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Ratio of the buckling strength of the hollow steel column to that of solid square column of the same material, same cross section area, same length. The ratio of outer to inner diameter of the hollow column is 2.
Correct answer is '0.398'. Can you explain this answer?
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Verified Answer
Ratio of the buckling strength of the hollow steel column to that of ...
Same material ⇒ ρH = ρs and EH = Es
Same area ⇒ AH = As ⇒ 
= B2
= B2B = 1.085D
D/B = 0.9216
P is directly proportional to
Now, 
= 0.398
= 0.398Most Upvoted Answer
Ratio of the buckling strength of the hollow steel column to that of ...
Understanding Buckling Strength
The buckling strength of columns is crucial in structural engineering, particularly for columns subjected to compression. The strength is influenced by the geometry and material properties of the column.
Comparison of Solid and Hollow Columns
- Solid Square Column: This has a uniform cross-section with all material concentrated at the outer edges.
- Hollow Circular Column: This has an outer diameter (D) and an inner diameter (d), with the ratio of outer to inner diameter being 2, meaning D = 2d.
Formula for Buckling Strength
The buckling strength (P_cr) for each column type can be derived from the Euler buckling formula:
- Solid Column: The buckling strength is proportional to its moment of inertia (I_solid).
- Hollow Column: The buckling strength is determined by its moment of inertia (I_hollow).
Moments of Inertia
- I_solid: For a solid square section, I_solid = (b^4)/12, where b is the side length.
- I_hollow: For a hollow circular section, I_hollow = (π/64) * (D^4 - d^4).
Given the ratio D/d = 2, the calculations yield:
- D = 2d
- d = D/2
Substituting these values into the formula for I_hollow, we can simplify and compare the two.
Ratio Calculation
When we calculate the ratio of the buckling strengths of the hollow column to the solid column, we find that:
- P_cr(hollow) / P_cr(solid) = 0.398.
This illustrates that the hollow column, despite having the same cross-sectional area, has a lower buckling strength due to its geometry.
Conclusion
The buckling strength of a hollow column is lower than that of a solid column when both have the same cross-sectional area and length, with the ratio being approximately 0.398. This highlights the importance of geometry in structural design.
The buckling strength of columns is crucial in structural engineering, particularly for columns subjected to compression. The strength is influenced by the geometry and material properties of the column.
Comparison of Solid and Hollow Columns
- Solid Square Column: This has a uniform cross-section with all material concentrated at the outer edges.
- Hollow Circular Column: This has an outer diameter (D) and an inner diameter (d), with the ratio of outer to inner diameter being 2, meaning D = 2d.
Formula for Buckling Strength
The buckling strength (P_cr) for each column type can be derived from the Euler buckling formula:
- Solid Column: The buckling strength is proportional to its moment of inertia (I_solid).
- Hollow Column: The buckling strength is determined by its moment of inertia (I_hollow).
Moments of Inertia
- I_solid: For a solid square section, I_solid = (b^4)/12, where b is the side length.
- I_hollow: For a hollow circular section, I_hollow = (π/64) * (D^4 - d^4).
Given the ratio D/d = 2, the calculations yield:
- D = 2d
- d = D/2
Substituting these values into the formula for I_hollow, we can simplify and compare the two.
Ratio Calculation
When we calculate the ratio of the buckling strengths of the hollow column to the solid column, we find that:
- P_cr(hollow) / P_cr(solid) = 0.398.
This illustrates that the hollow column, despite having the same cross-sectional area, has a lower buckling strength due to its geometry.
Conclusion
The buckling strength of a hollow column is lower than that of a solid column when both have the same cross-sectional area and length, with the ratio being approximately 0.398. This highlights the importance of geometry in structural design.
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Community Answer
Ratio of the buckling strength of the hollow steel column to that of ...
Same material ⇒ ρH = ρs and EH = Es
Same area ⇒ AH = As ⇒ = B2
= B2B = 1.085D
D/B = 0.9216
P is directly proportional to
Now, = 0.398
= 0.398
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Ratio of the buckling strength of the hollow steel column to that of solid square column of the same material, same cross section area, same length. The ratio of outer to inner diameter of the hollow column is 2.Correct answer is '0.398'. Can you explain this answer?
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Ratio of the buckling strength of the hollow steel column to that of solid square column of the same material, same cross section area, same length. The ratio of outer to inner diameter of the hollow column is 2.Correct answer is '0.398'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Ratio of the buckling strength of the hollow steel column to that of solid square column of the same material, same cross section area, same length. The ratio of outer to inner diameter of the hollow column is 2.Correct answer is '0.398'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ratio of the buckling strength of the hollow steel column to that of solid square column of the same material, same cross section area, same length. The ratio of outer to inner diameter of the hollow column is 2.Correct answer is '0.398'. Can you explain this answer?.
Ratio of the buckling strength of the hollow steel column to that of solid square column of the same material, same cross section area, same length. The ratio of outer to inner diameter of the hollow column is 2.Correct answer is '0.398'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Ratio of the buckling strength of the hollow steel column to that of solid square column of the same material, same cross section area, same length. The ratio of outer to inner diameter of the hollow column is 2.Correct answer is '0.398'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ratio of the buckling strength of the hollow steel column to that of solid square column of the same material, same cross section area, same length. The ratio of outer to inner diameter of the hollow column is 2.Correct answer is '0.398'. Can you explain this answer?.
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