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FIGURE 39.9 Thermal stress functions for thick cylindrical shell. (From Ref. [39.9].)
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39.8 DESIGN OF PRESSURE CYLINDERS
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Cylindrical shells are commonly used in industrial applications for their adequate structural strength, ease of fabrication, and economical consumption of material. The vessels, depending on their function, can be vertical or horizontal. A vertical orientation is often preferred for thin-walled vessels operating under low internal pressure because of the additional bending stresses resulting from the weights of the vessel itself and the fluid in the vessel.
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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.
PRESSURE CYLINDERS 39.19
PRESSURE CYLINDERS
Cylindrical shells of such elastic materials as steels, nonferrous metals, and most alloys that operate under internal pressures up to 10 MPa are fabricated mostly of rolled and subsequently welded sheets. The joint connections of cylindrical shells made of copper or brass sheets are made by soldering with suitable solders. Cylindrical vessels of steel operating under pressures greater than 10 MPa are commonly fabricated of forged pieces that are heat-treated. Cylindrical shells of brittle materials for vessels operating under low internal pressures (approximately up to 0.8 MPa) are molded. Cast shells are usually fabricated with a bottom. In some cases, cast shells are made of elastic metals and their alloys. The fabrication of the cylindrical vessels by the rolling of sheets is a very common method of manufacturing low- and medium-pressure (1.75 to 10.0 MPa) vessels. Azbel and Cheremisinoff [39.1] give the following general guidelines for designing welded and soldered cylindrical shells: 1. 2. 3. 4. 5. The length of the seams should be minimized. The minimum number of longitudinal seams should be provided. Longitudinal and circumferential seams must be butt welded. All joints should be accessible for inspection and repair. It is not permissible to provide holes, access holes, or any opening on the seams, especially on longitudinal seams.
Shell thicknesses of vessels operating under very low pressures are not designed; they are selected on the basis of manufacturing considerations. Durability is estimated from the available information regarding corrosion resistance of the material. The minimum thicknesses of a shell rolled from sheet metals are given as follows: carbon and low-alloy steel, 4 mm; austenite steel, 3.0 to 4.0 mm; copper, 2.5 to 3.0 mm; and cast materials, 2.0 to 2.5 mm.
39.8.1 Design of Welded Cylindrical Shells The structural design of cylindrical shells is based on membrane theory. In order to express the design relations in convenient form, it is necessary to (1) select the strength theory best reflecting the material behavior, (2) consider the weakening of the construction induced by welding and other connections, (3) consider wall thinning as a result of corrosion effects, and (4) establish a factor of safety and allowable stresses. The distortion-energy theory (see Chap. 28) gives the basic design stress as d = [ 2 + 2 + 2 2( t + t r + r)]1/2 t r (39.46)
where t, , and r = principal circumferential, longitudinal, and radial stresses, respectively. For a thin-walled cylindrical shell operating under an internal pressure pi, the radial stress is assumed to be equal to zero, and the longitudinal stress induced in the shell is given by = pidi 4t (39.16)
where di = inside diameter, and t = the thickness of the shell. The circumferential stress induced in the shell is given by
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.
PRESSURE CYLINDERS 39.20
CLASSICAL STRESS AND DEFORMATION ANALYSIS
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