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A steel member has an outside diameter of 100mm and an area of 2000mm². Determine the axial force P that cause the outside diameter to increase by 0.01 percent?
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A steel member has an outside diameter of 100mm and an area of 2000mm²...
Introduction
To determine the axial force (P) that causes an increase in the outside diameter of a steel member, we need to consider material properties, geometry, and the relationship between stress and strain.
Given Data
- Outside Diameter (D) = 100 mm
- Area (A) = 2000 mm²
- Increase in Diameter = 0.01%
Calculations
1. Calculate the Increase in Diameter
- Increase in Diameter = 0.01% of 100 mm = 0.01 mm
2. Calculate the Strain
- Strain (ε) = Change in Diameter / Original Diameter
- ε = 0.01 mm / 100 mm = 0.0001
3. Material Properties
- Assume Young's Modulus (E) for steel = 200 GPa = 200,000 MPa
4. Calculate the Stress
- Stress (σ) = E × ε
- σ = 200,000 MPa × 0.0001 = 20 MPa
5. Calculate the Axial Force (P)
- Using the formula P = σ × A
- P = 20 MPa × 2000 mm² = 40,000 N
Conclusion
The axial force (P) required to cause the outside diameter of the steel member to increase by 0.01 percent is 40,000 N. This calculation incorporates the fundamental relationships between stress, strain, and material properties, ensuring an accurate representation of the conditions required for the specified deformation.
To determine the axial force (P) that causes an increase in the outside diameter of a steel member, we need to consider material properties, geometry, and the relationship between stress and strain.
Given Data
- Outside Diameter (D) = 100 mm
- Area (A) = 2000 mm²
- Increase in Diameter = 0.01%
Calculations
1. Calculate the Increase in Diameter
- Increase in Diameter = 0.01% of 100 mm = 0.01 mm
2. Calculate the Strain
- Strain (ε) = Change in Diameter / Original Diameter
- ε = 0.01 mm / 100 mm = 0.0001
3. Material Properties
- Assume Young's Modulus (E) for steel = 200 GPa = 200,000 MPa
4. Calculate the Stress
- Stress (σ) = E × ε
- σ = 200,000 MPa × 0.0001 = 20 MPa
5. Calculate the Axial Force (P)
- Using the formula P = σ × A
- P = 20 MPa × 2000 mm² = 40,000 N
Conclusion
The axial force (P) required to cause the outside diameter of the steel member to increase by 0.01 percent is 40,000 N. This calculation incorporates the fundamental relationships between stress, strain, and material properties, ensuring an accurate representation of the conditions required for the specified deformation.
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A steel member has an outside diameter of 100mm and an area of 2000mm². Determine the axial force P that cause the outside diameter to increase by 0.01 percent?
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A steel member has an outside diameter of 100mm and an area of 2000mm². Determine the axial force P that cause the outside diameter to increase by 0.01 percent? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A steel member has an outside diameter of 100mm and an area of 2000mm². Determine the axial force P that cause the outside diameter to increase by 0.01 percent? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A steel member has an outside diameter of 100mm and an area of 2000mm². Determine the axial force P that cause the outside diameter to increase by 0.01 percent?.
A steel member has an outside diameter of 100mm and an area of 2000mm². Determine the axial force P that cause the outside diameter to increase by 0.01 percent? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A steel member has an outside diameter of 100mm and an area of 2000mm². Determine the axial force P that cause the outside diameter to increase by 0.01 percent? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A steel member has an outside diameter of 100mm and an area of 2000mm². Determine the axial force P that cause the outside diameter to increase by 0.01 percent?.
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