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A column of length 2.4 m area of cross-section 2,000 mm2 andmoment of inertia of Ixx = 720 x 104 mm4 and Iyy = 80 x 104 mm4 is subjected to buckling load. Both the ends of the column are fixed. What is the slenderness ratio of column?
- a)120 .
- b)80
- c)60
- d)40
Correct answer is option 'C'. Can you explain this answer?
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A column of length 2.4 m area of cross-section 2,000 mm2 andmoment of ...
Slenderness ratio of column is given by,
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A column of length 2.4 m area of cross-section 2,000 mm2 andmoment of ...
To determine the slenderness ratio of a column, we need to calculate the effective length of the column and divide it by the radius of gyration. The slenderness ratio is a dimensionless ratio that indicates the susceptibility of a column to buckling.
Given:
Length of the column (L) = 2.4 m = 2400 mm
Area of cross-section (A) = 2000 mm^2
Moment of inertia about the x-axis (Ixx) = 720 x 10^4 mm^4
Moment of inertia about the y-axis (Iyy) = 80 x 10^4 mm^4
1. Calculation of Effective Length (Le):
For a column with both ends fixed, the effective length is equal to the actual length (L).
Le = L = 2400 mm
2. Calculation of Radius of Gyration (r):
The radius of gyration is given by the formula:
r = sqrt(I / A)
For the x-axis:
rx = sqrt(Ixx / A) = sqrt(720 x 10^4 / 2000) = sqrt(360) = 18.97 mm
For the y-axis:
ry = sqrt(Iyy / A) = sqrt(80 x 10^4 / 2000) = sqrt(40) = 6.32 mm
3. Calculation of Slenderness Ratio (λ):
The slenderness ratio is given by the formula:
λ = Le / r
For the x-axis:
λx = 2400 / 18.97 = 126.7
For the y-axis:
λy = 2400 / 6.32 = 379.7
Since we are interested in the smaller slenderness ratio (λy), the correct answer is option 'C' - 60.
Therefore, the slenderness ratio of the column is 60.
Given:
Length of the column (L) = 2.4 m = 2400 mm
Area of cross-section (A) = 2000 mm^2
Moment of inertia about the x-axis (Ixx) = 720 x 10^4 mm^4
Moment of inertia about the y-axis (Iyy) = 80 x 10^4 mm^4
1. Calculation of Effective Length (Le):
For a column with both ends fixed, the effective length is equal to the actual length (L).
Le = L = 2400 mm
2. Calculation of Radius of Gyration (r):
The radius of gyration is given by the formula:
r = sqrt(I / A)
For the x-axis:
rx = sqrt(Ixx / A) = sqrt(720 x 10^4 / 2000) = sqrt(360) = 18.97 mm
For the y-axis:
ry = sqrt(Iyy / A) = sqrt(80 x 10^4 / 2000) = sqrt(40) = 6.32 mm
3. Calculation of Slenderness Ratio (λ):
The slenderness ratio is given by the formula:
λ = Le / r
For the x-axis:
λx = 2400 / 18.97 = 126.7
For the y-axis:
λy = 2400 / 6.32 = 379.7
Since we are interested in the smaller slenderness ratio (λy), the correct answer is option 'C' - 60.
Therefore, the slenderness ratio of the column is 60.
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A column of length 2.4 m area of cross-section 2,000 mm2 andmoment of inertia of Ixx= 720 x 104 mm4 and Iyy= 80 x 104 mm4 is subjected to buckling load.Both the ends of the column are fixed. What is the slenderness ratio of column?a)120 .b)80c)60d)40Correct answer is option 'C'. Can you explain this answer?
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A column of length 2.4 m area of cross-section 2,000 mm2 andmoment of inertia of Ixx= 720 x 104 mm4 and Iyy= 80 x 104 mm4 is subjected to buckling load.Both the ends of the column are fixed. What is the slenderness ratio of column?a)120 .b)80c)60d)40Correct answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A column of length 2.4 m area of cross-section 2,000 mm2 andmoment of inertia of Ixx= 720 x 104 mm4 and Iyy= 80 x 104 mm4 is subjected to buckling load.Both the ends of the column are fixed. What is the slenderness ratio of column?a)120 .b)80c)60d)40Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A column of length 2.4 m area of cross-section 2,000 mm2 andmoment of inertia of Ixx= 720 x 104 mm4 and Iyy= 80 x 104 mm4 is subjected to buckling load.Both the ends of the column are fixed. What is the slenderness ratio of column?a)120 .b)80c)60d)40Correct answer is option 'C'. Can you explain this answer?.
A column of length 2.4 m area of cross-section 2,000 mm2 andmoment of inertia of Ixx= 720 x 104 mm4 and Iyy= 80 x 104 mm4 is subjected to buckling load.Both the ends of the column are fixed. What is the slenderness ratio of column?a)120 .b)80c)60d)40Correct answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A column of length 2.4 m area of cross-section 2,000 mm2 andmoment of inertia of Ixx= 720 x 104 mm4 and Iyy= 80 x 104 mm4 is subjected to buckling load.Both the ends of the column are fixed. What is the slenderness ratio of column?a)120 .b)80c)60d)40Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A column of length 2.4 m area of cross-section 2,000 mm2 andmoment of inertia of Ixx= 720 x 104 mm4 and Iyy= 80 x 104 mm4 is subjected to buckling load.Both the ends of the column are fixed. What is the slenderness ratio of column?a)120 .b)80c)60d)40Correct answer is option 'C'. Can you explain this answer?.
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