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The slenderness ratio of a section is
- a)directly proportional to the radius of gyration
- b)directly proportional to the moment of inertia
- c)inversely proportional to the area
- d)inversely proportional to the radius of gyration
Correct answer is option 'D'. Can you explain this answer?
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The slenderness ratio of a section isa)directly proportional to the ra...
Explanation:
Slenderness ratio of a section is defined as the ratio of the effective length of the column to the least radius of gyration of its cross-section. It is denoted by the symbol "λ".
Slenderness Ratio and Radius of Gyration:
- The slenderness ratio of a section is inversely proportional to the radius of gyration.
- This means that as the radius of gyration increases, the slenderness ratio decreases, and vice versa.
- The radius of gyration is a measure of how the cross-sectional area of a shape is distributed around its centroid.
Importance of Slenderness Ratio:
- The slenderness ratio plays a crucial role in determining the critical buckling load of a column or beam.
- A higher slenderness ratio indicates a greater tendency for buckling to occur, which can lead to structural failure.
- Therefore, it is essential to design structures with an appropriate slenderness ratio to ensure stability and safety.
In conclusion, the slenderness ratio of a section is inversely proportional to the radius of gyration. This relationship highlights the significance of considering both parameters in structural design to prevent buckling and ensure structural integrity.
Slenderness ratio of a section is defined as the ratio of the effective length of the column to the least radius of gyration of its cross-section. It is denoted by the symbol "λ".
Slenderness Ratio and Radius of Gyration:
- The slenderness ratio of a section is inversely proportional to the radius of gyration.
- This means that as the radius of gyration increases, the slenderness ratio decreases, and vice versa.
- The radius of gyration is a measure of how the cross-sectional area of a shape is distributed around its centroid.
Importance of Slenderness Ratio:
- The slenderness ratio plays a crucial role in determining the critical buckling load of a column or beam.
- A higher slenderness ratio indicates a greater tendency for buckling to occur, which can lead to structural failure.
- Therefore, it is essential to design structures with an appropriate slenderness ratio to ensure stability and safety.
In conclusion, the slenderness ratio of a section is inversely proportional to the radius of gyration. This relationship highlights the significance of considering both parameters in structural design to prevent buckling and ensure structural integrity.
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