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A thick cylinder of internal radius and external radius a and b is subjected to internal pressure p as well as external pressure p. Which one of the following statements is correct?
The magnitude of circumferential stress developed is:
- a)Maximum at radius r = a
- b)Maximum at radius r = b
- c)Maximum at radius r = √ab
- d)Constant
Correct answer is option 'D'. Can you explain this answer?
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A thick cylinder of internal radius and external radius a and b is sub...
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Explanation:
Circumferential stress is the stress developed in the circumferential direction of a cylinder. In this case, the cylinder is subjected to both internal and external pressures. Let us analyze the stress distribution in the cylinder.
Stress Distribution:
The stress distribution in the cylinder can be analyzed using Lame's equation. According to Lame's equation, the circumferential stress (σθ) can be given by the following formula:
σθ = (pi*r^2*(b^2-a^2))/(r^3-a^3)
where r is the radius of the cylinder.
From the above equation, we can observe that the circumferential stress is directly proportional to the internal and external pressure and the square of the radial distance. Therefore, the stress distribution in the cylinder is as follows:
- The stress is maximum at the inner surface of the cylinder (r = a) and minimum at the outer surface of the cylinder (r = b).
- The stress is constant over any radial section of the cylinder.
Therefore, the correct option is 'D' i.e., the magnitude of circumferential stress is constant.
Circumferential stress is the stress developed in the circumferential direction of a cylinder. In this case, the cylinder is subjected to both internal and external pressures. Let us analyze the stress distribution in the cylinder.
Stress Distribution:
The stress distribution in the cylinder can be analyzed using Lame's equation. According to Lame's equation, the circumferential stress (σθ) can be given by the following formula:
σθ = (pi*r^2*(b^2-a^2))/(r^3-a^3)
where r is the radius of the cylinder.
From the above equation, we can observe that the circumferential stress is directly proportional to the internal and external pressure and the square of the radial distance. Therefore, the stress distribution in the cylinder is as follows:
- The stress is maximum at the inner surface of the cylinder (r = a) and minimum at the outer surface of the cylinder (r = b).
- The stress is constant over any radial section of the cylinder.
Therefore, the correct option is 'D' i.e., the magnitude of circumferential stress is constant.
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A thick cylinder of internal radius and external radius a and b is subjected to internal pressure p as well as external pressure p. Which one of the following statements is correct?The magnitude of circumferential stress developed is:a)Maximum at radius r = ab)Maximum at radius r = bc)Maximum at radius r = √abd)ConstantCorrect answer is option 'D'. Can you explain this answer?
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