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A column consisting of SC 140 @ 33.31 kgf/m has an unsupported length of 400 cm. At one end, the column is held in a position and cannot rotate. At the other end, the column cannot rotate, but is also not held in position. Determine the axial load in kN. (Assume fy = 250 N/mm2, A1 = 4.24 × 103 mm2, rx = 58.5 mm, ry = 32.1 mm) (Answer up to the nearest integer)
Correct answer is '192'. Can you explain this answer?
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A column consisting of SC 140 @ 33.31 kgf/m has an unsupported length...
Actual length of the column = 4 m
Effective length = 1.20 L = 1.2 × 4 = 4800 mm
Maximum slenderness ratio, λ = l/rmin = 4800/32.1 = 149.53
By interpolation method,σac = 51 – × 9.53 = 45.29 MPa
Axial load, P = σac × A = 45.29 × 4.24 × 103 = 191989 N = 191.99 kN or 192 kN
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A column consisting of SC 140 @ 33.31 kgf/m has an unsupported length...
Given data:
- Length of the column (L) = 400 cm = 4 m
- Modulus of elasticity of steel (E) = 210 GPa = 210 × 10^3 N/mm²
- Yield strength of steel (fy) = 250 N/mm²
- Area of the column (A1) = 4.24 × 10^3 mm²
- Distance from the centroid of the column to the extreme fiber in the x-direction (rx) = 58.5 mm
- Distance from the centroid of the column to the extreme fiber in the y-direction (ry) = 32.1 mm
Calculating the axial load:
The axial load (P) in the column can be determined using the formula:
P = (E × A × ΔL) / L
Where:
- E is the modulus of elasticity
- A is the cross-sectional area of the column
- ΔL is the change in length of the column
- L is the length of the column
Calculating the change in length:
The change in length (ΔL) can be calculated using the formula:
ΔL = (P × L) / (E × A)
Calculating the slenderness ratio:
The slenderness ratio (λ) of the column can be calculated using the formula:
λ = (L × rx) / (ry × √(fy / E))
Where:
- L is the length of the column
- rx is the distance from the centroid of the column to the extreme fiber in the x-direction
- ry is the distance from the centroid of the column to the extreme fiber in the y-direction
- fy is the yield strength of steel
- E is the modulus of elasticity
Determining the column behavior:
Based on the slenderness ratio (λ), the behavior of the column can be determined. In this case, the column falls under the category of a short column since λ < />
Calculating the axial load:
Since the column is short and fixed at one end, the axial load can be determined using the formula:
P = A × fy
P = (4.24 × 10^3 mm²) × (250 N/mm²)
P = 1.06 × 10^6 N
Converting the load from N to kN:
P = 1.06 × 10^6 N / 1000
P = 1060 kN
Conclusion:
The axial load in the column is 1060 kN, which when rounded to the nearest integer is 1060 kN. However, the given correct answer is 192 kN, which seems to be incorrect based on the provided information and calculations.
- Length of the column (L) = 400 cm = 4 m
- Modulus of elasticity of steel (E) = 210 GPa = 210 × 10^3 N/mm²
- Yield strength of steel (fy) = 250 N/mm²
- Area of the column (A1) = 4.24 × 10^3 mm²
- Distance from the centroid of the column to the extreme fiber in the x-direction (rx) = 58.5 mm
- Distance from the centroid of the column to the extreme fiber in the y-direction (ry) = 32.1 mm
Calculating the axial load:
The axial load (P) in the column can be determined using the formula:
P = (E × A × ΔL) / L
Where:
- E is the modulus of elasticity
- A is the cross-sectional area of the column
- ΔL is the change in length of the column
- L is the length of the column
Calculating the change in length:
The change in length (ΔL) can be calculated using the formula:
ΔL = (P × L) / (E × A)
Calculating the slenderness ratio:
The slenderness ratio (λ) of the column can be calculated using the formula:
λ = (L × rx) / (ry × √(fy / E))
Where:
- L is the length of the column
- rx is the distance from the centroid of the column to the extreme fiber in the x-direction
- ry is the distance from the centroid of the column to the extreme fiber in the y-direction
- fy is the yield strength of steel
- E is the modulus of elasticity
Determining the column behavior:
Based on the slenderness ratio (λ), the behavior of the column can be determined. In this case, the column falls under the category of a short column since λ < />
Calculating the axial load:
Since the column is short and fixed at one end, the axial load can be determined using the formula:
P = A × fy
P = (4.24 × 10^3 mm²) × (250 N/mm²)
P = 1.06 × 10^6 N
Converting the load from N to kN:
P = 1.06 × 10^6 N / 1000
P = 1060 kN
Conclusion:
The axial load in the column is 1060 kN, which when rounded to the nearest integer is 1060 kN. However, the given correct answer is 192 kN, which seems to be incorrect based on the provided information and calculations.
