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A steel bar of length 1 m and cross section area 1600 mm^2 is heated from 20 degree centigrade to 80 degree centigrade and at the same time subjected to a pull of axial load P If the total extension of the rod is 0.85 mm, what should be the magnitude of P ? Consider coefficient of thermal expansion a for steel is 12 x 10^-6 per degree centigrade and the modulus of elasticity of steel is 200 GPa. (1) 70000 N (2) 60000N (3) 41600N (4) 50000 N?
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A steel bar of length 1 m and cross section area 1600 mm^2 is heated f...
**Given:**
- Length of the steel bar (L) = 1 m
- Cross-sectional area of the steel bar (A) = 1600 mm² = 1.6 x 10⁻³ m²
- Initial temperature (T₁) = 20 °C
- Final temperature (T₂) = 80 °C
- Total extension (ΔL) = 0.85 mm = 0.85 x 10⁻³ m
- Coefficient of thermal expansion for steel (α) = 12 x 10⁻⁶ /°C
- Modulus of elasticity for steel (E) = 200 GPa = 200 x 10⁹ N/m²
**To find:**
Magnitude of the axial load (P)
**Assumptions:**
- The steel bar is homogeneous and isotropic.
- The bar is free to expand or contract in the axial direction.
- There is no lateral strain or movement in the bar.
- The thermal expansion and axial deformation are linearly proportional.
- The stress-strain relationship is linear and follows Hooke's Law.
**Solution:**
1. Calculate the change in length of the bar due to temperature change:
- ΔL₁ = α * L * (T₂ - T₁)
- ΔL₁ = 12 x 10⁻⁶ * 1 * (80 - 20)
- ΔL₁ = 480 x 10⁻⁶ m
2. Calculate the change in length of the bar due to axial load:
- ΔL₂ = P * L / (A * E)
- ΔL₂ = P * 1 / (1.6 x 10⁻³ * 200 x 10⁹)
- ΔL₂ = P / (3.2 x 10⁻⁴ x 10⁹)
- ΔL₂ = P / (3.2 x 10⁵ x 10⁴)
- ΔL₂ = P / 3.2 x 10⁹
3. Total change in length of the bar:
- ΔL = ΔL₁ + ΔL₂
- 0.85 x 10⁻³ = 480 x 10⁻⁶ + P / 3.2 x 10⁹
4. Solve for P:
- P / 3.2 x 10⁹ = 0.85 x 10⁻³ - 480 x 10⁻⁶
- P = (0.85 x 10⁻³ - 480 x 10⁻⁶) * 3.2 x 10⁹
- P = 2.72 x 10⁶ - 1.536 x 10⁶
- P = 1.184 x 10⁶ N
Therefore, the magnitude of the axial load (P) is approximately 1.184 x 10⁶ N, which is equivalent to 1.184 MN.
**Answer:**
The magnitude of the axial load (P) is approximately 1.184 MN or 1,184,000 N.
- Length of the steel bar (L) = 1 m
- Cross-sectional area of the steel bar (A) = 1600 mm² = 1.6 x 10⁻³ m²
- Initial temperature (T₁) = 20 °C
- Final temperature (T₂) = 80 °C
- Total extension (ΔL) = 0.85 mm = 0.85 x 10⁻³ m
- Coefficient of thermal expansion for steel (α) = 12 x 10⁻⁶ /°C
- Modulus of elasticity for steel (E) = 200 GPa = 200 x 10⁹ N/m²
**To find:**
Magnitude of the axial load (P)
**Assumptions:**
- The steel bar is homogeneous and isotropic.
- The bar is free to expand or contract in the axial direction.
- There is no lateral strain or movement in the bar.
- The thermal expansion and axial deformation are linearly proportional.
- The stress-strain relationship is linear and follows Hooke's Law.
