Stiffness, defined

Stiffness — Defines the ability to carry stress without changing dimension. The magnitude of the modulus of elasticity is a measure of this ability or property. 

For all materials (other than fabrics, for which the concept is not relevant) the basic parameter is a measure of stiffness or modulus derived from the stress-strain curve. As with tensile tests, because the stress -strain relation is generally not linear, care must be taken to compare only measures of stiffness defined in the same way. With rigid foams and plastics there are additionally measures of yield or strength. 

Rope stiffness, defined as the product of modulus of elasticity and cross sectional area, for synthetic rope = 134 MN, compared with 160 MN for steel rope... 

It is not possible to apply (C2.1.1) down to the level of monomers and replace by the degree of polymerization N and f by the sum of the squares of the bond lengths in the monomer because the chemical constitution imposes some stiffness to the chain on the length scale of a few monomer units. This effect is accounted for by introducing the characteristic ratio defined as C- — The characteristic ratio can be detennined... 

Although the elemental stiffness Equation (2.55) has a common form for all of the elements in the mesh, its utilization based on the shape functions defined in the global coordinate system is not convenient. Tliis is readily ascertained considering that shape functions defined in the global system have different coefficients in each element. For example... 

A number of high melting poiat semiaromatic nylons, iatroduced ia the 1990s, have lower moisture absorption and iacreased stiffness and strength. Apart from nylon-6 /6,T (copolymer of 6 and 6,T), the exact stmcture of these is usually proprietary and they are identified by trade names. Examples iaclude Zytel HTN (Du Pont) Amodel, referred to as polyphthalamide or PPA (Amoco) and Aden (Mitsui Petrochemical). Properties for polyphthalamide are given ia Table 2. A polyphthalamide has been defined by ASTM as "a polyamide ia which the residues of terephthaUc acid or isophthahc acid or a combination of the two comprise at least 60 molar percent of the dicarboxyhc acid portion of the repeating stmctural units ia the polymer chain" (18). 

Textile fibers must be flexible to be useful. The flexural rigidity or stiffness of a fiber is defined as the couple required to bend the fiber to unit curvature (3). The stiffness of an ideal cylindrical rod is proportional to the square of the linear density. Because the linear density is proportional to the square of the diameter, stiffness increases in proportion to the fourth power of the filament diameter. In addition, the shape of the filament cross-section must be considered also. For textile purposes and when flexibiUty is requisite, shear and torsional stresses are relatively minor factors compared to tensile stresses. Techniques for measuring flexural rigidity of fibers have been given in the Hterature (67—73). 

Drape can be measured by placing a circular fabric specimen over a round table or pedestal and viewing from direcdy overhead. A drape coefficient is defined as the ratio of the area of the fabric s actual shadow to the area of the shadow if the fabric were rigid. Drape is closely related to stiffness the drape coefficient for a stiff fabric approaches a value of 1 a limp fabric has a drape coefficient near 0. The Cusick drape tester is an example of this type of measurement. Eor this method, the relative weights of paper rings representing tracings of the fabric s shadows are used to calculate drape coefficient. 

Quasi-isotropic laminates have the same ia-plane stiffness properties ia all directions (1), which are defined ia terms of the [A] matrix of the laminate. For the laminate to be quasi-isotropic. 

Materials respond to stress by straining. Under a given stress, a stiff material (like steel) strains only slightly a floppy or compliant material (like polyethylene) strains much more. The modulus of the material describes this property, but before we can measure it, or even define it, we must define strain properly. 

As we showed in Chapter 4, atoms in crystals are held together by bonds which behave like little springs. We defined the stiffness of one of these bonds as... 

When considering relea.se mechanisms, the physical and chemical heterogeneity of the adhesive/release interface cannot be ignored. At its most basic level, roughness of the release and PSA surface, the stiffness of the PSA and the method in which the PSA and release surface are brought together define the contact area of the interface. The area of contact between the PSA and release material defines not only the area over which chemical interactions are possible, but al.so potential mechanical obstacles to release. In practice, a differential liner for a transfer adhesive can be made to depend in part on the substrate roughness for the differences in release properties [21],... 

In any particular material, the flexural stiffness will be defined by the second moment of area, /, for the cross-section. As with a property such as area, the second moment of area is independent of the material - it is purely a function of geometry. If we consider a variety of cross-sections as follows, we can easily see the benefits of choosing carefully the cross-sectional geometry of a moulded plastic component. 

Now that the basic stiffnesses and strengths have been defined for the principal material coordinates, we can proceed to determine how an orthotropic lamina behaves under biaxial stress states in Section 2.9. There, we must combine the information in principal material coordinates in order to define the stiffness and strength of a lamina at arbitrary orientations under arbitrary biaxial stress states. 

In Section 2.2, the stress-strain relations (generalized Hooke s law) for anisotropic and orthotropic as well as isotropic materials are discussed. These relations have two commonly accepted manners of expression compliances and stiffnesses as coefficients (elastic constants) of the stress-strain relations. The most attractive form of the stress-strain relations for orthotropic materials involves the engineering constants described in Section 2.3. The engineering constants are particularly helpful in describing composite material behavior because they are defined by the use of very obvious and simple physical measurements. Restrictions in the form of bounds are derived for the elastic constants in Section 2.4. These restrictions are useful in understanding the unusual behavior of composite materials relative to conventional isotropic materials. Attention is focused in Section 2.5 on stress-strain relations for an orthotropic material under plane stress conditions, the most common use of a composite lamina. These stress-strain relations are transformed in Section 2.6 to coordinate systems that are not aligned with the principal material... 

The reduced stiffnesses, Qy, are defined in terms of the engineering constants in Equation (2.66). In any other coordinate system in the plane of the lamina, the stresses are... 

For a specially orthotropic square boron-epoxy plate with stiffness ratios 0 /022= 10 and (Di2-t-2D66) = 1, the four lowest frequencies are displayed in Table 5-3 along with the four lowest frequencies of an isotropic plate. There, the factor k is defined as... 

Tsai and Pagano further defined the isotropic stiffness and shear rigidity [7-16] to be... 

To understand the interactions of mass and stiffness, consider the case of undamped free vibration of a single mass that only moves vertically, which is illustrated in Figure 43.12. In this figure, the mass, M, is supported by a spring that has a stiffness, K (also referred to as the spring constant), which is defined as the number of pounds tension necessary to extend the spring one inch. 

Torsional stiffness is defined as the externally applied torque, T, in inch-pounds needed to turn the disk one radian (57.3°). Torque can be represented by the following equations ... 

The unique natural frequencies of dynamic machine components are determined by the mass, freedom of movement, support stiffness, and other factors. These factors define the response characteristics of the rotor assembly (i.e., rotor dynamics) at various operating conditions. 

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