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PRESSURE CYLINDERS 39.2
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39.2 DESIGN PRINCIPLES OF PRESSURE CYLINDERS
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In the design of a pressure vessel as a unit, a number of criteria should be considered. These are (1) selection of the material for construction of the vessel based on a working knowledge of the properties of the material, (2) determination of the magnitude of the induced stress in conformity with the requirements of standard codes, and (3) determination of the elastic stability. To simplify the design and keep the cost of fabrication low, the components of a vessel should be made in the form of simple geometric shapes, such as spherical, cylindrical, or conical. A spherical geometry provides minimum surface area per unit volume and requires minimum wall thickness for a given pressure. From the point of view of material savings and uniform distribution of induced stresses in the shell wall, a spherical shape is favorable. However, the fabrication of spherical vessels is more complicated and expensive than that of cylindrical ones. Spherical vessels are used commonly for storage of gas and liquids. For large-volume, low-pressure storage, spherical vessels are economical. But for higher-pressure storage, cylindrical vessels are more economical. The most common types of vessels can be classified according to their 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Functions: Storage vessels, reactors, boilers, mixers, and heat exchangers Structural materials: Steel, cast iron, copper, plastics, etc. Method of fabrication: Welded, cast, brazed, flanged, etc. Geometry: Cylindrical, spherical, conical, combined Scheme of loading: Working under internal or external pressure Wall temperatures: Heated, unheated Corrosion action: Moderate or high corrosion effects Orientation in space: Vertical, horizontal, sloped Method of assembly: Detachable, nondetachable Wall thickness: Thin-walled (do/di < 1.5); thick-walled (do/di 1.5)
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Most vessels are designed as cylindrical shells fabricated of rolled sheet metal or as cylindrical shells that are cast. From the point of view of simplified structural design, the stressed state of the material of a thin-wall shell is considered biaxial. This is permissible because the magnitude of the radial stress in such a vessel wall is very small. The stressed state of the shell wall is generally the sum of the two basic components: (1) stressed state due to uniformly distributed forces on the surface as a result of fluid pressure, and (2) stressed state due to the action of the forces and moments distributed around the contour. The stressed condition due to uniform pressure of fluid on the surface of the shell can be determined either by the membrane or moment theory. The membrane theory yields accurate enough results for most engineering applications and is widely used for structural designs. The moment theory is not usually applied for the determination of stresses due to uniformly distributed fluid forces on a surface. The equations resulting from the application of the moment theory are complex and the design process is quite involved. End forces and moments are calculated in sections where a sudden change in load, wall thickness, or the properties of the shell material occurs. The stressed state induced by the applied end forces and moments are determined by application of the moment theory [39.1]. The induced stress and deformations due to end effects
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Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
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PRESSURE CYLINDERS 39.3
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PRESSURE CYLINDERS
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influence mostly the zones where the end forces and moments are applied. In general, end stresses should be carefully evaluated, and design measures must be taken to keep them within the safe limit. High values of end stresses are to be avoided, especially for brittle materials and vessels operating under high alternating loads. The structural reliability of the equipment parts is determined by two different approaches. The theory of elasticity requires that the strength be determined by the ultimate stress which the part can withstand without rupture, whereas the theory of plasticity suggests that the strength be determined by the ultimate load the part can withstand without residual deformation. The elastic theory is based on the assumption that the material of the component parts of the vessel is in an elastic state everywhere and nowhere does the state of stress exceed the yield point. The parts of a pressure vessel are not generally bonded uniformly. When the structural design is based on the ultimate stress occurring at the most loaded region of the construction, the required material consumption could be excessive. In design works using the membrane theory, only average stresses are assumed, and no efforts are made to include the local stresses of significant magnitude. However, the designer should consider the probable adverse effects of very high local stress intensities and modify the design accordingly. In heavily loaded parts of pressure vessels made of plastic materials, partial transition to the elastic-plastic state occurs. The plastic design method permits a realistic evaluation of the maximum load this vessel can withstand without failure.
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