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Where does the maximum hoop stress in a thick cylinder under external pressure occur ?
- a)At the outer surface
- b)At the inner surface
- c)At the mid-thickness
- d)At the 2/3rd outer radius
Correct answer is option 'B'. Can you explain this answer?
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Where does the maximum hoop stress in a thick cylinder under external ...
Maximum Hoop Stress in a Thick Cylinder under External Pressure
The maximum hoop stress in a thick cylinder occurs at the inner surface. To understand why this is the case, let's break down the concept step by step.
Thick Cylinder
A thick cylinder is a cylindrical structure with a relatively large ratio of its inner radius to its wall thickness. It is used in various engineering applications, such as pressure vessels, pipes, and hydraulic cylinders. The thickness of the cylinder is significant enough to affect the distribution of stress within the structure.
Hoop Stress
Hoop stress is a type of stress that occurs circumferentially around a cylinder or pipe. It is caused by the internal or external pressure acting on the cylinder. The hoop stress is given by the formula:
σ_h = (P * r_i) / (r_o - r_i)
where σ_h is the hoop stress, P is the external pressure, r_i is the inner radius, and r_o is the outer radius of the cylinder.
Analysis of Hoop Stress Distribution
To analyze the distribution of hoop stress within a thick cylinder, we can consider a small element within the cylinder wall. This element has an inner radius r_i and an outer radius r_o, with a thickness δr.
Stress Variation with Radius
The stress within the cylinder wall varies linearly with the radial distance. At the inner surface (r = r_i), the stress is maximum, and it decreases linearly towards the outer surface (r = r_o). This variation is due to the mechanics of the cylinder under external pressure.
Explanation
The maximum hoop stress occurs at the inner surface of the thick cylinder due to the following reasons:
1. Internal Pressure: The external pressure acting on the cylinder causes a compressive stress on the inner surface. This results in the maximum hoop stress at the inner surface.
2. Stress Concentration: The stress concentration factor, which is the ratio of maximum stress to average stress, is higher at the inner surface compared to the outer surface. This is because the inner surface has a smaller radius, leading to a higher stress concentration.
3. Material Strength: The inner surface experiences higher stress levels compared to the outer surface. Therefore, the material at the inner surface must have higher strength to withstand the maximum hoop stress.
Conclusion
In conclusion, the maximum hoop stress in a thick cylinder under external pressure occurs at the inner surface. This is due to the compressive stress caused by the external pressure and the stress concentration at the smaller radius of the inner surface. Understanding the distribution of hoop stress is crucial for designing safe and reliable thick cylinders in various engineering applications.
The maximum hoop stress in a thick cylinder occurs at the inner surface. To understand why this is the case, let's break down the concept step by step.
Thick Cylinder
A thick cylinder is a cylindrical structure with a relatively large ratio of its inner radius to its wall thickness. It is used in various engineering applications, such as pressure vessels, pipes, and hydraulic cylinders. The thickness of the cylinder is significant enough to affect the distribution of stress within the structure.
Hoop Stress
Hoop stress is a type of stress that occurs circumferentially around a cylinder or pipe. It is caused by the internal or external pressure acting on the cylinder. The hoop stress is given by the formula:
σ_h = (P * r_i) / (r_o - r_i)
where σ_h is the hoop stress, P is the external pressure, r_i is the inner radius, and r_o is the outer radius of the cylinder.
Analysis of Hoop Stress Distribution
To analyze the distribution of hoop stress within a thick cylinder, we can consider a small element within the cylinder wall. This element has an inner radius r_i and an outer radius r_o, with a thickness δr.
Stress Variation with Radius
The stress within the cylinder wall varies linearly with the radial distance. At the inner surface (r = r_i), the stress is maximum, and it decreases linearly towards the outer surface (r = r_o). This variation is due to the mechanics of the cylinder under external pressure.
Explanation
The maximum hoop stress occurs at the inner surface of the thick cylinder due to the following reasons:
1. Internal Pressure: The external pressure acting on the cylinder causes a compressive stress on the inner surface. This results in the maximum hoop stress at the inner surface.
2. Stress Concentration: The stress concentration factor, which is the ratio of maximum stress to average stress, is higher at the inner surface compared to the outer surface. This is because the inner surface has a smaller radius, leading to a higher stress concentration.
3. Material Strength: The inner surface experiences higher stress levels compared to the outer surface. Therefore, the material at the inner surface must have higher strength to withstand the maximum hoop stress.
Conclusion
In conclusion, the maximum hoop stress in a thick cylinder under external pressure occurs at the inner surface. This is due to the compressive stress caused by the external pressure and the stress concentration at the smaller radius of the inner surface. Understanding the distribution of hoop stress is crucial for designing safe and reliable thick cylinders in various engineering applications.
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Where does the maximum hoop stress in a thick cylinder under external pressure occur ?a)At the outer surfaceb)At the inner surfacec)At the mid-thicknessd)At the 2/3rd outer radiusCorrect answer is option 'B'. Can you explain this answer?
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Where does the maximum hoop stress in a thick cylinder under external pressure occur ?a)At the outer surfaceb)At the inner surfacec)At the mid-thicknessd)At the 2/3rd outer radiusCorrect answer is option 'B'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Where does the maximum hoop stress in a thick cylinder under external pressure occur ?a)At the outer surfaceb)At the inner surfacec)At the mid-thicknessd)At the 2/3rd outer radiusCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Where does the maximum hoop stress in a thick cylinder under external pressure occur ?a)At the outer surfaceb)At the inner surfacec)At the mid-thicknessd)At the 2/3rd outer radiusCorrect answer is option 'B'. Can you explain this answer?.
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