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A 3m high pole stands as a vertical cantilever fixed at its base. It has to support a horizontal load of 10kN at its top. Find the minimum diameter required if the pole is of wood, if the permissible bending stress is 15N/mm2
- a)221 mm
- b)546 mm
- c)273 mm
- d)190 mm
Correct answer is option 'C'. Can you explain this answer?
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A 3m high pole stands as a verticalcantilever fixed at its base. It ha...
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To determine the minimum diameter required for the wooden pole to support a horizontal load of 10kN at its top, we need to consider the bending stress experienced by the pole. The permissible bending stress is given as 15 N/mm2.
Let's analyze the problem step by step:
1. Identifying the forces:
- Vertical load: The weight of the pole itself is neglected in this problem.
- Horizontal load: 10kN at the top of the pole.
2. Calculating the bending moment:
The bending moment is the product of the horizontal load and the height of the pole. In this case, the bending moment is given by:
Bending Moment = Load × Height
Bending Moment = 10kN × 3m = 30kNm
3. Calculating the section modulus:
The section modulus is a property of the cross-section of the pole and is related to its ability to resist bending. For a circular cross-section, the section modulus is given by:
Section Modulus (Z) = πd^3/32, where d is the diameter of the pole.
4. Calculating the bending stress:
The bending stress is given by the formula:
Bending Stress = Bending Moment / Section Modulus
5. Determining the minimum diameter:
We can rearrange the formula for the section modulus to solve for the diameter:
d = 2∛(32Z/π)
where Z = Bending Moment / Bending Stress
Now, substituting the given values:
Z = 30kNm / 15N/mm2 = 2000mm3
d = 2∛(32 × 2000 / π)
d ≈ 273mm
Therefore, the minimum diameter required for the wooden pole to support the given load is approximately 273 mm. Hence, the correct answer is option 'C' (273 mm).
Let's analyze the problem step by step:
1. Identifying the forces:
- Vertical load: The weight of the pole itself is neglected in this problem.
- Horizontal load: 10kN at the top of the pole.
2. Calculating the bending moment:
The bending moment is the product of the horizontal load and the height of the pole. In this case, the bending moment is given by:
Bending Moment = Load × Height
Bending Moment = 10kN × 3m = 30kNm
3. Calculating the section modulus:
The section modulus is a property of the cross-section of the pole and is related to its ability to resist bending. For a circular cross-section, the section modulus is given by:
Section Modulus (Z) = πd^3/32, where d is the diameter of the pole.
4. Calculating the bending stress:
The bending stress is given by the formula:
Bending Stress = Bending Moment / Section Modulus
5. Determining the minimum diameter:
We can rearrange the formula for the section modulus to solve for the diameter:
d = 2∛(32Z/π)
where Z = Bending Moment / Bending Stress
Now, substituting the given values:
Z = 30kNm / 15N/mm2 = 2000mm3
d = 2∛(32 × 2000 / π)
d ≈ 273mm
Therefore, the minimum diameter required for the wooden pole to support the given load is approximately 273 mm. Hence, the correct answer is option 'C' (273 mm).
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A 3m high pole stands as a verticalcantilever fixed at its base. It has tosupport a horizontal load of 10kNat its top. Find the minimumdiameter required if the pole is ofwood, if the permissible bendingstress is 15N/mm2a)221 mmb)546 mmc)273 mmd)190 mmCorrect answer is option 'C'. Can you explain this answer?
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A 3m high pole stands as a verticalcantilever fixed at its base. It has tosupport a horizontal load of 10kNat its top. Find the minimumdiameter required if the pole is ofwood, if the permissible bendingstress is 15N/mm2a)221 mmb)546 mmc)273 mmd)190 mmCorrect answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A 3m high pole stands as a verticalcantilever fixed at its base. It has tosupport a horizontal load of 10kNat its top. Find the minimumdiameter required if the pole is ofwood, if the permissible bendingstress is 15N/mm2a)221 mmb)546 mmc)273 mmd)190 mmCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 3m high pole stands as a verticalcantilever fixed at its base. It has tosupport a horizontal load of 10kNat its top. Find the minimumdiameter required if the pole is ofwood, if the permissible bendingstress is 15N/mm2a)221 mmb)546 mmc)273 mmd)190 mmCorrect answer is option 'C'. Can you explain this answer?.
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