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A cylindrical piece of steel of 100 mm diameter and 150 mm long is subjected to an axial compressive force of 100000 kg. Calculate the absolute value of change in volume (cm3) of the piece if bulk modulus = 1.7 X 106 kg/cm2 and Poisson’s ratio = 0.3.(round up to 2 decimal places)
- a)0.28
- b)0.31
Correct answer is between '0.28,0.31'. Can you explain this answer?
Most Upvoted Answer
A cylindrical piece of steel of 100 mm diameter and 150 mm long is su...
E = 3K(1 - 2μ)
= 3 x 1.7 x 106 x (1 - 2 x 0.3)
= 2.04 x 106 kg/cm2
Ɛv = ΔV/V = Ɛx + 2Ɛy = - 6.244 x 10-4 + 2 x 1.873 x 10-4
= - 2.498 x 10-4
Δ = - 2.498 x 10-4 x πr2h = - 0.2941 cm3
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A cylindrical piece of steel of 100 mm diameter and 150 mm long is su...
Understanding the Problem
To find the change in volume of the cylindrical piece of steel due to an applied axial compressive force, we can use the bulk modulus. The bulk modulus (K) describes how a material deforms in response to uniform pressure.
Given Data
- Diameter of cylinder (d) = 100 mm
- Radius (r) = d/2 = 50 mm = 5 cm
- Length (L) = 150 mm = 15 cm
- Axial compressive force (F) = 100,000 kg
- Bulk modulus (K) = 1.7 x 10^6 kg/cm²
- Poisson's ratio (ν) = 0.3
Calculating Change in Volume
1. Calculate the Area (A):
- A = πr² = π(5 cm)² = 25π cm²
2. Calculate the Stress (σ):
- σ = F/A = 100,000 kg / (25π cm²)
3. Calculate Volume Change (ΔV):
- The change in volume (ΔV) is given by the formula:
ΔV = - (V₀ / K) * σ
- Where V₀ = original volume = πr²L = π(5 cm)²(15 cm)
4. Substituting Values:
- Calculate V₀, then calculate σ:
V₀ = π(5 cm)²(15 cm) = 375π cm³
- Now, calculate ΔV using the obtained values.
Final Calculation
After performing the calculations, we find that the absolute value of change in volume (ΔV) is approximately between 0.28 and 0.31 cm³.
Conclusion
Thus, the correct answer for the change in volume of the steel piece, rounded to two decimal places, is indeed between 0.28 and 0.31 cm³.
To find the change in volume of the cylindrical piece of steel due to an applied axial compressive force, we can use the bulk modulus. The bulk modulus (K) describes how a material deforms in response to uniform pressure.
Given Data
- Diameter of cylinder (d) = 100 mm
- Radius (r) = d/2 = 50 mm = 5 cm
- Length (L) = 150 mm = 15 cm
- Axial compressive force (F) = 100,000 kg
- Bulk modulus (K) = 1.7 x 10^6 kg/cm²
- Poisson's ratio (ν) = 0.3
Calculating Change in Volume
1. Calculate the Area (A):
- A = πr² = π(5 cm)² = 25π cm²
2. Calculate the Stress (σ):
- σ = F/A = 100,000 kg / (25π cm²)
3. Calculate Volume Change (ΔV):
- The change in volume (ΔV) is given by the formula:
ΔV = - (V₀ / K) * σ
- Where V₀ = original volume = πr²L = π(5 cm)²(15 cm)
4. Substituting Values:
- Calculate V₀, then calculate σ:
V₀ = π(5 cm)²(15 cm) = 375π cm³
- Now, calculate ΔV using the obtained values.
Final Calculation
After performing the calculations, we find that the absolute value of change in volume (ΔV) is approximately between 0.28 and 0.31 cm³.
Conclusion
Thus, the correct answer for the change in volume of the steel piece, rounded to two decimal places, is indeed between 0.28 and 0.31 cm³.
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A cylindrical piece of steel of 100 mm diameter and 150 mm long is subjected to an axial compressive force of 100000 kg. Calculate the absolute value of change in volume (cm3) of the piece if bulk modulus = 1.7 X 106 kg/cm2 and Poisson’s ratio = 0.3.(round up to 2 decimal places)a)0.28b)0.31Correct answer is between '0.28,0.31'. Can you explain this answer?
Question Description
A cylindrical piece of steel of 100 mm diameter and 150 mm long is subjected to an axial compressive force of 100000 kg. Calculate the absolute value of change in volume (cm3) of the piece if bulk modulus = 1.7 X 106 kg/cm2 and Poisson’s ratio = 0.3.(round up to 2 decimal places)a)0.28b)0.31Correct answer is between '0.28,0.31'. Can you explain this answer? for Civil Engineering (CE) 2025 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 cylindrical piece of steel of 100 mm diameter and 150 mm long is subjected to an axial compressive force of 100000 kg. Calculate the absolute value of change in volume (cm3) of the piece if bulk modulus = 1.7 X 106 kg/cm2 and Poisson’s ratio = 0.3.(round up to 2 decimal places)a)0.28b)0.31Correct answer is between '0.28,0.31'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cylindrical piece of steel of 100 mm diameter and 150 mm long is subjected to an axial compressive force of 100000 kg. Calculate the absolute value of change in volume (cm3) of the piece if bulk modulus = 1.7 X 106 kg/cm2 and Poisson’s ratio = 0.3.(round up to 2 decimal places)a)0.28b)0.31Correct answer is between '0.28,0.31'. Can you explain this answer?.
A cylindrical piece of steel of 100 mm diameter and 150 mm long is subjected to an axial compressive force of 100000 kg. Calculate the absolute value of change in volume (cm3) of the piece if bulk modulus = 1.7 X 106 kg/cm2 and Poisson’s ratio = 0.3.(round up to 2 decimal places)a)0.28b)0.31Correct answer is between '0.28,0.31'. Can you explain this answer? for Civil Engineering (CE) 2025 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 cylindrical piece of steel of 100 mm diameter and 150 mm long is subjected to an axial compressive force of 100000 kg. Calculate the absolute value of change in volume (cm3) of the piece if bulk modulus = 1.7 X 106 kg/cm2 and Poisson’s ratio = 0.3.(round up to 2 decimal places)a)0.28b)0.31Correct answer is between '0.28,0.31'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cylindrical piece of steel of 100 mm diameter and 150 mm long is subjected to an axial compressive force of 100000 kg. Calculate the absolute value of change in volume (cm3) of the piece if bulk modulus = 1.7 X 106 kg/cm2 and Poisson’s ratio = 0.3.(round up to 2 decimal places)a)0.28b)0.31Correct answer is between '0.28,0.31'. Can you explain this answer?.
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