Unit elasticity

These are obviously extreme examples, most products behave much more closely to what is termed unit elasticity— which is defined as being when a 1% reduction in price will cause a 1 % increase in demand (sales). The equihbrium price can then be defined as the price at which supply=demand (Figure 13.9 b and c). Of course the actual price will vary with the grade of product made and thus its end use, examples include pharmaceutical or technical grade chemicals, or potable or fuel alcohols. Obviously the price-demand behaviour of inelastic products demonstrates their vital importance to some consumers, especially when unchallenged by other producer companies or competing products. This class of products is obviously attractive, not least because of the relative ease with which high R D costs can be recovered. The demand, or lack of demand for products and also other considerations, such as brand loyalty on the part of the consumer and restrictions in supply due to companies exploitation of their patents tend to distort precise descriptions of market behaviour. 

Compare elastic and non-elastic demands for products, give examples of eaeh, and define unit elasticity and negative elastieity . 

Demand is said to be elastic if elasticity is greater than unit, inelastic when elasticity is less than unit, and unit elastic when elasticity equals one. When substitutes are available, demand would be also dependent on prices of alternative fuels, so... 

The indicator of first natural frequency is thus defined as The natural frequency of a structure with a unit length (L = lm) composed of members working at a unit stress (a = 1 Pa) and with a unit elastic modulus (E = 1 Pa) for which the ratio of the co-vibrating loads to the total load is equal to z in Serviceability Limit State. 

Mia = absolute value of the negative unit elastic radial moment on the cap periphery... 

Gio, G20, Gia = coefficient of unit elastic moments produced by total permanent load... 

The criterion for solving the problem of the plastic design of two-way reinforced cap is the minimum redistribution criterion . In the case of a fixed ended circular cap subjected to a symmetrical pressure load, the most stressed points are its centre and the unit elastic radial and annular moments are maxima. Let... 

The density of dislocations is usually stated in terms of the number of dislocation lines intersecting unit area in the crystal it ranges from 10 cm for good crystals to 10 cm" in cold-worked metals. Thus, dislocations are separated by 10 -10 A, or every crystal grain larger than about 100 A will have dislocations on its surface one surface atom in a thousand is apt to be near a dislocation. By elastic theory, the increased potential energy of the lattice near... 

The identity of target elements is established by the energy of the scattered particles after an elastic collision. The number of atoms per unit area, N, is found from the number of detected particles (called the yield, Y) for a given number Q of particles incident on the target. The connection is given by the scattering cross section a(9) by... 

Cp is tire number of elasticity active chains per volume unit. The comparison between experimental data and tire prediction by (C2.1.20) shows a reasonable agreement up to large defonnation (figure C2.1.16). For large values of X, strain hardening arises because of tire limited extensibility of tire chains or because of shear-induced crystallization. 

The elastic and viscoelastic properties of materials are less familiar in chemistry than many other physical properties hence it is necessary to spend a fair amount of time describing the experiments and the observed response of the polymer. There are a large number of possible modes of deformation that might be considered We shall consider only elongation and shear. For each of these we consider the stress associated with a unit strain and the strain associated with a unit stress the former is called the modulus, the latter the compliance. Experiments can be time independent (equilibrium), time dependent (transient), or periodic (dynamic). Just to define and describe these basic combinations takes us into a fair amount of detail and affords some possibilities for confusion. Pay close attention to the definitions of terms and symbols. 

In the Maxwell model, the two units are connected in series, so that each bears the full stress individually and the deformations of the elastic and viscous components are additive ... 

Let C i be a bounded domain with a smooth boundary L, and n = (ni,n2,n3) be a unit outward normal vector to L. Introduce the stress and strain tensors of linear elasticity (see Section 1.1.1),... 

Here i —> i is the convex and continuous function describing a plasticity yield condition, the dot denotes a derivative with respect to t, n = (ni,ri2) is the unit normal vector to the boundary F. The function v describes a vertical velocity of the plate, rriij are bending moments, (5.175) is the equilibrium equation, and equations (5.176) give a decomposition of the curvature velocities —Vij as a sum of elastic and plastic parts aijkiirikiy Vijy respectively. Let aijki x) = ajiki x) = akuj x), i,j,k,l = 1,2, and there exist two positive constants ci,C2 such that for all m = rriij ... 

The elasticity of a fiber describes its abiUty to return to original dimensions upon release of a deforming stress, and is quantitatively described by the stress or tenacity at the yield point. The final fiber quaUty factor is its toughness, which describes its abiUty to absorb work. Toughness may be quantitatively designated by the work required to mpture the fiber, which may be evaluated from the area under the total stress-strain curve. The usual textile unit for this property is mass pet unit linear density. The toughness index, defined as one-half the product of the stress and strain at break also in units of mass pet unit linear density, is frequentiy used as an approximation of the work required to mpture a fiber. The stress-strain curves of some typical textile fibers ate shown in Figure 5. 

Metallurgy. Lithium forms alloys with numerous metals. Early uses of lithium alloys were made in Germany with the production of the lead alloy, BahnmetaH (0.04% Li), which was used for bearings for railroad cars, and the aluminum alloy, Scleron. In the United States, the aluminum alloy X-2020 (4.5% Cu, 1.1% Li, 0.5% Mn, 0.2% Cd, balance Al) was introduced in 1957 for stmctural components of naval aircraft. The lower density and stmctural strength enhancement of aluminum lithium alloys compared to normal aluminum alloys make it attractive for uses in airframes. A distinct lithium—aluminum phase (Al Li) forms in the alloy which bonds tightly to the host aluminum matrix to yield about a 10% increase in the modules of elasticity of the aluminum lithium alloys produced by the main aluminum producers. The density of the alloys is about 10% less than that of other stmctural aluminum alloys. 

The low elastic swell, unique to PVC, results from the presence of the biUion molecule flow units. Other plastics have higher die swell, which... 

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