Resistance functions

Selenium and selenium compounds are also used in electroless nickel-plating baths, delayed-action blasting caps, lithium batteries, xeroradiography, cyanine- and noncyanine-type dyes, thin-film field effect transistors (FET), thin-film lasers, and fire-resistant functional fluids in aeronautics (see... 

The increased impulse capacity of a structure is proportional to the square root of the increase in the area under the resistance-deflection curve. The effect of mass can be easily shown with the following equation for the impulse capacity of a ductile element with large allowable deflection and a perfectly plastic resistance function (as shown in Figure 4b). 

The polycarbonate glazing is modeled as a simply supported plate subjected to nonlinear center deflections up to 15 times the pane thickness. Using the finite element solution of Moore (Reference 4), the resistance function is generated for each pane under consideration. Typically, the resistance is concave up, as illustrated for typical pane sizes in Figure 1. This occurs because membrane stresses induced by the stretching of the neutral axis of the pane become more pronounced as the ratio of the center pane deflection to the pane... 

In many cases, the dynamic amplification factor or the ratio of static load to dynamic load capacity will exceed two. This is because of the concave up shape of the resistance function and the mobilization of membrane resistance at large deflection to thickness ratios. Because of this phenomenon, it is unconservative to assume the blast capacity of polycarbonate glazing to be no less than one half of its static pressure load capacity. 

Resistance functions have been evaluated in numerical compu-tations15831 for low Reynolds number flows past spherical particles, droplets and bubbles in cylindrical tubes. The undisturbed fluid may be at rest or subject to a pressure-driven flow. A spectral boundary element method was employed to calculate the resistance force for torque-free bodies in three cases (a) rigid solids, (b) fluid droplets with viscosity ratio of unity, and (c) bubbles with viscosity ratio of zero. A lubrication theory was developed to predict the limiting resistance of bodies near contact with the cylinder walls. Compact algebraic expressions were derived to accurately represent the numerical data over the entire range of particle positions in a tube for all particle diameters ranging from nearly zero up to almost the tube diameter. The resistance functions formulated are consistent with known analytical results and are presented in a form suitable for further studies of particle migration in cylindrical vessels. 

Several important concepts should be kept in mind while designing buildings for blast resistance. These concepts include energy absorption, safety factors, limit states, load combinations, resistance functions, structural performance considerations, and most importantly, redundancy. A design satisfying all required strength and performance criteria would be unsatisfactory without redundancy. 

These force versus deflection relationships are usually nonlinear (due to materials or geometry) and are called resistance functions. They are an essential input parameter for the analysis of equivalent single degree of freedom (SDOF) systems, Resistance functions are not usually needed for analyses of multi-degree of freedom (MDOF) systems. Material models employing nonlinear stress versus strain data, as discussed in Chapter 5, are used in MDOF systems. 

The first step in developing a resistance function is to determine the plastic section capacities, such as plastic moment, Mp, as shown in Figure 7.1. The next step is to determine the sequence of plastic hinge formation and the corresponding load and deformation values. This is done by incrementally applying loads until a collapse mechanism is formed as illustrated in Figure 7.2 for a fixed end beam with a uniform load. 

The piecewise linear curve representing the resistance function shown in Figure 7.1 is an approximation made to simplify the analysis and design process. This approximation ignores some nonlinear effects such as ... 

FIGURE 7.2 Resistance Function for Member With Sequential Plastic Hinges... 

Preloads are sometimes considered in developing resistance functions. Preloads are any dead or live loads which cause a deformation in the member and thereby use up some of the available strain energy. Effects of preload on equivalent SDOF system analyses are sometimes handled by reducing the calculated available resistance by the amount of the preload. Another approach is to simply superimpose the preload on top of the blast load. 

FIGURE 7.3 Typical Simplified Eiasto-Plnstic Resistance Function... 

The measured G(x) value of representative epoxy polymers is approximately 10, but this value depends strongly on the structure of the polymer, its glass transition temperature and other characteristics. Since the crosslinking reaction that characterizes the COP resist functionality is a chain reaction, in theory, a single, electron-initiated event could result in the insolublization of an entire film of the resist material. Fortunately, because of the existence of chain terminating reactions, this does not occur and high resolution imaging of the resist material can be accomplished. 

Attempts to improve the DUV sensitivity of PMMA have spawned a variety of new DUV resist materials. Notable among these are copolymers of methyl methacrylate and indenone (80) which are reported to provide positive-tone resist function at 20 to 60 mJicnP in the DUV and copolymers of methyl methacrylate and 3-oximino-2-butanone (81). The latter materials provide a substantial increase in sensitivity over PMMA and are capable of 1 micron resolution. 

Here i = ujR0I/V0 is the dimensionless current —the control parameter of this model. Furthermore, f(pt) is the dimensionless stationary resistance function of a general shape sketched in Fig. 6.1.3 and k = k/sv 1 is the dimensionless relaxation parameter, assumed large in accordance with Teorell s intuitive ideas. 

We thus observe that M is positive for all w, A > 0 and, therefore, the bifurcation is supercritical. This stands in contrast with the result for the classical Teorell model discussed in the previous section. Recall that there the type of bifurcation depended on the properties of the postulated stationary resistance function /( ), specifically on the sign of / "(0) whenever... 

Side chains of alkylbenzenes are oxidized to benzoic acid derivatives by treatment with hot potassium permanganate or hot chromic acid. Because this oxidation requires severe conditions, it is useful only for making benzoic acid derivatives with no oxidizable functional groups. Oxidation-resistant functional groups such as —Cl, —NO2, —SO3H, and —COOH may be present (Section 17-15A). 

The membrane is a resistor and transmits the flow in a dissipative process. A steady-state membrane relates the thermodynamic force X to the conjugate flow J through a resistance function R, and we have... 

Again, we extrapolate our data to 1200 K for use here. Figure 6 shows the substratecoating interfacial resistance function. 

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