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A mild steel bar of square cross-section 40 mm x 40 mm is 400 mm long. It is subjected to a longitudinal tensile stress of 440 N/mm2 and a lateral compressive stress of 200 N/mm2 in perpendicular directions. E = 2 x 10-5 N/ mm2, μ = 0.3. What is the approximate elongation of the bar in the longitudinal direction?
- a)0.44 mm
- b)0.88 mm
- c)0.22 mm
- d)1.0 mm
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A mild steel bar of square cross-section 40 mm x 40 mm is 400 mm long....
= 2.5 x 10-3 x 400 = 1mm
Most Upvoted Answer
A mild steel bar of square cross-section 40 mm x 40 mm is 400 mm long....
Given data:
- Cross-sectional area of the bar: 40 mm x 40 mm = 1600 mm^2
- Length of the bar: 400 mm
- Longitudinal tensile stress: 440 N/mm^2
- Lateral compressive stress: 200 N/mm^2
- Young's modulus (E): 2 x 10^5 N/mm^2
- Poisson's ratio (ν): 0.3
To find: Approximate elongation of the bar in the longitudinal direction
Using the formula for longitudinal strain (ε_longitudinal), we can calculate the elongation:
ε_longitudinal = σ_longitudinal / E
where σ_longitudinal is the longitudinal stress and E is the Young's modulus.
Substituting the given values:
ε_longitudinal = 440 N/mm^2 / 2 x 10^5 N/mm^2 = 0.0022
The lateral compressive stress will cause lateral strain in the bar. Using Poisson's ratio (ν), we can calculate the lateral strain (ε_lateral):
ε_lateral = -ν * (σ_longitudinal / E)
Substituting the given values:
ε_lateral = -0.3 * (200 N/mm^2 / 2 x 10^5 N/mm^2) = -0.001
The net strain in the longitudinal direction (ε_net) can be calculated by adding the longitudinal strain and lateral strain:
ε_net = ε_longitudinal + ε_lateral = 0.0022 - 0.001 = 0.0012
The elongation (ΔL) of the bar can be calculated using the formula:
ΔL = ε_net * L
where L is the length of the bar.
Substituting the given values:
ΔL = 0.0012 * 400 mm = 0.48 mm
Since the question asks for the approximate elongation, we can round the value to the nearest whole number:
Approximate elongation = 1 mm
Therefore, the correct answer is option D) 1.0 mm.
- Cross-sectional area of the bar: 40 mm x 40 mm = 1600 mm^2
- Length of the bar: 400 mm
- Longitudinal tensile stress: 440 N/mm^2
- Lateral compressive stress: 200 N/mm^2
- Young's modulus (E): 2 x 10^5 N/mm^2
- Poisson's ratio (ν): 0.3
To find: Approximate elongation of the bar in the longitudinal direction
Using the formula for longitudinal strain (ε_longitudinal), we can calculate the elongation:
ε_longitudinal = σ_longitudinal / E
where σ_longitudinal is the longitudinal stress and E is the Young's modulus.
Substituting the given values:
ε_longitudinal = 440 N/mm^2 / 2 x 10^5 N/mm^2 = 0.0022
The lateral compressive stress will cause lateral strain in the bar. Using Poisson's ratio (ν), we can calculate the lateral strain (ε_lateral):
ε_lateral = -ν * (σ_longitudinal / E)
Substituting the given values:
ε_lateral = -0.3 * (200 N/mm^2 / 2 x 10^5 N/mm^2) = -0.001
The net strain in the longitudinal direction (ε_net) can be calculated by adding the longitudinal strain and lateral strain:
ε_net = ε_longitudinal + ε_lateral = 0.0022 - 0.001 = 0.0012
The elongation (ΔL) of the bar can be calculated using the formula:
ΔL = ε_net * L
where L is the length of the bar.
Substituting the given values:
ΔL = 0.0012 * 400 mm = 0.48 mm
Since the question asks for the approximate elongation, we can round the value to the nearest whole number:
Approximate elongation = 1 mm
Therefore, the correct answer is option D) 1.0 mm.
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A mild steel bar of square cross-section 40 mm x 40 mm is 400 mm long. It is subjected to a longitudinal tensile stress of 440 N/mm2 and a lateral compressive stress of 200 N/mm2 in perpendicular directions. E = 2 x 10-5 N/ mm2, μ= 0.3. What is the approximate elongation of the bar in the longitudinal direction?a)0.44 mm b)0.88 mmc)0.22 mm d)1.0 mmCorrect answer is option 'D'. Can you explain this answer?
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A mild steel bar of square cross-section 40 mm x 40 mm is 400 mm long. It is subjected to a longitudinal tensile stress of 440 N/mm2 and a lateral compressive stress of 200 N/mm2 in perpendicular directions. E = 2 x 10-5 N/ mm2, μ= 0.3. What is the approximate elongation of the bar in the longitudinal direction?a)0.44 mm b)0.88 mmc)0.22 mm d)1.0 mmCorrect answer is option 'D'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A mild steel bar of square cross-section 40 mm x 40 mm is 400 mm long. It is subjected to a longitudinal tensile stress of 440 N/mm2 and a lateral compressive stress of 200 N/mm2 in perpendicular directions. E = 2 x 10-5 N/ mm2, μ= 0.3. What is the approximate elongation of the bar in the longitudinal direction?a)0.44 mm b)0.88 mmc)0.22 mm d)1.0 mmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A mild steel bar of square cross-section 40 mm x 40 mm is 400 mm long. It is subjected to a longitudinal tensile stress of 440 N/mm2 and a lateral compressive stress of 200 N/mm2 in perpendicular directions. E = 2 x 10-5 N/ mm2, μ= 0.3. What is the approximate elongation of the bar in the longitudinal direction?a)0.44 mm b)0.88 mmc)0.22 mm d)1.0 mmCorrect answer is option 'D'. Can you explain this answer?.
A mild steel bar of square cross-section 40 mm x 40 mm is 400 mm long. It is subjected to a longitudinal tensile stress of 440 N/mm2 and a lateral compressive stress of 200 N/mm2 in perpendicular directions. E = 2 x 10-5 N/ mm2, μ= 0.3. What is the approximate elongation of the bar in the longitudinal direction?a)0.44 mm b)0.88 mmc)0.22 mm d)1.0 mmCorrect answer is option 'D'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A mild steel bar of square cross-section 40 mm x 40 mm is 400 mm long. It is subjected to a longitudinal tensile stress of 440 N/mm2 and a lateral compressive stress of 200 N/mm2 in perpendicular directions. E = 2 x 10-5 N/ mm2, μ= 0.3. What is the approximate elongation of the bar in the longitudinal direction?a)0.44 mm b)0.88 mmc)0.22 mm d)1.0 mmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A mild steel bar of square cross-section 40 mm x 40 mm is 400 mm long. It is subjected to a longitudinal tensile stress of 440 N/mm2 and a lateral compressive stress of 200 N/mm2 in perpendicular directions. E = 2 x 10-5 N/ mm2, μ= 0.3. What is the approximate elongation of the bar in the longitudinal direction?a)0.44 mm b)0.88 mmc)0.22 mm d)1.0 mmCorrect answer is option 'D'. Can you explain this answer?.
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