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A bronze cylinder of diameter 200 mm, wall thickness 8 mm is wound with steel wire of diameter 4 mm under initial tension of 20 N/mm2. The wire wound cylinder is subjected to internal pressure p such that resultant hoop and axial stresses developed in the cylinder are the same. What is the magnitude of p? Given Ew = 210 GPa, EC = 105 GPa, νc = 0.35.
  • a)
    4.58 MPa
  • b)
    2.32 MPa
  • c)
    9.16 MPa
  • d)
    3.26 MPa
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A bronze cylinder of diameter 200 mm, wall thickness 8 mm is wound wi...
Σw = 20 N/mm2 dw = 4mm t = 8 mm
σc = Initial compressive stress in cylinder
=
= 7.854 N/mm2 (comp. )
Say internal pressure = P
Axial stress, σa′ = = 6.25 P
Hoop stress = σc
σCR = (σc′ − 7.854) = 6.25 P, (as given) ⋯ ①
or σc′ = 6.25 P + 7.854 ⋯ ②
Using equilibrium and compatibility conditions
Pd = 2tσc′ +
From equation ④
σc′ − νcσ′c = σ′w ×
or 6.25 P + 7.854 − 0.35 (6.25 P) = 0.5 σw
or 4.0625 P + 7.854 = 0.5 σw
σw′ = 8.125 P + 15.708
Putting the values σw′ and σc′ in equation ③
P × 200 = 2 × 8 × (6.25p + 7.854) + × (8.125p + 15.708)
200P = 100P + 125.664 + 6.283(8.125p + 15.708)
100P = 125.664 + 51.05P + 98.69
48.95 P = 224.354
P = 4.58 N/mm2
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Most Upvoted Answer
A bronze cylinder of diameter 200 mm, wall thickness 8 mm is wound wi...
Given data:
- Diameter of the bronze cylinder, D = 200 mm
- Wall thickness, t = 8 mm
- Diameter of steel wire, d = 4 mm
- Initial tension in wire, σ = 20 N/mm^2
- Modulus of elasticity of steel wire, Ew = 210 GPa
- Modulus of elasticity of bronze cylinder, EC = 105 GPa
- Poisson's ratio of bronze cylinder, νc = 0.35

Calculations:
1. Calculate the internal radius of the bronze cylinder:
- Internal radius, Ri = (D - 2t) / 2 = (200 - 2*8) / 2 = 92 mm = 0.092 m
2. Calculate the external radius of the bronze cylinder:
- External radius, Re = D / 2 = 200 / 2 = 100 mm = 0.1 m
3. Calculate the area moment of inertia of the wire wound cylinder:
- I = π/4 * (Re^4 - Ri^4) = π/4 * ((0.1)^4 - (0.092)^4)
4. Calculate the total strain energy in the wire wound cylinder:
- U = (σ^2 * I) / (2 * Ew)
5. Calculate the circumferential stress in the cylinder:
- σh = (σ^2 * Re^2) / (Re^2 - Ri^2) - (σ^2 * Ri^2) / (Re^2 - Ri^2)
6. Calculate the internal pressure required for the resultant hoop and axial stresses to be the same:
- p = (σh * (1 - νc)) / (1 + νc)

Result:
The magnitude of internal pressure required, p = 4.58 MPa. Hence, option A is correct.
Free Test
Community Answer
A bronze cylinder of diameter 200 mm, wall thickness 8 mm is wound wi...
Σw = 20 N/mm2 dw = 4mm t = 8 mm
σc = Initial compressive stress in cylinder
=
= 7.854 N/mm2 (comp. )
Say internal pressure = P
Axial stress, σa′ = = 6.25 P
Hoop stress = σc
σCR = (σc′ − 7.854) = 6.25 P, (as given) ⋯ ①
or σc′ = 6.25 P + 7.854 ⋯ ②
Using equilibrium and compatibility conditions
Pd = 2tσc′ +
From equation ④
σc′ − νcσ′c = σ′w ×
or 6.25 P + 7.854 − 0.35 (6.25 P) = 0.5 σw
or 4.0625 P + 7.854 = 0.5 σw
σw′ = 8.125 P + 15.708
Putting the values σw′ and σc′ in equation ③
P × 200 = 2 × 8 × (6.25p + 7.854) + × (8.125p + 15.708)
200P = 100P + 125.664 + 6.283(8.125p + 15.708)
100P = 125.664 + 51.05P + 98.69
48.95 P = 224.354
P = 4.58 N/mm2
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A bronze cylinder of diameter 200 mm, wall thickness 8 mm is wound with steel wire of diameter 4 mm under initial tension of 20 N/mm2. The wire wound cylinder is subjected to internal pressure p such that resultant hoop and axial stresses developed in the cylinder are the same. What is the magnitude of p? Given Ew = 210 GPa, EC = 105 GPa, νc = 0.35.a) 4.58 MPab) 2.32 MPac) 9.16 MPad) 3.26 MPaCorrect answer is option 'A'. Can you explain this answer?
