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A Cantilever beam of rectangular cross-section is 1m deep and 0.6 m thick. If the beam were to be 0.6 m deep and 1m 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 'B'. Can you explain this answer?
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The bending strength of a beam is directly proportional to the moment of inertia of its cross-section. The moment of inertia of a rectangular cross-section is given by the equation I = (1/12)bh^3, where b is the width and h is the depth of the beam.

Given:
- Original beam: b=0.6m, h=1m
- Modified beam: b=1m, h=0.6m

To compare the moment of inertia of the original and modified beams, we can use the ratio of their moment of inertia:

I_modified / I_original = (1/12)(1m)(0.6m)^3 / (1/12)(0.6m)(1m)^3
= (0.6)^2

Therefore, the moment of inertia of the modified beam is weakened by a factor of (0.6)^2 = 0.36.

Since the bending strength of a beam is directly proportional to its moment of inertia, the modified beam is weakened by the same factor of 0.36.

Therefore, the correct answer is option B: the modified beam is weakened by 0.6 times.
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A Cantilever beam of rectangular cross-section is 1m deep and 0.6 m thick. If the beam were to be 0.6 m deep and 1m thick, then the beam would.a)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 'B'. Can you explain this answer?
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A Cantilever beam of rectangular cross-section is 1m deep and 0.6 m thick. If the beam were to be 0.6 m deep and 1m thick, then the beam would.a)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 '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 A Cantilever beam of rectangular cross-section is 1m deep and 0.6 m thick. If the beam were to be 0.6 m deep and 1m thick, then the beam would.a)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 '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 A Cantilever beam of rectangular cross-section is 1m deep and 0.6 m thick. If the beam were to be 0.6 m deep and 1m thick, then the beam would.a)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 'B'. Can you explain this answer?.
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