Basic Design Theories

In designing RPs, certain important assumptions are made so that two materials act together and the stretching, compression, twisting of fibers and of plastics under load is the same that is, the strains in fiber and plastic are equal. Another assumption is that the RP is elastic, that is, strains are directly proportional to the stress applied, and when a load is removed the deformation disappears. In engineering terms, the material obeys Hooke s Law. This assumption is a close approximation to the actual behavior in direct stress below the proportional limit, particularly in tension, where the fibers carry essentially all the stress. The assumption is possibly less vaUd in shear where the plastic carries a substantial portion of the stress. 

In this analysis it is assumed that all the glass fibers are straight however, it is unlikely that this is true, particularly with fabrics. In practice, the load is increased with fibers not necessarily failing at the same time. Values of a number of elastic constants must be known in addition to strength properties of the resins, fibers, and combinations. In this analysis, arbitrary values are used that are low for elastic constants and strength values. Any values can be used here the theory is illustrated. 

Any material, when stressed, stretches or is otherwise deformed. If the plastic and fiber are firmly bonded together, the deformation is the same. Since the fiber is more unyielding, a higher stress is developed in the glass than the plastic. If the stress-strain relationships of fiber and plastic are known, the stresses developed in each for a given strain can be computed and their combined action determined. Fig. 2.27 stress-strain (S-S) diagrams provide the basis for this analysis it provides related data such as strengths and modulus. 

These S-S diagrams may be applied to investigate a rod in which half of the volume is glass and the other half is plastic. If the fibers are parallel to the axis of the rod, at any cross-section, half of the total is fiber with half plastic. If the rod is stretched 0.5%, the S-S diagrams show that the glass is stressed to 50,000 psi (345 MPa), resin B at 7,500 psi (52 MPa), and resin C at 2,500 psi (17 MPa). If the rod has a total cross-section of Vi in, the glass is A in. The total load on the glass is Vi x 50,000 or 12,500 lb. Similarly resin B is 1,875 lb and resin C is 625 lb. 

The load required to stretch the rod made of resin B becomes the sum of glass and resin load or 14,375 lb. With resin C the load is 13,125 lb. 

Fiber-reinforced plastics differ from many other materials because they combine two essentially different materials of fibers and a plastic into a single composite. In this way they are somewhat analogous to reinforced concrete, that combines concrete and steel. However, in the RPs the fibers are generally much more evenly distributed throughout the 

In designing fibrous-reinforced plastics it is necessary to take into account the combined actions of the fiber and the plastic. At times the combination can be considered homogeneous, but in most cases homogeneity cannot be assumed. 

it is necessary to allow for the fact that two widely dissimilar materials have been combined into a single unit. In the basic design approach certain fundamental assumptions are made. The first, and most important assumption, is that the two materials act together. With a load applied (stretching, compression, twisting, etc.) the fibers and plastic under load is the same that is, the 

More or less implicit in the theory of materials of this type is the assumption that all the fibers are straight and unstressed or that the initial stresses in the individual fibers are essentially equal. In practice this is quite unlikely to be true. It is expected, therefore, that as the load is increased some fibers will reach their breaking points first. As they fail, their loads will be transferred to other as yet unbroken fibers, so that the successive breaking of fibers rather than the simultaneous breaking of all of them will cause failure. As reviewed in Chapter 2 (SHORT TERM LOAD BEHAVIOR, Tensile Stress-Strain, Modulus of elasticity) the result is usually the development of two or three moduli. 

---

In this subsection, basic design theory for preliminary sizing and specifying equipment are reviewed. Some sample design calculations are included. References cited at the end of tlie chapter can be consulted for more detailed information and design methods. For solid-liquid separation methods, the reader should refer to Liquid Filtration, 2" edition, by N. P. Cheremisinoff, Butterworth-Heinemarui Publishers (1998). 

Orientation of reinforcement The behavior of RPs is dominated by the arrangement and the interaction of the stiff, strong fibers with the less stiff, weaker plastic matrix. The features of the structure and the construction determine the behavior of RPs that is important to the designer. A major advantage is the fact that directional properties can be maximized in the plane of the sheet. As shown in Fig. 8-55 they can be isotropic, orthotropic, etc. Basic design theories of combining actions of plastics and reinforcements... 

Three-phase separation in which oil wen streams are separated into gas, oil and tree water is a key element in producing systems used throughout the oil industry. This anide. an extension of the discussion of two-phase separation that appeared in the November issue of World Oil, describes available three-phase equipment and control methods, basic design theory of three-phase units, and examples for sizing and selecting such vessels. 

None of this should be taken to suggest that the eye functions poorly. It is a superb visual instrument that serves us exceedingly well... The key to the intelligent design theory. .. is not whether an organ or system works well but whether its basic structural plan is the obvious product of design. The structural plan of the eye is not.16... 

Westerberg, A.W., Stephanopoulos, G. and Shah, J.V., "The Synthesis Problem with some Thoughts on Evolutionary Synthesis in the Design of Engineering Systems," Symp. on Basic Questions in Design Theory, Columbia University, 1974. 

Shah, R.K. and Sekulic, D.P. Chapter 3, Basic thermal design theory for recuperators. In Fundamentals of Heat Exchanger Design. Hoboken, NJ John Wiley Sons, 2003, pp. 186—190. 

Wet Surface Air Cooler Basics The theory and principles for the design of WSACs are a combination of those known for evaporative cooling tower design and HX design. However, the design practices for engineering WSAC equipment remain a largely proprietary, technical... 

In chap 11 an overview of the basic designs, principles of operation, and modeling of fixed packed bed reactors is presented. The basic theory is applied to describe the performance of particular chemical processes operated in fixed packed bed reactors. That is, porous media reactive flow model simulations of particular packed bed sorption enhanced steam reforming processes are assessed. 

Extensions of the Basic Recuperator Thermal Design Theory... 

---