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The diameter of the concrete flag post varies from 200mm at base and 100mm at the top. If the height of the post is 8m and a horizontal load of 500N is acting at the top a) find the section at which the stress is maximum? b) Find the maximum stress?
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The diameter of the concrete flag post varies from 200mm at base and 1...
Determining the Section of Maximum Stress and the Maximum Stress in a Concrete Flag Post
To determine the section at which the stress is maximum and the maximum stress in a concrete flag post, we need to analyze the variation in diameter along the height of the post and consider the applied horizontal load.
Given data:
- Diameter at the base (D1) = 200mm
- Diameter at the top (D2) = 100mm
- Height of the post (h) = 8m
- Applied horizontal load (F) = 500N
Section at which the stress is maximum:
The stress in a cylindrical object like a flag post is directly proportional to the bending moment. The bending moment is maximum at the base and decreases linearly towards the top. Therefore, the section at which the stress is maximum is at the base of the flag post.
Maximum stress:
The maximum stress can be calculated using the bending moment formula:
Stress = (M * y) / I
Where:
- M = Bending moment
- y = Distance from the neutral axis to the outermost fiber
- I = Moment of inertia
Calculating the maximum stress:
1. Determine the bending moment at the base of the flag post using the formula:
M = F * h
Where:
- F = Applied horizontal load
- h = Height of the post
Substituting the given values:
M = 500N * 8m = 4000 Nm
2. Calculate the distance from the neutral axis to the outermost fiber (y) at the base:
y = D1 / 2
Substituting D1 = 200mm = 0.2m:
y = 0.2m / 2 = 0.1m
3. Determine the moment of inertia (I) for the circular cross-section:
I = (π/64) * (D1^4 - D2^4)
Substituting D1 = 200mm = 0.2m and D2 = 100mm = 0.1m:
I = (π/64) * (0.2^4 - 0.1^4) = 0.0003927 m^4
4. Substitute the values into the stress formula:
Stress = (M * y) / I
Stress = (4000 Nm * 0.1m) / 0.0003927 m^4 = 1.016 x 10^8 N/m^2
Conclusion:
a) The section at which the stress is maximum is at the base of the flag post.
b) The maximum stress in the flag post is approximately 1.016 x 10^8 N/m^2.
To determine the section at which the stress is maximum and the maximum stress in a concrete flag post, we need to analyze the variation in diameter along the height of the post and consider the applied horizontal load.
Given data:
- Diameter at the base (D1) = 200mm
- Diameter at the top (D2) = 100mm
- Height of the post (h) = 8m
- Applied horizontal load (F) = 500N
Section at which the stress is maximum:
The stress in a cylindrical object like a flag post is directly proportional to the bending moment. The bending moment is maximum at the base and decreases linearly towards the top. Therefore, the section at which the stress is maximum is at the base of the flag post.
Maximum stress:
The maximum stress can be calculated using the bending moment formula:
Stress = (M * y) / I
Where:
- M = Bending moment
- y = Distance from the neutral axis to the outermost fiber
- I = Moment of inertia
Calculating the maximum stress:
1. Determine the bending moment at the base of the flag post using the formula:
M = F * h
Where:
- F = Applied horizontal load
- h = Height of the post
Substituting the given values:
M = 500N * 8m = 4000 Nm
2. Calculate the distance from the neutral axis to the outermost fiber (y) at the base:
y = D1 / 2
Substituting D1 = 200mm = 0.2m:
y = 0.2m / 2 = 0.1m
3. Determine the moment of inertia (I) for the circular cross-section:
I = (π/64) * (D1^4 - D2^4)
Substituting D1 = 200mm = 0.2m and D2 = 100mm = 0.1m:
I = (π/64) * (0.2^4 - 0.1^4) = 0.0003927 m^4
4. Substitute the values into the stress formula:
Stress = (M * y) / I
Stress = (4000 Nm * 0.1m) / 0.0003927 m^4 = 1.016 x 10^8 N/m^2
Conclusion:
a) The section at which the stress is maximum is at the base of the flag post.
b) The maximum stress in the flag post is approximately 1.016 x 10^8 N/m^2.
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The diameter of the concrete flag post varies from 200mm at base and 100mm at the top. If the height of the post is 8m and a horizontal load of 500N is acting at the top a) find the section at which the stress is maximum? b) Find the maximum stress?
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The diameter of the concrete flag post varies from 200mm at base and 100mm at the top. If the height of the post is 8m and a horizontal load of 500N is acting at the top a) find the section at which the stress is maximum? b) Find the maximum stress? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The diameter of the concrete flag post varies from 200mm at base and 100mm at the top. If the height of the post is 8m and a horizontal load of 500N is acting at the top a) find the section at which the stress is maximum? b) Find the maximum stress? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The diameter of the concrete flag post varies from 200mm at base and 100mm at the top. If the height of the post is 8m and a horizontal load of 500N is acting at the top a) find the section at which the stress is maximum? b) Find the maximum stress?.
The diameter of the concrete flag post varies from 200mm at base and 100mm at the top. If the height of the post is 8m and a horizontal load of 500N is acting at the top a) find the section at which the stress is maximum? b) Find the maximum stress? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The diameter of the concrete flag post varies from 200mm at base and 100mm at the top. If the height of the post is 8m and a horizontal load of 500N is acting at the top a) find the section at which the stress is maximum? b) Find the maximum stress? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The diameter of the concrete flag post varies from 200mm at base and 100mm at the top. If the height of the post is 8m and a horizontal load of 500N is acting at the top a) find the section at which the stress is maximum? b) Find the maximum stress?.
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