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A column consisting of SC 140 @ 33.31 kgf/m has an unsupported length of 400 cm. At one end, the column is held in a position and cannot rotate. At the other end, the column cannot rotate, but is also not held in position. Determine the axial load in kN. (Assume fy = 250 N/mm2, A1 = 4.24 × 103 mm2, rx = 58.5 mm, ry = 32.1 mm) (Answer up to the nearest integer)Correct answer is '192'. Can you explain this answer?
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A column consisting of SC 140 @ 33.31 kgf/m has an unsupported length of 400 cm. At one end, the column is held in a position and cannot rotate. At the other end, the column cannot rotate, but is also not held in position. Determine the axial load in kN. (Assume fy = 250 N/mm2, A1 = 4.24 × 103 mm2, rx = 58.5 mm, ry = 32.1 mm) (Answer up to the nearest integer)Correct answer is '192'. Can you explain this answer? for Civil Engineering (CE) 2024 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 consisting of SC 140 @ 33.31 kgf/m has an unsupported length of 400 cm. At one end, the column is held in a position and cannot rotate. At the other end, the column cannot rotate, but is also not held in position. Determine the axial load in kN. (Assume fy = 250 N/mm2, A1 = 4.24 × 103 mm2, rx = 58.5 mm, ry = 32.1 mm) (Answer up to the nearest integer)Correct answer is '192'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A column consisting of SC 140 @ 33.31 kgf/m has an unsupported length of 400 cm. At one end, the column is held in a position and cannot rotate. At the other end, the column cannot rotate, but is also not held in position. Determine the axial load in kN. (Assume fy = 250 N/mm2, A1 = 4.24 × 103 mm2, rx = 58.5 mm, ry = 32.1 mm) (Answer up to the nearest integer)Correct answer is '192'. Can you explain this answer?.
A column consisting of SC 140 @ 33.31 kgf/m has an unsupported length of 400 cm. At one end, the column is held in a position and cannot rotate. At the other end, the column cannot rotate, but is also not held in position. Determine the axial load in kN. (Assume fy = 250 N/mm2, A1 = 4.24 × 103 mm2, rx = 58.5 mm, ry = 32.1 mm) (Answer up to the nearest integer)Correct answer is '192'. Can you explain this answer? for Civil Engineering (CE) 2024 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 consisting of SC 140 @ 33.31 kgf/m has an unsupported length of 400 cm. At one end, the column is held in a position and cannot rotate. At the other end, the column cannot rotate, but is also not held in position. Determine the axial load in kN. (Assume fy = 250 N/mm2, A1 = 4.24 × 103 mm2, rx = 58.5 mm, ry = 32.1 mm) (Answer up to the nearest integer)Correct answer is '192'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A column consisting of SC 140 @ 33.31 kgf/m has an unsupported length of 400 cm. At one end, the column is held in a position and cannot rotate. At the other end, the column cannot rotate, but is also not held in position. Determine the axial load in kN. (Assume fy = 250 N/mm2, A1 = 4.24 × 103 mm2, rx = 58.5 mm, ry = 32.1 mm) (Answer up to the nearest integer)Correct answer is '192'. Can you explain this answer?.
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A column consisting of SC 140 @ 33.31 kgf/m has an unsupported length of 400 cm. At one end, the column is held in a position and cannot rotate. At the other end, the column cannot rotate, but is also not held in position. Determine the axial load in kN. (Assume fy = 250 N/mm2, A1 = 4.24 × 103 mm2, rx = 58.5 mm, ry = 32.1 mm) (Answer up to the nearest integer)Correct answer is '192'. Can you explain this answer?, a detailed solution for A column consisting of SC 140 @ 33.31 kgf/m has an unsupported length of 400 cm. At one end, the column is held in a position and cannot rotate. At the other end, the column cannot rotate, but is also not held in position. Determine the axial load in kN. (Assume fy = 250 N/mm2, A1 = 4.24 × 103 mm2, rx = 58.5 mm, ry = 32.1 mm) (Answer up to the nearest integer)Correct answer is '192'. Can you explain this answer? has been provided alongside types of A column consisting of SC 140 @ 33.31 kgf/m has an unsupported length of 400 cm. At one end, the column is held in a position and cannot rotate. At the other end, the column cannot rotate, but is also not held in position. Determine the axial load in kN. (Assume fy = 250 N/mm2, A1 = 4.24 × 103 mm2, rx = 58.5 mm, ry = 32.1 mm) (Answer up to the nearest integer)Correct answer is '192'. Can you explain this answer? theory, EduRev gives you an
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