Thin-wall cylinder, internal pressure

Figure 8.27 Fibrous glass-reinforced plastic thin-wall cylinder (a) internal pressure alone and (b) internal pressure plus twisting moment...

A thin walled cylinder with closed ends of radius r and wall thickness is fabricated from a polymer with a yield stress in pure shear of k. Calculate the internal pressure required to produce yielding of the cylinder walls if the yield criterion under appropriate conditions of temperature and strain rate may be written as... 

Example 5 In the case of a heavy-walled cylinder under internal pressure (see Fig. 3-61). Using methods similar to those used for the thin-walled cylinder, the creep type of radial expansion for a heavy-walled cylinder can be shown to be... 

Figure 6-47. A fiberglass-reinforced plastic thin-walled cylinder showing internal pressure alone.

Pipe-Wall Thickness. Once the design pressure and temperature have been established and the pipe material and size selected, the wall thickness is calculated using the appropriate section of the code. In rare cases, a thin pipe must be made thicker to withstand handling. Occasionally the thickness is affected by external loads or vibrations. All codes prescribe essentially the same design formula for metallic hoUow circular cylinders under internal pressure ... 

The pipe wall thickness is selected to resist the internal pressure, with an allowance for corrosion. Processes pipes can normally be considered as thin cylinders only high-pressure pipes, such as high-pressure steam lines, are likely to be classified as thick cylinders and must be given special consideration (see Chapter 13). 

Figure 8.8 Element of the wall of a thin cylinder subjected to internal pressure P. Reprinted, by permission, from G. Lewis, Selection of Engineering Materials, p. 140. Copyright 1990 by Prentice-Hill, Inc.

Stresses in thick- and thin-walled hollow cylinders p internal pressure N/mm2 a stress N/mm2 u = DJD, diameter ratio... 

The structure of this formula can quickly be related to the thin-walled pressure vessel cylinder equation. Using the equation that calculates the stress at the center of the vessel wall, ux = P R + 0.5t)/t, and rearranging to solve for the thickness, results m. t = PR/ ux — 0.5P. The addition of the weld joint efficiency, E, and changing the coefficient before P to 0.6 results in the ASME code formula, t = PR/ SE — 0.6P), which they feel best represents the minimum wall thickness required to contain an internal pressure, P, in a cylindrical vessel having a radius, R, and made of a material with an allowable stress, S. 

A simple example of a statically determinate problem is a thin-walled cylindrical pressure vessel with spherical end-caps, containing a gas or fluid exerting a pressure P. The geometry is shown in Figs. 4.3 and 4.4 the cylindrical section has a radius r, length L and thickness t, such that L r t. The cylinder is being expanded by the internal pressure and the principal axes are easily... 

Find a solution for the radial displacement in a thin-wall cylindrical pressure vessel with closed (spherical) ends. Assume a step input in internal pressine, the cylinder is made of a polymer whose properties are elastic in bulk and Maxwellian in shear. 

Thin-wallcd and thick-walled cylinders arc forms of pipeline primarily used in the offshore industry to transport gas and hquid under pressure. Cylindrical pipes are also used as a stmctural load bearing member to restrain the motion of a platform, for example, in response to wind, waves and currents (to within a specified limit). When a pipe is exposed to a combination of internal and external pressure, the pipe material will be subjected to pressure loading and, as a result, will develop stresses in all directions. The resulting normal stresses induced by the pressure loading are functions of the pipe diameter, wall thickness and cylindrical shell boundary conditions (open-ended cylinder or closed-ended cylinder) (Kashani and Young, 2008). 

The membranes are manufactured from acetylcellulose or, more preferably, polyamide. The technical construction is complicated and made expensive by the large pressure differences and the need for thin membranes. Bundles of coiled thin hollow capillaries (external diameter 0.1 mm, internal diameter 0.04 mm) are, for example, placed in a pressure cylinder (Fig. 1.1-3). The.se capillaries protrude from the ends of the cylinder through plastic sealing layers. Of the (high salt content)-water fed into the cylinder from the other side, 30% passes through the capillary walls into the capillaries and the rest is run off as concentrate and disposed of. An intensive and expensive pretreatment of the feed water is also necessary in addition to the removal of all colloidal and biological impurities, treatment of the feed water is also necessary e.g. by acid addition. The use of feed water from wells in the neighborhood of beaches is particularly favored. 

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