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A short cast iron column carries a load of 50 tonn. If the original diameter is 8 cm, E = 1 x 10° kg/cm² and Poisson's ratio = 0.25, the increase in diameter of the column?
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A short cast iron column carries a load of 50 tonn. If the original di...
Introduction
To determine the increase in diameter of a cast iron column under a load, we use the principles of elasticity, specifically considering the effects of axial loading on circumferential dimensions.
Given Data
- Load (P) = 50 tons = 50 x 1000 kg = 50000 kg
- Original Diameter (D) = 8 cm
- Modulus of Elasticity (E) = 1 x 10^6 kg/cm²
- Poisson's Ratio (ν) = 0.25
Calculation of Stress
- Cross-sectional Area (A):
- A = π(D/2)² = π(4 cm)² = 16π cm²
- Axial Stress (σ):
- σ = P/A = 50000 kg / (16π cm²) = 50000 / 50.27 cm² ≈ 995.61 kg/cm²
Calculation of Strain
- Longitudinal Strain (ε):
- ε = σ/E = 995.61 kg/cm² / (1 x 10^6 kg/cm²) = 0.00099561
Lateral Strain
- Lateral Strain (ε_lat):
- ε_lat = -ν * ε = -0.25 * 0.00099561 ≈ -0.0002489
Increase in Diameter
- Change in Diameter (ΔD):
- ΔD = D * ε_lat = 8 cm * (-0.0002489) ≈ -0.0019912 cm
- Final Increase in Diameter:
- Since we are looking for the increase, we take the absolute value: ΔD ≈ 0.00199 cm or 0.0199 mm.
Conclusion
The increase in diameter of the column under the applied load is approximately 0.0199 mm. This calculation highlights the importance of considering both axial and lateral strains in structural analysis.
To determine the increase in diameter of a cast iron column under a load, we use the principles of elasticity, specifically considering the effects of axial loading on circumferential dimensions.
Given Data
- Load (P) = 50 tons = 50 x 1000 kg = 50000 kg
- Original Diameter (D) = 8 cm
- Modulus of Elasticity (E) = 1 x 10^6 kg/cm²
- Poisson's Ratio (ν) = 0.25
Calculation of Stress
- Cross-sectional Area (A):
- A = π(D/2)² = π(4 cm)² = 16π cm²
- Axial Stress (σ):
- σ = P/A = 50000 kg / (16π cm²) = 50000 / 50.27 cm² ≈ 995.61 kg/cm²
Calculation of Strain
- Longitudinal Strain (ε):
- ε = σ/E = 995.61 kg/cm² / (1 x 10^6 kg/cm²) = 0.00099561
Lateral Strain
- Lateral Strain (ε_lat):
- ε_lat = -ν * ε = -0.25 * 0.00099561 ≈ -0.0002489
Increase in Diameter
- Change in Diameter (ΔD):
- ΔD = D * ε_lat = 8 cm * (-0.0002489) ≈ -0.0019912 cm
- Final Increase in Diameter:
- Since we are looking for the increase, we take the absolute value: ΔD ≈ 0.00199 cm or 0.0199 mm.
Conclusion
The increase in diameter of the column under the applied load is approximately 0.0199 mm. This calculation highlights the importance of considering both axial and lateral strains in structural analysis.
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A short cast iron column carries a load of 50 tonn. If the original diameter is 8 cm, E = 1 x 10° kg/cm² and Poisson's ratio = 0.25, the increase in diameter of the column?
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A short cast iron column carries a load of 50 tonn. If the original diameter is 8 cm, E = 1 x 10° kg/cm² and Poisson's ratio = 0.25, the increase in diameter of the column? 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 short cast iron column carries a load of 50 tonn. If the original diameter is 8 cm, E = 1 x 10° kg/cm² and Poisson's ratio = 0.25, the increase in diameter of the column? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A short cast iron column carries a load of 50 tonn. If the original diameter is 8 cm, E = 1 x 10° kg/cm² and Poisson's ratio = 0.25, the increase in diameter of the column?.
A short cast iron column carries a load of 50 tonn. If the original diameter is 8 cm, E = 1 x 10° kg/cm² and Poisson's ratio = 0.25, the increase in diameter of the column? 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 short cast iron column carries a load of 50 tonn. If the original diameter is 8 cm, E = 1 x 10° kg/cm² and Poisson's ratio = 0.25, the increase in diameter of the column? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A short cast iron column carries a load of 50 tonn. If the original diameter is 8 cm, E = 1 x 10° kg/cm² and Poisson's ratio = 0.25, the increase in diameter of the column?.
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