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The slenderness ratio is the ratio of
- a)area of column to least radius of gyration
- b)length of column to least radius of gyration
- c)least radius of gyration to area of column
- d)least radius of gyration to length of column
Correct answer is option 'B'. Can you explain this answer?
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The slenderness ratio is the ratio ofa)area of column to least radius ...
Explanation:
The slenderness ratio is a measure of the ability of a column to resist buckling when subjected to an axial compressive load. It is defined as the ratio of length of the column to the least radius of gyration of its cross-section.
Formula: Slenderness ratio (λ) = Length of column (l) / Least radius of gyration (r)
Calculating the least radius of gyration:
The least radius of gyration is the distance from the centroid of the cross-sectional area of the column to the point where the entire cross-sectional area can be assumed to be concentrated. It is given by the formula:
r = √(I/A)
Where, I is the moment of inertia of the cross-sectional area about the axis passing through the centroid and A is the cross-sectional area of the column.
Importance of slenderness ratio:
The slenderness ratio is an important parameter in the design of columns. When the slenderness ratio is high, the column is more prone to buckling. Therefore, the slenderness ratio must be kept within a certain limit to ensure that the column does not buckle under load.
Factors affecting the slenderness ratio:
The slenderness ratio of a column depends on the following factors:
- Length of the column
- Cross-sectional area of the column
- Moment of inertia of the cross-sectional area
Conclusion:
Hence, from the above explanation, we can conclude that the slenderness ratio is the ratio of length of column to the least radius of gyration of its cross-section.
The slenderness ratio is a measure of the ability of a column to resist buckling when subjected to an axial compressive load. It is defined as the ratio of length of the column to the least radius of gyration of its cross-section.
Formula: Slenderness ratio (λ) = Length of column (l) / Least radius of gyration (r)
Calculating the least radius of gyration:
The least radius of gyration is the distance from the centroid of the cross-sectional area of the column to the point where the entire cross-sectional area can be assumed to be concentrated. It is given by the formula:
r = √(I/A)
Where, I is the moment of inertia of the cross-sectional area about the axis passing through the centroid and A is the cross-sectional area of the column.
Importance of slenderness ratio:
The slenderness ratio is an important parameter in the design of columns. When the slenderness ratio is high, the column is more prone to buckling. Therefore, the slenderness ratio must be kept within a certain limit to ensure that the column does not buckle under load.
Factors affecting the slenderness ratio:
The slenderness ratio of a column depends on the following factors:
- Length of the column
- Cross-sectional area of the column
- Moment of inertia of the cross-sectional area
Conclusion:
Hence, from the above explanation, we can conclude that the slenderness ratio is the ratio of length of column to the least radius of gyration of its cross-section.
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The slenderness ratio is the ratio ofa)area of column to least radius of gyrationb)length of column to least radius of gyrationc)least radius of gyration to area of columnd)least radius of gyration to length of columnCorrect answer is option 'B'. Can you explain this answer?
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