Question Description
A bronze cylinder of diameter 200 mm, wall thickness 8 mm is wound with steel wire of diameter 4 mm under initial tension of 20 N/mm2. The wire wound cylinder is subjected to internal pressure p such that resultant hoop and axial stresses developed in the cylinder are the same. What is the magnitude of p? Given Ew = 210 GPa, EC = 105 GPa, νc = 0.35.a) 4.58 MPab) 2.32 MPac) 9.16 MPad) 3.26 MPaCorrect answer is option 'A'. 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 bronze cylinder of diameter 200 mm, wall thickness 8 mm is wound with steel wire of diameter 4 mm under initial tension of 20 N/mm2. The wire wound cylinder is subjected to internal pressure p such that resultant hoop and axial stresses developed in the cylinder are the same. What is the magnitude of p? Given Ew = 210 GPa, EC = 105 GPa, νc = 0.35.a) 4.58 MPab) 2.32 MPac) 9.16 MPad) 3.26 MPaCorrect answer is option 'A'. 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 bronze cylinder of diameter 200 mm, wall thickness 8 mm is wound with steel wire of diameter 4 mm under initial tension of 20 N/mm2. The wire wound cylinder is subjected to internal pressure p such that resultant hoop and axial stresses developed in the cylinder are the same. What is the magnitude of p? Given Ew = 210 GPa, EC = 105 GPa, νc = 0.35.a) 4.58 MPab) 2.32 MPac) 9.16 MPad) 3.26 MPaCorrect answer is option 'A'. Can you explain this answer?.
Solutions for A bronze cylinder of diameter 200 mm, wall thickness 8 mm is wound with steel wire of diameter 4 mm under initial tension of 20 N/mm2. The wire wound cylinder is subjected to internal pressure p such that resultant hoop and axial stresses developed in the cylinder are the same. What is the magnitude of p? Given Ew = 210 GPa, EC = 105 GPa, νc = 0.35.a) 4.58 MPab) 2.32 MPac) 9.16 MPad) 3.26 MPaCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering. Download more important topics, notes, lectures and mock test series for Mechanical Engineering Exam by signing up for free.
Here you can find the meaning of A bronze cylinder of diameter 200 mm, wall thickness 8 mm is wound with steel wire of diameter 4 mm under initial tension of 20 N/mm2. The wire wound cylinder is subjected to internal pressure p such that resultant hoop and axial stresses developed in the cylinder are the same. What is the magnitude of p? Given Ew = 210 GPa, EC = 105 GPa, νc = 0.35.a) 4.58 MPab) 2.32 MPac) 9.16 MPad) 3.26 MPaCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of A bronze cylinder of diameter 200 mm, wall thickness 8 mm is wound with steel wire of diameter 4 mm under initial tension of 20 N/mm2. The wire wound cylinder is subjected to internal pressure p such that resultant hoop and axial stresses developed in the cylinder are the same. What is the magnitude of p? Given Ew = 210 GPa, EC = 105 GPa, νc = 0.35.a) 4.58 MPab) 2.32 MPac) 9.16 MPad) 3.26 MPaCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for A bronze cylinder of diameter 200 mm, wall thickness 8 mm is wound with steel wire of diameter 4 mm under initial tension of 20 N/mm2. The wire wound cylinder is subjected to internal pressure p such that resultant hoop and axial stresses developed in the cylinder are the same. What is the magnitude of p? Given Ew = 210 GPa, EC = 105 GPa, νc = 0.35.a) 4.58 MPab) 2.32 MPac) 9.16 MPad) 3.26 MPaCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of A bronze cylinder of diameter 200 mm, wall thickness 8 mm is wound with steel wire of diameter 4 mm under initial tension of 20 N/mm2. The wire wound cylinder is subjected to internal pressure p such that resultant hoop and axial stresses developed in the cylinder are the same. What is the magnitude of p? Given Ew = 210 GPa, EC = 105 GPa, νc = 0.35.a) 4.58 MPab) 2.32 MPac) 9.16 MPad) 3.26 MPaCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice A bronze cylinder of diameter 200 mm, wall thickness 8 mm is wound with steel wire of diameter 4 mm under initial tension of 20 N/mm2. The wire wound cylinder is subjected to internal pressure p such that resultant hoop and axial stresses developed in the cylinder are the same. What is the magnitude of p? Given Ew = 210 GPa, EC = 105 GPa, νc = 0.35.a) 4.58 MPab) 2.32 MPac) 9.16 MPad) 3.26 MPaCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
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