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The column of length 240 cm, area of cross- section 20 cm 2, moment of inertia 1XX = 720 cm4 and Iyy = 80 cm4 is subject to buckling load. The data corresponds to slenderness ratio
- a)40
- b)80
- c)120
- d)160
Correct answer is option 'C'. Can you explain this answer?
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The column of length 240 cm, area of cross- section 20 cm 2, moment of...
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Slenderness ratio is the ratio of length and least radius of gyration
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The column of length 240 cm, area of cross- section 20 cm 2, moment of...
Slenderness Ratio:
The slenderness ratio of a column is a measure of its tendency to buckle under compressive load. It is defined as the ratio of the effective length of the column to its least radius of gyration.
Effective Length:
The effective length of a column is the length of an equivalent pin-ended column that would buckle under the same compressive load as the actual column. It depends on the boundary conditions and the type of column.
Least Radius of Gyration:
The least radius of gyration is a measure of the distribution of the area of the cross-section with respect to its centroid. It is calculated as the square root of the ratio of the moment of inertia about an axis to the area of the cross-section.
Given Parameters:
- Length of the column (L) = 240 cm
- Area of cross-section (A) = 20 cm^2
- Moment of inertia about x-axis (Ixx) = 720 cm^4
- Moment of inertia about y-axis (Iyy) = 80 cm^4
Calculating the Slenderness Ratio:
To calculate the slenderness ratio, we need to find the effective length and the least radius of gyration.
Effective Length:
The effective length depends on the boundary conditions. Assuming the column is pin-ended, the effective length is equal to the actual length of the column, which is 240 cm.
Least Radius of Gyration:
The least radius of gyration can be calculated using the formula:
k = sqrt(I/A)
For the x-axis:
kx = sqrt(Ixx/A) = sqrt(720 cm^4 / 20 cm^2) = sqrt(36 cm^2) = 6 cm
For the y-axis:
ky = sqrt(Iyy/A) = sqrt(80 cm^4 / 20 cm^2) = sqrt(4 cm^2) = 2 cm
Slenderness Ratio:
The slenderness ratio (λ) is calculated as the ratio of the effective length to the least radius of gyration:
λ = L/k = 240 cm / 2 cm = 120
Therefore, the slenderness ratio is 120.
The slenderness ratio of a column is a measure of its tendency to buckle under compressive load. It is defined as the ratio of the effective length of the column to its least radius of gyration.
Effective Length:
The effective length of a column is the length of an equivalent pin-ended column that would buckle under the same compressive load as the actual column. It depends on the boundary conditions and the type of column.
Least Radius of Gyration:
The least radius of gyration is a measure of the distribution of the area of the cross-section with respect to its centroid. It is calculated as the square root of the ratio of the moment of inertia about an axis to the area of the cross-section.
Given Parameters:
- Length of the column (L) = 240 cm
- Area of cross-section (A) = 20 cm^2
- Moment of inertia about x-axis (Ixx) = 720 cm^4
- Moment of inertia about y-axis (Iyy) = 80 cm^4
Calculating the Slenderness Ratio:
To calculate the slenderness ratio, we need to find the effective length and the least radius of gyration.
Effective Length:
The effective length depends on the boundary conditions. Assuming the column is pin-ended, the effective length is equal to the actual length of the column, which is 240 cm.
Least Radius of Gyration:
The least radius of gyration can be calculated using the formula:
k = sqrt(I/A)
For the x-axis:
kx = sqrt(Ixx/A) = sqrt(720 cm^4 / 20 cm^2) = sqrt(36 cm^2) = 6 cm
For the y-axis:
ky = sqrt(Iyy/A) = sqrt(80 cm^4 / 20 cm^2) = sqrt(4 cm^2) = 2 cm
Slenderness Ratio:
The slenderness ratio (λ) is calculated as the ratio of the effective length to the least radius of gyration:
λ = L/k = 240 cm / 2 cm = 120
Therefore, the slenderness ratio is 120.
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The column of length 240 cm, area of cross- section 20 cm 2, moment of inertia 1XX = 720 cm4 and Iyy = 80 cm4 is subject to buckling load. The data corresponds to slenderness ratioa)40b)80c)120d)160Correct answer is option 'C'. Can you explain this answer?
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The column of length 240 cm, area of cross- section 20 cm 2, moment of inertia 1XX = 720 cm4 and Iyy = 80 cm4 is subject to buckling load. The data corresponds to slenderness ratioa)40b)80c)120d)160Correct answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The column of length 240 cm, area of cross- section 20 cm 2, moment of inertia 1XX = 720 cm4 and Iyy = 80 cm4 is subject to buckling load. The data corresponds to slenderness ratioa)40b)80c)120d)160Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The column of length 240 cm, area of cross- section 20 cm 2, moment of inertia 1XX = 720 cm4 and Iyy = 80 cm4 is subject to buckling load. The data corresponds to slenderness ratioa)40b)80c)120d)160Correct answer is option 'C'. Can you explain this answer?.
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