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The ratio of the slenderness ratio of a vertical column of square cross-section of side 15cm to the slenderness ratio of a vertical column of circular cross-section of diameter 15cm having Same effective length will be?
- a)1.225
- b)1.00
- c)1.154
- d)0.866
Correct answer is option 'D'. Can you explain this answer?
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The ratio of the slenderness ratio of a vertical column of square cros...
**Given:**
- Side of square cross-section = 15 cm
- Diameter of circular cross-section = 15 cm
**To find:**
The ratio of the slenderness ratio of the square column to the slenderness ratio of the circular column.
**Explanation:**
The slenderness ratio is a measure of the column's ability to resist buckling under compressive loads. It is defined as the ratio of the effective length of the column to the least radius of gyration.
The effective length of a column is the length between its points of lateral support. In this case, since both columns are vertical, the effective length will be the same for both.
The radius of gyration is a measure of how the cross-section is distributed about its centroid. It is given by the formula:
r = √(I/A)
Where:
- r is the radius of gyration
- I is the moment of inertia of the cross-section
- A is the area of the cross-section
**For the square column:**
- Area (A) = (side)^2 = 15^2 = 225 cm^2
- Moment of inertia (I) = (side^4)/12 = (15^4)/12 = 2812.5 cm^4
- Radius of gyration (r) = √(2812.5/225) = √12.5 = 3.536 cm
**For the circular column:**
- Area (A) = π(radius)^2 = π(7.5)^2 = 176.71 cm^2
- Moment of inertia (I) = (π/4)(radius)^4 = (π/4)(7.5)^4 = 2193.75 cm^4
- Radius of gyration (r) = √(2193.75/176.71) = √12.41 = 3.519 cm
**Slenderness ratio:**
The slenderness ratio (SR) is given by the formula:
SR = (effective length)/(radius of gyration)
Since the effective length is the same for both columns, the ratio of the slenderness ratios will be:
SR(square)/SR(circular) = (SR(square))/(SR(circular)) = (r(square))/(r(circular))
Substituting the values of r(square) and r(circular):
= 3.536 cm / 3.519 cm ≈ 1.00
Therefore, the ratio of the slenderness ratio of the square column to the slenderness ratio of the circular column is approximately 1.00.
Hence, the correct answer is option b) 1.00.
- Side of square cross-section = 15 cm
- Diameter of circular cross-section = 15 cm
**To find:**
The ratio of the slenderness ratio of the square column to the slenderness ratio of the circular column.
**Explanation:**
The slenderness ratio is a measure of the column's ability to resist buckling under compressive loads. It is defined as the ratio of the effective length of the column to the least radius of gyration.
The effective length of a column is the length between its points of lateral support. In this case, since both columns are vertical, the effective length will be the same for both.
The radius of gyration is a measure of how the cross-section is distributed about its centroid. It is given by the formula:
r = √(I/A)
Where:
- r is the radius of gyration
- I is the moment of inertia of the cross-section
- A is the area of the cross-section
**For the square column:**
- Area (A) = (side)^2 = 15^2 = 225 cm^2
- Moment of inertia (I) = (side^4)/12 = (15^4)/12 = 2812.5 cm^4
- Radius of gyration (r) = √(2812.5/225) = √12.5 = 3.536 cm
**For the circular column:**
- Area (A) = π(radius)^2 = π(7.5)^2 = 176.71 cm^2
- Moment of inertia (I) = (π/4)(radius)^4 = (π/4)(7.5)^4 = 2193.75 cm^4
- Radius of gyration (r) = √(2193.75/176.71) = √12.41 = 3.519 cm
**Slenderness ratio:**
The slenderness ratio (SR) is given by the formula:
SR = (effective length)/(radius of gyration)
Since the effective length is the same for both columns, the ratio of the slenderness ratios will be:
SR(square)/SR(circular) = (SR(square))/(SR(circular)) = (r(square))/(r(circular))
Substituting the values of r(square) and r(circular):
= 3.536 cm / 3.519 cm ≈ 1.00
Therefore, the ratio of the slenderness ratio of the square column to the slenderness ratio of the circular column is approximately 1.00.
Hence, the correct answer is option b) 1.00.
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The ratio of the slenderness ratio of a vertical column of square cross-section of side 15cm to the slenderness ratio of a vertical column of circular cross-section of diameter 15cm having Same effective length will be?a)1.225b)1.00c)1.154d)0.866Correct answer is option 'D'. Can you explain this answer?
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The ratio of the slenderness ratio of a vertical column of square cross-section of side 15cm to the slenderness ratio of a vertical column of circular cross-section of diameter 15cm having Same effective length will be?a)1.225b)1.00c)1.154d)0.866Correct answer is option 'D'. 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 The ratio of the slenderness ratio of a vertical column of square cross-section of side 15cm to the slenderness ratio of a vertical column of circular cross-section of diameter 15cm having Same effective length will be?a)1.225b)1.00c)1.154d)0.866Correct answer is option 'D'. 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 The ratio of the slenderness ratio of a vertical column of square cross-section of side 15cm to the slenderness ratio of a vertical column of circular cross-section of diameter 15cm having Same effective length will be?a)1.225b)1.00c)1.154d)0.866Correct answer is option 'D'. Can you explain this answer?.
The ratio of the slenderness ratio of a vertical column of square cross-section of side 15cm to the slenderness ratio of a vertical column of circular cross-section of diameter 15cm having Same effective length will be?a)1.225b)1.00c)1.154d)0.866Correct answer is option 'D'. 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 The ratio of the slenderness ratio of a vertical column of square cross-section of side 15cm to the slenderness ratio of a vertical column of circular cross-section of diameter 15cm having Same effective length will be?a)1.225b)1.00c)1.154d)0.866Correct answer is option 'D'. 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 The ratio of the slenderness ratio of a vertical column of square cross-section of side 15cm to the slenderness ratio of a vertical column of circular cross-section of diameter 15cm having Same effective length will be?a)1.225b)1.00c)1.154d)0.866Correct answer is option 'D'. Can you explain this answer?.
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