Mechanical Engineering Exam > Mechanical Engineering Questions > Consider a beam with circular cross-section o...
Start Learning for Free
Consider a beam with circular cross-section of diameter d. The ratio of the second moment of area about the neutral axis to the section modulus of the area is.
- a)d/2
- b)πd/2
- c)d
- d)πd
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Consider a beam with circular cross-section of diameter d. The ratio o...
For a solid circular cross-section
Ymax=d/2
Most Upvoted Answer
Consider a beam with circular cross-section of diameter d. The ratio o...
Understanding the Beam Properties
To analyze the properties of a circular cross-section beam, we need to define two key terms: the second moment of area (I) and the section modulus (Z).
Second Moment of Area (I)
- For a circular cross-section with diameter d, the second moment of area about the neutral axis is given by:
I = (π/64) * d^4
Section Modulus (Z)
- The section modulus is derived from the moment of inertia and is used to determine the strength of the beam. For a circular section:
Z = I / (d/2) = (π/32) * d^3
Calculating the Ratio
To find the ratio of the second moment of area to the section modulus, we perform the following calculation:
- Ratio = I / Z
Substituting the expressions for I and Z:
- Ratio = [(π/64) * d^4] / [(π/32) * d^3]
This simplifies to:
- Ratio = (1/2) * d = d/2
Conclusion
Thus, the ratio of the second moment of area to the section modulus for a beam with a circular cross-section of diameter d is indeed d/2, confirming that option 'A' is correct. This relationship is crucial for engineers to understand the beam's ability to resist bending and deflection.
To analyze the properties of a circular cross-section beam, we need to define two key terms: the second moment of area (I) and the section modulus (Z).
Second Moment of Area (I)
- For a circular cross-section with diameter d, the second moment of area about the neutral axis is given by:
I = (π/64) * d^4
Section Modulus (Z)
- The section modulus is derived from the moment of inertia and is used to determine the strength of the beam. For a circular section:
Z = I / (d/2) = (π/32) * d^3
Calculating the Ratio
To find the ratio of the second moment of area to the section modulus, we perform the following calculation:
- Ratio = I / Z
Substituting the expressions for I and Z:
- Ratio = [(π/64) * d^4] / [(π/32) * d^3]
This simplifies to:
- Ratio = (1/2) * d = d/2
Conclusion
Thus, the ratio of the second moment of area to the section modulus for a beam with a circular cross-section of diameter d is indeed d/2, confirming that option 'A' is correct. This relationship is crucial for engineers to understand the beam's ability to resist bending and deflection.
|
Explore Courses for Mechanical Engineering exam
|
|
Similar Mechanical Engineering Doubts
Top Courses for Mechanical EngineeringView all
Consider a beam with circular cross-section of diameter d. The ratio of the second moment of area about the neutral axis to the section modulus of the area is.a)d/2b)πd/2c)dd)πdCorrect answer is option 'A'. Can you explain this answer?
Question Description
Consider a beam with circular cross-section of diameter d. The ratio of the second moment of area about the neutral axis to the section modulus of the area is.a)d/2b)πd/2c)dd)πdCorrect answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Consider a beam with circular cross-section of diameter d. The ratio of the second moment of area about the neutral axis to the section modulus of the area is.a)d/2b)πd/2c)dd)πdCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a beam with circular cross-section of diameter d. The ratio of the second moment of area about the neutral axis to the section modulus of the area is.a)d/2b)πd/2c)dd)πdCorrect answer is option 'A'. Can you explain this answer?.
Consider a beam with circular cross-section of diameter d. The ratio of the second moment of area about the neutral axis to the section modulus of the area is.a)d/2b)πd/2c)dd)πdCorrect answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Consider a beam with circular cross-section of diameter d. The ratio of the second moment of area about the neutral axis to the section modulus of the area is.a)d/2b)πd/2c)dd)πdCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a beam with circular cross-section of diameter d. The ratio of the second moment of area about the neutral axis to the section modulus of the area is.a)d/2b)πd/2c)dd)πdCorrect answer is option 'A'. Can you explain this answer?.
Solutions for Consider a beam with circular cross-section of diameter d. The ratio of the second moment of area about the neutral axis to the section modulus of the area is.a)d/2b)πd/2c)dd)πdCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
Download more important topics, notes, lectures and mock test series for Mechanical Engineering Exam by signing up for free.
Here you can find the meaning of Consider a beam with circular cross-section of diameter d. The ratio of the second moment of area about the neutral axis to the section modulus of the area is.a)d/2b)πd/2c)dd)πdCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Consider a beam with circular cross-section of diameter d. The ratio of the second moment of area about the neutral axis to the section modulus of the area is.a)d/2b)πd/2c)dd)πdCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for Consider a beam with circular cross-section of diameter d. The ratio of the second moment of area about the neutral axis to the section modulus of the area is.a)d/2b)πd/2c)dd)πdCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of Consider a beam with circular cross-section of diameter d. The ratio of the second moment of area about the neutral axis to the section modulus of the area is.a)d/2b)πd/2c)dd)πdCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Consider a beam with circular cross-section of diameter d. The ratio of the second moment of area about the neutral axis to the section modulus of the area is.a)d/2b)πd/2c)dd)πdCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
|
|
Explore Courses for Mechanical Engineering exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup