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A hollow circular section of an internal and external diameter of 80mm and 40mm and a solid circular section of diameter same as that of the outer diameter of the hollow section is subjected to eccentric loading. The ratio of kerns of the hollow section to the solid section is(round up to 2 decimal places)
- a)1.22
- b)1.28
Correct answer is between '1.22,1.28'. Can you explain this answer?
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A hollow circular section of an internal and external diameter of 80m...
Given data:
- Internal diameter of hollow circular section (di): 80mm
- External diameter of hollow circular section (do): 40mm
- Diameter of solid circular section (ds): 40mm
To find: Ratio of kerns of hollow section to solid section
Assumptions:
- The material is homogeneous and isotropic
- The load is applied eccentrically, causing bending stresses
Formula:
- Kern of a section is the distance from the neutral axis to the point where the stress is maximum.
- Neutral axis is the line passing through the centroid of the section, where the stresses are zero.
- For a circular section, the neutral axis is at the center of the circle.
- The ratio of kerns of two sections can be found by dividing their respective distances from the neutral axis to the point where the stress is maximum.
Solution:
1. Calculate the distance between the centroid and the outer surface (r) for both sections:
- For hollow section: r = (do + di) / 4 = (80 + 40) / 4 = 30mm
- For solid section: r = ds / 2 = 20mm
2. Calculate the maximum stress (σmax) for both sections:
- For hollow section: σmax = M / (Zp - Zc)
- M = eccentric moment
- Zp = section modulus about the point where the stress is maximum (i.e. outer surface)
- Zc = section modulus about the centroid
- Zp = π/32 x (do^4 - di^4) / do = π/32 x (40^4 - 80^4) / 40 = 1.37 x 10^6 mm^3
- Zc = π/64 x (do^4 - di^4) / do = π/64 x (40^4 - 80^4) / 40 = 6.86 x 10^5 mm^3
- σmax = 100 Nm / (1.37 x 10^6 - 6.86 x 10^5) = 146.3 N/mm^2
- For solid section: σmax = M / (Zp - Zc)
- M = eccentric moment
- Zp = section modulus about the point where the stress is maximum (i.e. outer surface)
- Zc = section modulus about the centroid
- Zp = π/32 x ds^3 = π/32 x 40^3 = 5.05 x 10^5 mm^3
- Zc = π/64 x ds^3 = π/64 x 40^3 = 2.53 x 10^5 mm^3
- σmax = 100 Nm / (5.05 x 10^5 - 2.53 x 10^5) = 200 N/mm^2
3. Calculate the distance between the neutral axis and the point where the stress is maximum (y) for both sections:
- For hollow section: y = r x (σmax / E)
- E = modulus of elasticity = 200 GPa = 200 x 10^3 N/mm^2
- y = 30 x (146.3 / 200 x
- Internal diameter of hollow circular section (di): 80mm
- External diameter of hollow circular section (do): 40mm
- Diameter of solid circular section (ds): 40mm
To find: Ratio of kerns of hollow section to solid section
Assumptions:
- The material is homogeneous and isotropic
- The load is applied eccentrically, causing bending stresses
Formula:
- Kern of a section is the distance from the neutral axis to the point where the stress is maximum.
- Neutral axis is the line passing through the centroid of the section, where the stresses are zero.
- For a circular section, the neutral axis is at the center of the circle.
- The ratio of kerns of two sections can be found by dividing their respective distances from the neutral axis to the point where the stress is maximum.
Solution:
1. Calculate the distance between the centroid and the outer surface (r) for both sections:
- For hollow section: r = (do + di) / 4 = (80 + 40) / 4 = 30mm
- For solid section: r = ds / 2 = 20mm
2. Calculate the maximum stress (σmax) for both sections:
- For hollow section: σmax = M / (Zp - Zc)
- M = eccentric moment
- Zp = section modulus about the point where the stress is maximum (i.e. outer surface)
- Zc = section modulus about the centroid
- Zp = π/32 x (do^4 - di^4) / do = π/32 x (40^4 - 80^4) / 40 = 1.37 x 10^6 mm^3
- Zc = π/64 x (do^4 - di^4) / do = π/64 x (40^4 - 80^4) / 40 = 6.86 x 10^5 mm^3
- σmax = 100 Nm / (1.37 x 10^6 - 6.86 x 10^5) = 146.3 N/mm^2
- For solid section: σmax = M / (Zp - Zc)
- M = eccentric moment
- Zp = section modulus about the point where the stress is maximum (i.e. outer surface)
- Zc = section modulus about the centroid
- Zp = π/32 x ds^3 = π/32 x 40^3 = 5.05 x 10^5 mm^3
- Zc = π/64 x ds^3 = π/64 x 40^3 = 2.53 x 10^5 mm^3
- σmax = 100 Nm / (5.05 x 10^5 - 2.53 x 10^5) = 200 N/mm^2
3. Calculate the distance between the neutral axis and the point where the stress is maximum (y) for both sections:
- For hollow section: y = r x (σmax / E)
- E = modulus of elasticity = 200 GPa = 200 x 10^3 N/mm^2
- y = 30 x (146.3 / 200 x
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Community Answer
A hollow circular section of an internal and external diameter of 80m...
Kern of a section is eccentricty along which the section is never subjected to tension.
For a solid circular section subjected to eccentric loading,
For a hollow circular section subjected to eccentric loading,
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A hollow circular section of an internal and external diameter of 80mm and 40mm and a solid circular section of diameter same as that of the outer diameter of the hollow section is subjected to eccentric loading. The ratio of kerns of the hollow section to the solid section is(round up to 2 decimal places)a)1.22b)1.28Correct answer is between '1.22,1.28'. Can you explain this answer?
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A hollow circular section of an internal and external diameter of 80mm and 40mm and a solid circular section of diameter same as that of the outer diameter of the hollow section is subjected to eccentric loading. The ratio of kerns of the hollow section to the solid section is(round up to 2 decimal places)a)1.22b)1.28Correct answer is between '1.22,1.28'. Can you explain this answer? 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 A hollow circular section of an internal and external diameter of 80mm and 40mm and a solid circular section of diameter same as that of the outer diameter of the hollow section is subjected to eccentric loading. The ratio of kerns of the hollow section to the solid section is(round up to 2 decimal places)a)1.22b)1.28Correct answer is between '1.22,1.28'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A hollow circular section of an internal and external diameter of 80mm and 40mm and a solid circular section of diameter same as that of the outer diameter of the hollow section is subjected to eccentric loading. The ratio of kerns of the hollow section to the solid section is(round up to 2 decimal places)a)1.22b)1.28Correct answer is between '1.22,1.28'. Can you explain this answer?.
A hollow circular section of an internal and external diameter of 80mm and 40mm and a solid circular section of diameter same as that of the outer diameter of the hollow section is subjected to eccentric loading. The ratio of kerns of the hollow section to the solid section is(round up to 2 decimal places)a)1.22b)1.28Correct answer is between '1.22,1.28'. Can you explain this answer? 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 A hollow circular section of an internal and external diameter of 80mm and 40mm and a solid circular section of diameter same as that of the outer diameter of the hollow section is subjected to eccentric loading. The ratio of kerns of the hollow section to the solid section is(round up to 2 decimal places)a)1.22b)1.28Correct answer is between '1.22,1.28'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A hollow circular section of an internal and external diameter of 80mm and 40mm and a solid circular section of diameter same as that of the outer diameter of the hollow section is subjected to eccentric loading. The ratio of kerns of the hollow section to the solid section is(round up to 2 decimal places)a)1.22b)1.28Correct answer is between '1.22,1.28'. Can you explain this answer?.
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