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A thin cylinder with both ends closed is subjected to internal pressure p. The longitudinal stress at the surface has been calculated as so. maximum shear stress at the surface will be equal to
- a)2s0
- b)1.5s0
- c)s0
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
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A thin cylinder with both ends closed is subjected to internal pressur...
Given: A thin cylinder with both ends closed is subjected to internal pressure p. The longitudinal stress at the surface has been calculated as so.
To find: The maximum shear stress at the surface.
Solution:
- Longitudinal stress at the surface of the cylinder can be given by the formula:
σL = pd/2t
Where, p = internal pressure, d = diameter of the cylinder, and t = thickness of the cylinder.
- The maximum shear stress at the surface of the cylinder can be given by the formula:
τmax = σL/2
- Substituting the value of σL in the above formula, we get:
τmax = pd/4t
- As we know, the hoop stress at the surface of the cylinder can be given by the formula:
σH = pd/4t
- Since maximum shear stress is equal to half of hoop stress, we can say that:
τmax = σH/2
- Substituting the value of σH in the above equation, we get:
τmax = pd/8t
- Therefore, the maximum shear stress at the surface of the cylinder is given by pd/8t.
- From the given options, we can see that option C (s0) is the correct answer.
- Hence, the maximum shear stress at the surface of the cylinder is equal to s0.
Conclusion: The maximum shear stress at the surface of a thin cylinder with both ends closed subjected to internal pressure is given by pd/8t, which is equal to s0.
To find: The maximum shear stress at the surface.
Solution:
- Longitudinal stress at the surface of the cylinder can be given by the formula:
σL = pd/2t
Where, p = internal pressure, d = diameter of the cylinder, and t = thickness of the cylinder.
- The maximum shear stress at the surface of the cylinder can be given by the formula:
τmax = σL/2
- Substituting the value of σL in the above formula, we get:
τmax = pd/4t
- As we know, the hoop stress at the surface of the cylinder can be given by the formula:
σH = pd/4t
- Since maximum shear stress is equal to half of hoop stress, we can say that:
τmax = σH/2
- Substituting the value of σH in the above equation, we get:
τmax = pd/8t
- Therefore, the maximum shear stress at the surface of the cylinder is given by pd/8t.
- From the given options, we can see that option C (s0) is the correct answer.
- Hence, the maximum shear stress at the surface of the cylinder is equal to s0.
Conclusion: The maximum shear stress at the surface of a thin cylinder with both ends closed subjected to internal pressure is given by pd/8t, which is equal to s0.
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Community Answer
A thin cylinder with both ends closed is subjected to internal pressur...
Option 2 is correct as shear stress is half of longitudnal stress.( not sure)
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A thin cylinder with both ends closed is subjected to internal pressure p. The longitudinal stress at the surface has been calculated as so. maximum shear stress at the surface will be equal toa)2s0b)1.5s0c)s0d)None of theseCorrect answer is option 'C'. Can you explain this answer?
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