**Solution:**
1. Calculate the change in length of the bar due to temperature change:
- ΔL₁ = α * L * (T₂ - T₁)
- ΔL₁ = 12 x 10⁻⁶ * 1 * (80 - 20)
- ΔL₁ = 480 x 10⁻⁶ m
2. Calculate the change in length of the bar due to axial load:
- ΔL₂ = P * L / (A * E)
- ΔL₂ = P * 1 / (1.6 x 10⁻³ * 200 x 10⁹)
- ΔL₂ = P / (3.2 x 10⁻⁴ x 10⁹)
- ΔL₂ = P / (3.2 x 10⁵ x 10⁴)
- ΔL₂ = P / 3.2 x 10⁹
3. Total change in length of the bar:
- ΔL = ΔL₁ + ΔL₂
- 0.85 x 10⁻³ = 480 x 10⁻⁶ + P / 3.2 x 10⁹
4. Solve for P:
- P / 3.2 x 10⁹ = 0.85 x 10⁻³ - 480 x 10⁻⁶
- P = (0.85 x 10⁻³ - 480 x 10⁻⁶) * 3.2 x 10⁹
- P = 2.72 x 10⁶ - 1.536 x 10⁶
- P = 1.184 x 10⁶ N
Therefore, the magnitude of the axial load (P) is approximately 1.184 x 10⁶ N, which is equivalent to 1.184 MN.
**Answer:**
The magnitude of the axial load (P) is approximately 1.184 MN or 1,184,000 N.
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A steel bar of length 1 m and cross section area 1600 mm^2 is heated from 20 degree centigrade to 80 degree centigrade and at the same time subjected to a pull of axial load P If the total extension of the rod is 0.85 mm, what should be the magnitude of P ? Consider coefficient of thermal expansion a for steel is 12 x 10^-6 per degree centigrade and the modulus of elasticity of steel is 200 GPa. (1) 70000 N (2) 60000N (3) 41600N (4) 50000 N?
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A steel bar of length 1 m and cross section area 1600 mm^2 is heated from 20 degree centigrade to 80 degree centigrade and at the same time subjected to a pull of axial load P If the total extension of the rod is 0.85 mm, what should be the magnitude of P ? Consider coefficient of thermal expansion a for steel is 12 x 10^-6 per degree centigrade and the modulus of elasticity of steel is 200 GPa. (1) 70000 N (2) 60000N (3) 41600N (4) 50000 N? 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 steel bar of length 1 m and cross section area 1600 mm^2 is heated from 20 degree centigrade to 80 degree centigrade and at the same time subjected to a pull of axial load P If the total extension of the rod is 0.85 mm, what should be the magnitude of P ? Consider coefficient of thermal expansion a for steel is 12 x 10^-6 per degree centigrade and the modulus of elasticity of steel is 200 GPa. (1) 70000 N (2) 60000N (3) 41600N (4) 50000 N? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A steel bar of length 1 m and cross section area 1600 mm^2 is heated from 20 degree centigrade to 80 degree centigrade and at the same time subjected to a pull of axial load P If the total extension of the rod is 0.85 mm, what should be the magnitude of P ? Consider coefficient of thermal expansion a for steel is 12 x 10^-6 per degree centigrade and the modulus of elasticity of steel is 200 GPa. (1) 70000 N (2) 60000N (3) 41600N (4) 50000 N?.
A steel bar of length 1 m and cross section area 1600 mm^2 is heated from 20 degree centigrade to 80 degree centigrade and at the same time subjected to a pull of axial load P If the total extension of the rod is 0.85 mm, what should be the magnitude of P ? Consider coefficient of thermal expansion a for steel is 12 x 10^-6 per degree centigrade and the modulus of elasticity of steel is 200 GPa. (1) 70000 N (2) 60000N (3) 41600N (4) 50000 N? 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 steel bar of length 1 m and cross section area 1600 mm^2 is heated from 20 degree centigrade to 80 degree centigrade and at the same time subjected to a pull of axial load P If the total extension of the rod is 0.85 mm, what should be the magnitude of P ? Consider coefficient of thermal expansion a for steel is 12 x 10^-6 per degree centigrade and the modulus of elasticity of steel is 200 GPa. (1) 70000 N (2) 60000N (3) 41600N (4) 50000 N? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A steel bar of length 1 m and cross section area 1600 mm^2 is heated from 20 degree centigrade to 80 degree centigrade and at the same time subjected to a pull of axial load P If the total extension of the rod is 0.85 mm, what should be the magnitude of P ? Consider coefficient of thermal expansion a for steel is 12 x 10^-6 per degree centigrade and the modulus of elasticity of steel is 200 GPa. (1) 70000 N (2) 60000N (3) 41600N (4) 50000 N?.
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