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A thick-walled hollow cylinder having outside and inside radii of 90 mm and 40 mm respectively is subjected to an external pressure of 800 MN/m2. The maximum circumferential stress in the cylinder will occur at a radius of
- a)40 mm
- b)60 mm
- c)65 mm
- d)90 mm
Correct answer is option 'A'. Can you explain this answer?
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A thick-walled hollow cylinder having outside and inside radii of 90 m...
The maximum hoop stress will always occurs at inner most radii irrespective of the location of pressure.
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A thick-walled hollow cylinder having outside and inside radii of 90 m...
The maximum hoop stress will always occurs at inner most radii irrespective of the location of pressure.
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A thick-walled hollow cylinder having outside and inside radii of 90 m...
The maximum circumferential stress in a thick-walled hollow cylinder can be determined using the formula:
σθ = P × (ro^2 - ri^2) / (ro^2 + ri^2)
Where:
σθ = maximum circumferential stress
P = external pressure
ro = outside radius
ri = inside radius
In this case, the given values are:
P = 800 MN/m^2
ro = 90 mm
ri = 40 mm
To determine the maximum circumferential stress, plug in these values into the formula:
σθ = (800 × 10^6) × ((90 × 10^-3)^2 - (40 × 10^-3)^2) / ((90 × 10^-3)^2 + (40 × 10^-3)^2)
Calculating the above expression will give us the maximum circumferential stress. However, to find out at which radius this maximum stress occurs, we need to differentiate the above expression with respect to the radius 'r' and equate it to zero.
Differentiating the expression with respect to 'r' and equating to zero, we get:
dσθ/dr = 0
Solving this equation will give us the radius at which the maximum circumferential stress occurs. However, in this case, we don't need to solve this equation as we can see that the maximum circumferential stress occurs at the inner radius 'ri'.
Therefore, the correct answer is option 'A' - the maximum circumferential stress in the cylinder will occur at a radius of 40 mm.
σθ = P × (ro^2 - ri^2) / (ro^2 + ri^2)
Where:
σθ = maximum circumferential stress
P = external pressure
ro = outside radius
ri = inside radius
In this case, the given values are:
P = 800 MN/m^2
ro = 90 mm
ri = 40 mm
To determine the maximum circumferential stress, plug in these values into the formula:
σθ = (800 × 10^6) × ((90 × 10^-3)^2 - (40 × 10^-3)^2) / ((90 × 10^-3)^2 + (40 × 10^-3)^2)
Calculating the above expression will give us the maximum circumferential stress. However, to find out at which radius this maximum stress occurs, we need to differentiate the above expression with respect to the radius 'r' and equate it to zero.
Differentiating the expression with respect to 'r' and equating to zero, we get:
dσθ/dr = 0
Solving this equation will give us the radius at which the maximum circumferential stress occurs. However, in this case, we don't need to solve this equation as we can see that the maximum circumferential stress occurs at the inner radius 'ri'.
Therefore, the correct answer is option 'A' - the maximum circumferential stress in the cylinder will occur at a radius of 40 mm.
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A thick-walled hollow cylinder having outside and inside radii of 90 mm and 40 mm respectively is subjected to an external pressure of 800 MN/m2. The maximum circumferential stress in the cylinder will occur at a radius ofa)40 mmb)60 mmc)65 mmd)90 mmCorrect answer is option 'A'. Can you explain this answer?
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A thick-walled hollow cylinder having outside and inside radii of 90 mm and 40 mm respectively is subjected to an external pressure of 800 MN/m2. The maximum circumferential stress in the cylinder will occur at a radius ofa)40 mmb)60 mmc)65 mmd)90 mmCorrect 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 thick-walled hollow cylinder having outside and inside radii of 90 mm and 40 mm respectively is subjected to an external pressure of 800 MN/m2. The maximum circumferential stress in the cylinder will occur at a radius ofa)40 mmb)60 mmc)65 mmd)90 mmCorrect 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 thick-walled hollow cylinder having outside and inside radii of 90 mm and 40 mm respectively is subjected to an external pressure of 800 MN/m2. The maximum circumferential stress in the cylinder will occur at a radius ofa)40 mmb)60 mmc)65 mmd)90 mmCorrect answer is option 'A'. Can you explain this answer?.
A thick-walled hollow cylinder having outside and inside radii of 90 mm and 40 mm respectively is subjected to an external pressure of 800 MN/m2. The maximum circumferential stress in the cylinder will occur at a radius ofa)40 mmb)60 mmc)65 mmd)90 mmCorrect 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 thick-walled hollow cylinder having outside and inside radii of 90 mm and 40 mm respectively is subjected to an external pressure of 800 MN/m2. The maximum circumferential stress in the cylinder will occur at a radius ofa)40 mmb)60 mmc)65 mmd)90 mmCorrect 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 thick-walled hollow cylinder having outside and inside radii of 90 mm and 40 mm respectively is subjected to an external pressure of 800 MN/m2. The maximum circumferential stress in the cylinder will occur at a radius ofa)40 mmb)60 mmc)65 mmd)90 mmCorrect answer is option 'A'. Can you explain this answer?.
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