Internal pressure Subject

The maximum internal pressure, subject to the avoidanceof reversed yielding, is then given by... 

Elastic Behavior. In the following discussion of the equations relevant to the design of thick-walled hoUow cylinders, it should be assumed that the material of which the cylinder is made is isotropic and that the cylinder is long and initially free from stress. It may be shown (1,2) that if a cylinder of inner radius, and outer radius, is subjected to a uniform internal pressure, the principal stresses in the radial and tangential directions, and <7, at any radius r, such that > r > are given by... 

The state of stress in a cylinder subjected to an internal pressure has been shown to be equivalent to a simple shear stress, T, which varies across the wall thickness in accordance with equation 5 together with a superimposed uniform (triaxial) tensile stress (6). 

If it is assumed that uniform tensile stress, like uniform compressive stress (7), has no significant effect on yield, then the yield pressure of a cylinder subjected solely to an internal pressure may be calculated from... 

A more important effect of prestressiag is its effect on the mean stress at the bore of the cylinder when an internal pressure is appHed. It may be seen from Figure 6 that when an initially stress-free cylinder is subjected to an internal pressure, the shear stress at the bore of the cylinder increases from O to A. On the other hand, when a prestressed cylinder of the same dimensions is subjected to the same internal pressure, the shear stress at the bore changes from C to E. Although the range of shear stress is the same ia the two cases (distance OA = CE), the mean shear stress ia the prestressed cylinder, represented by point G, is smaller than that for the initially stress-free cylinder represented by point H. This reduction in the mean shear stress increases the fatigue strength of components subjected to repeated internal pressure. 

The residual shear stress distribution in the assembled cylinders, prior to the appHcation of internal pressure, may be calculated, from pressure P, generated across the interface. The resulting shear stress distribution in the compound cylinder, when subjected to an internal pressure may be calculated from the sum of the residual stress distribution and that which would have been generated elastically in a simple cylinder of the same overall radius ratio as that of the compound cylinder. 

It may be shown (33) that when the inner surface of a cylinder made of components of the same material is subjected to an internal pressure, the bote of each component experiences the same shear stress provided all components have the same diameter ratio. For these optimum conditions,... 

Fig. 12. Pressure and temperature stresses in a cylinder, k = 2 subjected to a steady temperature gradient of 100°C and an internal pressure of 138 MPa...

The combustor is assembled of flanged, spool-shaped water-cooled metal components, each with its own water-cooling circuit and pressure shell. No ceramic linings are used. Gas pressure is contained by stainless steel outer shells and the internal surfaces subject to high heat fluxes are lined with low alloy water-cooled panels. 

Tank Bottoms. The shape of cylindrical tank closures, both top and bottom, is a strong function of the internal pressure. Because of the varying conditions to which a tank bottom may be subjected, several types of tank bottoms (Fig. 7 Table 4) have evolved. These may be broadly classified as flat bottom, conical, or domed or spherical. Flat-bottom tanks only appear flat. These usually have designed slope and shape and are subclassifted according to the following flat, cone up, cone down, or single slope. 

There are four commonly occurring states of stress, shown in Fig. 3.2. The simplest is that of simple tension or compression (as in a tension member loaded by pin joints at its ends or in a pillar supporting a structure in compression). The stress is, of course, the force divided by the section area of the member or pillar. The second common state of stress is that of biaxial tension. If a spherical shell (like a balloon) contains an internal pressure, then the skin of the shell is loaded in two directions, not one, as shown in Fig. 3.2. This state of stress is called biaxial tension (unequal biaxial tension is obviously the state in which the two tensile stresses are unequal). The third common state of stress is that of hydrostatic pressure. This occurs deep in the earth s crust, or deep in the ocean, when a solid is subjected to equal compression on all sides. There is a convention that stresses are positive when they pull, as we have drawn them in earlier figures. Pressure,... 

A cylindrical tube in a chemical plant is subjected to an excess internal pressure of 6 MN m , which leads to a circumferential stress in the tube wall. The tube wall is required to withstand this stress at a temperature of 510°C for 9 years. A designer has specified tubes of 40 mm bore and 2 mm wall thickness made from a stainless alloy of iron with 15% by weight of chromium. The manufacturer s specification for this alloy gives the following information ... 

Example 23 A cylindrical polypropylene tank with a mean diameter of 1 m is to be subjected to an internal pressure of 0.2 MN/m. If the maximum strain in the tank is not to exceed 2% in a period of 1 year, estimate a suitable value for its wall thickness. AVhat is the ratio of the hoop strain to the axial strain in the tank. The creep curves in Fig. 2.5 may be used. 

Solution The maximum strain in a cylinder which is subjected to an internal pressure, p, is the hoop strain and the classical elastic equation for this is... 

The nylon ring may be considered as a thick wall cylinder subjected to this internal pressure (see Appendix D). At the inner surface of the ring there will be a hoop stress, <7, and a radial stress, Cr. Benham et al. shows these to be... 

A 200 mm diameter plastic pipe is to be subjected to an internal pressure of 0.5 MN/m for 3 years. If the creep rupture behaviour of the material is as shown in Fig. 3.10, calculate a suitable wall thickness for Ae pipe. You should use a safety factor of 1.5. 

A cylindrical steel pressure vessel (AlSl SAE 10.85, cold rolled) with a wall thickness of 0.1 in. and an inside diameter of 1 ft is subject to an internal pressure of 1,000 psia and a torque of 10,000 ft-lb (see Figure 2-30). What is the effective stress at point A in the wall What is the factor of safety in this design ... 

A relatively small pressure can result in a very large force if it is applied over a large area. Inadequately vented atmospheric storage tanks may therefore rupture if, for some reason, e.g. a high inflow, they are subjected to a relatively low internal pressure. Large side-on structures, windows, etc. are particularly prone to damage from an explosion even at a significant distance from the epicentre. 

The analysis of the membrane stresses induced in shells of revolution by internal pressure gives a basis for determining the minimum wall thickness required for vessel shells. The actual thickness required will also depend on the stresses arising from the other loads to which the vessel is subjected. 

Calculate the maximum membrane stress in the wall of shells having the shapes listed below. The vessel walls are 2 mm thick and subject to an internal pressure of 5 bar. 

ISO 3503 1976 Assembled joints between fittings and polyethylene (PE) pressure pipes -Test of leakproofness under internal pressure when subjected to bending ISO 3663 1976 Polyethylene (PE) pressure pipes and fittings, metric series - Dimensions... 

ISO 13783 1997 Plastics piping systems - Unplasticized poly(vinyl chloride) (PVC-U) end-load-bearing double-socket joints - Test method for leaktightness and strength while subjected to bending and internal pressure... 

The fuel tank must be resistant to corrosion, mechanical impact, temperature fluctuations, and internal pressure increases. Caps must not permit fuel to escape when the vehicle is turning, traveling up and down steep grades, or when subjected to minor jolts. Also, the tank must be fitted with appropriate relief valves to permit the escape of excessive pressure. 

The vessel is subjected to an internal pressure from the compressed air, which we shall designate as p. The internal pressure is uniformly distributed over the internal surfaces of the vessel, giving rise to both circumferential stress, also known as hoop stress, and longitudinal stress, (see Figure 8.7). We will examine each of these stresses independently before we begin the material selection process. In our development, we will make the following assumptions ... 

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.

Figure 13.13 Pressurized composite ring test A 20-in. diameter composite ring is loaded into the test fixture shown and subjected to internal pressure...

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