strength as the original beam because the cross-sectional area remains the sameCorrect answer is option 'C'. Can you explain this answer?.
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