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A square steel rod with a cross section of 400mm needs to support an axial compressive load of 100KN. Calculate the Shortening in a 50mm length . The modulus of Elasticity for Steel is 2.14×10^8 KN/m^2?
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A square steel rod with a cross section of 400mm needs to support an a...
Given Data
- Cross-sectional area (A) of the square rod = 400 mm x 400 mm = 160,000 mm² = 0.16 m²
- Axial compressive load (P) = 100 kN = 100,000 N
- Length of the rod (L) = 50 mm = 0.05 m
- Modulus of Elasticity (E) for Steel = 2.14 × 10^8 kN/m² = 2.14 × 10^11 N/m²
Step 1: Calculate the Stress
- Stress (σ) is calculated using the formula:
σ = P / A
- σ = 100,000 N / 0.16 m²
- σ = 625,000 N/m²
Step 2: Calculate the Strain
- Strain (ε) can be calculated using the formula:
ε = σ / E
- ε = 625,000 N/m² / 2.14 × 10^11 N/m²
- ε ≈ 2.92 × 10^-6
Step 3: Calculate the Shortening
- The shortening (ΔL) of the rod can be calculated using:
ΔL = ε × L
- ΔL = 2.92 × 10^-6 × 0.05 m
- ΔL ≈ 1.46 × 10^-7 m or 0.146 mm
Conclusion
The shortening of the 50 mm length of the square steel rod under a 100 kN axial compressive load is approximately 0.146 mm. This calculation demonstrates how material properties and dimensions affect deformation under load.
- Cross-sectional area (A) of the square rod = 400 mm x 400 mm = 160,000 mm² = 0.16 m²
- Axial compressive load (P) = 100 kN = 100,000 N
- Length of the rod (L) = 50 mm = 0.05 m
- Modulus of Elasticity (E) for Steel = 2.14 × 10^8 kN/m² = 2.14 × 10^11 N/m²
Step 1: Calculate the Stress
- Stress (σ) is calculated using the formula:
σ = P / A
- σ = 100,000 N / 0.16 m²
- σ = 625,000 N/m²
Step 2: Calculate the Strain
- Strain (ε) can be calculated using the formula:
ε = σ / E
- ε = 625,000 N/m² / 2.14 × 10^11 N/m²
- ε ≈ 2.92 × 10^-6
Step 3: Calculate the Shortening
- The shortening (ΔL) of the rod can be calculated using:
ΔL = ε × L
- ΔL = 2.92 × 10^-6 × 0.05 m
- ΔL ≈ 1.46 × 10^-7 m or 0.146 mm
Conclusion
The shortening of the 50 mm length of the square steel rod under a 100 kN axial compressive load is approximately 0.146 mm. This calculation demonstrates how material properties and dimensions affect deformation under load.
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A square steel rod with a cross section of 400mm needs to support an axial compressive load of 100KN. Calculate the Shortening in a 50mm length . The modulus of Elasticity for Steel is 2.14×10^8 KN/m^2?
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A square steel rod with a cross section of 400mm needs to support an axial compressive load of 100KN. Calculate the Shortening in a 50mm length . The modulus of Elasticity for Steel is 2.14×10^8 KN/m^2? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A square steel rod with a cross section of 400mm needs to support an axial compressive load of 100KN. Calculate the Shortening in a 50mm length . The modulus of Elasticity for Steel is 2.14×10^8 KN/m^2? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A square steel rod with a cross section of 400mm needs to support an axial compressive load of 100KN. Calculate the Shortening in a 50mm length . The modulus of Elasticity for Steel is 2.14×10^8 KN/m^2?.
A square steel rod with a cross section of 400mm needs to support an axial compressive load of 100KN. Calculate the Shortening in a 50mm length . The modulus of Elasticity for Steel is 2.14×10^8 KN/m^2? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A square steel rod with a cross section of 400mm needs to support an axial compressive load of 100KN. Calculate the Shortening in a 50mm length . The modulus of Elasticity for Steel is 2.14×10^8 KN/m^2? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A square steel rod with a cross section of 400mm needs to support an axial compressive load of 100KN. Calculate the Shortening in a 50mm length . The modulus of Elasticity for Steel is 2.14×10^8 KN/m^2?.
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