Flexibility ratio

Ms and V give the molecular mass of a chain segment and the specific volume V Ms = Nav represents the molar segment volume. The number of nearest-neighbor sites per chain amounts to qz=s(z -2) -I- 2, z being the coordination number. The quantity 3/3 c, called the flexibility ratio, is usually set to unity. This reference determines the molecular mass of the segment from the third equation of Eq. (8.7). 

From the plot of In S versus T (see Figure 8.19 for EVOH) and Eq. (8.36), the temperature dependence of flexibility ratio ds can be determined. The molar segmental area. As, was calculated from [VA(VMf) ], with Ms being the molecular mass of a segment. As can be seen, to a good approximation yAs/RT of EVOH follows the curve. For SAN, similar dependence is observed, but with a different slope. Functions In B and InS for these copolymers decrease linearly with T, but with different slopes from Eq. (8.36) for P = 0,... 

Using average values of the characteristic reducing temperature, T, one gets an approximately constant temperature coefficient of the flexibility ratio, ds ... 

Peck et al. (1972) proposed closed-form solutions in terms of thrust, bending moments, and displacement under external loading. The lining response was a function of structure compressibility and flexibility ratios, in situ overburden pressure, and at-rest earth coefficient. To adapt to seismic loading, the free-field shear stress replaces the in situ overburden pressure and earth coefficient. The stiffness of the tuimel relative to the ground is measured by the compressibility (C) and flexibility (F) ratios. Those are the extensional stiffness and flexural stif iess of the medium relative to the lining. 

Seismk Design of Tunnels, Fig. 13 Normalized lining deflection vs. flexibility ratio, fiill-slip interface, circular... 

The relative stiffness between soil and structure, stmcture geometry, input earthquake motions, and tunnel embedment depth are factors that contribute to the soil-stmcture interaction effect. The most important of those is the flexibility ratio (F) that refers to the shear stiffness of the soil relative to the stmcture that replaces it (Wang 1993) ... 

NCHRP 611 (Anderson et al. 2008) developed a relationship between the racking ratio (R) of rectangular conduits and the flexibility ratio (F), whereby... 

A particularly interesting and quite practical approach to utilize the above results from the wedge-splitting test is to assess the ratio of the area under the stable fracture curve from the initial loading point to the maximum, referred to as Gc above, and the total area of the stable load-displacement curve that yields the quantity referred to above as Gp- The ratio of the two quantities may be used to define a toughness, ductility, or flexibility ratio as... 

The factor s/3c in Eq. (A13) is called the flexibility ratio, which is usually set to 1. Other factors are the same as those in the Prigogine cell model. 

Commonly used isocyanates are toluene dhsocyanate, methylene diphenyl isocyanate, and polymeric isocyanates. Polyols used are macroglycols based on either polyester or polyether. The former [poly(ethylene phthalate) or poly(ethylene 1,6-hexanedioate)] have hydroxyl groups that are free to react with the isocyanate. Most flexible foam is made from 80/20 toluene dhsocyanate (which refers to the ratio of 2,4-toluene dhsocyanate to 2,6-toluene dhsocyanate). High-resilience foam contains about 80% 80/20 toluene dhsocyanate and 20% poly(methylene diphenyl isocyanate), while semi-flexible foam is almost always 100% poly(methylene diphenyl isocyanate). Much of the latter reacts by trimerization to form isocyanurate rings. 

Thermal ionization has three distinct advantages the ability to produce mass spectra free from background interference, the ability to regulate the flow of ions by altering the filament temperature, and the possibility of changing the filament material to obtain a work function matching ionization energies. This flexibility makes thermal ionization a useful technique for the precise measurement of isotope ratios in a variety of substrates. 

Attempts have been made to perform thermal retorting ia a gas barrier flexible pouch or tray. The retort pouch, under development for many years, has a higher surface-to-volume ratio than a can and employs a heat seal rather than a mechanical closure. Similarly, plastic retort trays have higher surface-to-volume ratios and are usually heat seal closed. Plastic cans iatended for microwave reheating are composed of bodies fabricated from multilayer plastic including a high oxygen barrier material, plus double-seam aluminum closures. 

Although 4-hydroxybenzaldehyde can be made by the saligenin route, it has been made historically by the Reimer-Tiemann process, which also produces sahcylaldehyde (64). Treatment of phenol with chloroform and aqueous sodium hydroxide results in the formation of benzal chlorides, which are rapidly hydrolyzed by the alkaline medium into aldehydes. Acidification of the phenoxides results in the formation of the final products, sahcylaldehyde and 4-hydroxybenzaldehyde. The ratio of ortho and para isomers is flexible and can be controlled within certain limits. The overall reaction scheme is shown in Figure 1. Product separation is accomphshed by distillation, but this process leads to environmental problems because of the quantities of sodium chloride produced. 

Flexibility and Stress-Intensification Factors. The flexibihty factor k (>1.0) is defined as the ratio between the rotation per unit length of the part in question produced by a given moment to the rotation of a straight pipe (of the same size and schedule) produced by the same moment. A close approximation of the flexibiUty factor that agrees quite well with theory and experiment for bends is as follows ... 

Polypyrroles. Highly stable, flexible films of polypyrrole ate obtained by electrolytic oxidation of the appropriate pyrrole monomers (46). The films are not affected by air and can be heated to 250°C with Htde effect. It is beheved that the pyrrole units remain intact and that linking is by the a-carbons. Copolymerization of pyrrole with /V-methy1pyrro1e yields compositions of varying electrical conductivity, depending on the monomer ratio. Conductivities as high as 10 /(n-m) have been reported (47) (see Electrically conductive polymers). 

Copolymers wet and adhere well to nonporous surfaces, such as plastics and metals. They form soft, flexible films, in contrast to the tough, horny films formed by homopolymers, and are more water-resistant. As the ratio of comonomer to vinyl acetate increases, the variety of plastics to which the copolymer adheres also increases. Comonomers containing functional groups often adhere to specific surfaces for example, carboxyl containing polymers adhere well to metals. 

Plastics and Synthetic Products. To prevent degradation of plastics at elevated processing temperatures, it is necessary to use suitable heat stabilizers. Eor example, flexible poly(vinyl chloride) (PVC) manifests uncontroUed color development in the absence of stabilizers. Accordingly, cadmium salts of organic acids are typically used in a synergistic combination with corresponding barium salts, in about a 1 3 cadmium barium ratio, to provide a cost-competitive heat stabilizer for flexible PVC. 

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