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39.4.3 Thin Cylindrical Shells under Internal Pressure When a thin cylinder is subjected to an internal pressure, three mutually perpendicular principal stresses hoop stress, longitudinal stress, and radial stress are developed in the cylinder material. If the ratio of thickness t and the inside diameter of the cylinder di is less than 1:20, membrane theory may be applied and we may assume that the hoop and longitudinal stresses are approximately constant across the wall thickness. The magnitude of radial stress is negligibly small and can be ignored. It is to be understood that this simplified approximation is used extensively for the design of thin cylindrical pressure vessels. However, in reality, radial stress varies from zero at the outside surface to a value equal to the internal pressure at the inside surface. The ends of the cylinder are assumed closed. Hoop stress is set up in resisting the bursting effect of the applied pressure and is treated by taking the equilibrium of half of the cylindrical vessel, as shown in Fig. 39.2. Total force acting on the half cylinder is Fh = pidiL (39.10)

where di = inside diameter of cylinder, and L = length of cylinder. The resisting force due to hoop stress h acting on the cylinder wall, for equilibrium, must equal the force Fh. Thus Fh = 2 htT (39.11)

Substituting for Fh from Eq. (39.10) into Eq. (39.11), one obtains the following relation: h = pidi 2t or h = piri t (39.12)

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Despite its simplicity, Eq. (39.12) has wide practical applications involving boiler drums, accumulators, piping, casing chemical processing vessels, and nuclear pressure vessels. Equation (39.12) gives the maximum tangential stress in the vessel wall on the assumption that the end closures do not provide any support, as is the case with long cylinders and pipes. Hoop stress can also be expressed in terms of the radius of the circle passing through the midpoint of the thickness. Then we can write h = pi(ri + 0.5t) t (39.13)

Just in case you have never come in contact with a particle system, I will start with the basics: what exactly constitutes a particle Particles can be any texture and are usually rendered as a textured quad (two triangles). Depending on the effect you are going for, your particle textures might be semitransparent like the simple white particle in Figure 1-6. Soft semitransparent particles will yield fuzzy effects quite well. This makes a nice effect because particles in a high concentration will be brighter and more intense, whereas out on the edges where there may be only a few particles, the overall effect is dimmer and blurry.

The shell thickness is then expressed as t= piri h 0.5pi (39.14)

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.

The code stress and shell thickness formulas based on inside radius approximate the more accurate thick-wall formula of Lam , which is t= piri Se 0.6pi (39.15)

S1 applies 5 V to the STAMP 2 via the 5-V regulator at U3 Momentary pushbutton S2 is the system reset button, which is used in the event of a system lockup You will need to locate or build a 9- to 2-Vdc power supply in order to power the radio DTMF controller You can elect to build a power supply or try to locate a wall wart power supply from a surplus electronic supplier The circuit can be assembled on a custom circuit board, a perfboard, or a BASIC STAMP 2 carrier board, and then mounted in a small plastic enclosure box to protect the circuit board The power switch S1 and the reset switch S2 are placed on the front of a plastic enclosure along with the serial LCD display unit.

where e = code weld-joint efficiency, and S = allowable code stress. Consideration of the equilibrium forces in the axial direction gives the longitudinal stress as = or = pidi 4t piri 2t (39.16)

Figure 1-6. A simple particle texture. This is about the simplest semitransparent texture you can get. It is just a white blur, 25 X 25 pixels.

Equations (39.12) and Eqs. (39.16) reveal that the efficiency of the circumferential joint needs only be one-half that of the longitudinal joint. The preceding relations are good for elastic deformation only. The consequent changes in length, diameter, and intervolume of the cylindrical vessel subjected to inside fluid pressure can be determined easily.

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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