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Pressure Vessels

Pressure vessels are designed to contain liquids or gases under significant pressure changes compared to ambient conditions. This chapter explores the mechanics of thin-walled and thick-walled cylinders, spherical shells, and combined thermo-mechanical stresses in pressure vessels. It also examines the applications of these principles in real-world scenarios, particularly in boilers, highlighting the importance of material selection and adherence to design codes for safety and performance.

Sections

Introduction to Pressure Vessels

Pressure vessels are specialized containers designed to hold gases or liquids under different pressure conditions than the ambient environment, ensuring structural integrity under various stress conditions.

1 Section Overview

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Thin-Walled Cylinders

Thin-walled cylinders are pressure vessels with a wall thickness significantly less than the radius, allowing for simplified stress analysis.

2 Section Overview

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2.1 Hoop (Circumferential) Stress

Hoop stress is the circumferential stress in thin-walled cylinders caused by internal pressure, calculated with the formula σh = p * r / t.

2.2 Axial (Longitudinal) Stress

This section discusses axial stress in pressure vessels, focusing on its calculation and significance in engineering design.

Thick-Walled Cylinders

Thick-walled cylinders analyze stress distribution under pressure where wall thickness is significant relative to radius.

3 Section Overview

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3.1 Radial Stress

This section covers the concept of radial stress in thick-walled cylinders, including the equations of Lame and the conditions for stress distribution under different pressures.

3.2 Hoop Stress

Hoop stress is the circumferential stress experienced by cylindrical pressure vessels, calculated as a function of internal pressure, radius, and wall thickness.

Spherical Shells

This section discusses spherical shells in the context of pressure vessels, focusing on stress distribution in thin spherical shells under internal pressure.

4 Section Overview

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Combined Thermo-Mechanical Stress

This section discusses the effects of combined mechanical and thermal stresses in pressure vessels, particularly under high-temperature conditions.

5 Section Overview

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Applications & Case Studies: Boilers

This section discusses the significance and characteristics of boilers as pressure vessels.

6 Section Overview

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Learning Objectives

  • Pressure vessels must maintain structural integrity under internal pressure and temperature changes.

  • The stress analysis of thin-walled cylinders simplifies using hoop and axial stress formulas, while thick-walled cylinders require Lame's equations due to radial stress variations.

  • Combined effects of mechanical and thermal stresses must be considered in the design of pressure vessels, particularly those operating at high temperatures.

Key Concepts

Pressure Vessels

Containers designed to hold liquids or gases significantly different from ambient pressures.

Thin-Walled Cylinder

A cylinder with a wall thickness that is much smaller than its radius, allowing simplifications in stress calculations.

Thick-Walled Cylinder

A cylinder where wall thickness cannot be neglected in stress analysis, requiring Lame's equations for accurate stress calculations.

Spherical Shells

Thin-walled structures where the stress is uniformly distributed in all directions, often used in storage applications.

Combined Thermo-Mechanical Stress

The cumulative stress from both mechanical pressures and thermal changes in a material.

Boilers

Common applications of pressure vessels that operate under high pressure and temperature, requiring careful analysis of stresses.

Practice Exercises

Total Questions

2

Estimated Time

4 min

Passing Score

70%

Instructions

  • Read each question carefully
  • You can use hints if you need help
  • Complete all questions before submitting

1 more question available

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