Stiffness bending

Antisymmetric angle-ply laminates were found in Section 4.3.3 to have extensional stiffnesses bending-extension... 

CEN EN 14771.2012. Bitumen and bituminous binders - Determination of the flexural creep stiffness-Bending beam rheometer (BBR). Brussels CEN. 

BiW is expected to possess a number of significant properties. It must have high tensile strength as well as high stiffness—bending, torsional, static, and dynamic. It must also provide good quality safety both to the car body and to its occupants against crashes of all... 

When the same energy terms are used in two force helds, it may be acceptable to transfer bond-stretching and angle-bending terms. These are fairly stiff motions that do not change excessively. The force constants for these terms vary between force helds, much more than the unstrained lengths and angles. 

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). 

Years of development have led to a standardized system for objective evaluation of fabric hand (129). This, the Kawabata evaluation system (KES), consists of four basic testing machines a tensile and shear tester, a bending tester, a compression tester, and a surface tester for measuring friction and surface roughness. To complete the evaluation, fabric weight and thickness are determined. The measurements result in 16 different hand parameters or characteristic values, which have been correlated to appraisals of fabric hand by panels of experts (121). Translation formulas have also been developed based on required levels of each hand property for specific end uses (129). The properties include stiffness, smoothness, and fullness levels as well as the total hand value. In more recent years, abundant research has been documented concerning hand assessment (130—133). 

Cord materials such as nylon, polyester, and steel wire conventionally used in tires are twisted and therefore exhibit a nonlinear stress—strain relationship. The cord is twisted to provide reduced bending stiffness and achieve high fatigue performance for cord—mbber composite stmcture. The detrimental effect of cord twist is reduced tensile strength. Analytical studies on the deformation of twisted cords and steel wire cables are available (22,56—59). The tensile modulus E of the twisted cord having diameter D and pitchp is expressed as follows (60) ... 

Corrugated pipe and corrugated and creased bends are also used to decrease stiffness. 

The design states that the roll must not deflect by more than 0.01 mm at its centre. To achieve this bending stiffness, each roll is to be backed up by one secondary roll as shown in Fig. 14.9(b). Calculate the secondary roll radius needed to meet the specification. The central deflection of the secondary roll is given by... 

At small strains the cell walls at first bend, like little beams of modulus E, built in at both ends. Figure 25.10 shows how a hexagonal array of cells is distorted by this bending. The deflection can be calculated from simple beam theory. From this we obtain the stiffness of a unit cell, and thus the modulus E of the foam, in terms of the length I and thickness t of the cell walls. But these are directly related to the relative density p/ps= t/lY for open-cell foams, the commonest kind. Using this gives the foam modulus as... 

The transverse modulus is lower partly because the cell wall is less stiff in this direction, but partly because the foam structure is intrinsically anisotropic because of the cell shape. When wood is loaded across the grain, the cell walls bend (Fig. 26.5b,c). It behaves like a foam (Chapter 25) for which... 

When the intersection points lie below the 0.5 slope line, the system is said to have a bending critical speed. It is important to identify these points, since they indicate the increasing importance of bending stiffness over support stiffness. 

Since most SWNTs have diameters in the range of 1 -2 nm, we can expect them to remain cylindrical when they form cables. The stiffness constant of the cable structures will then be the sum of the stiffness constants of the SWNTs. However, just as with MWNTs, the van der Waals binding between the tubes limits tensile strength unless the ends of all the tubes can be fused to a load. In the case of bending, a more exact... 

Knowledge of the variation of stress and strain through the laminate thickness is essential to the definition of the extensional and bending stiffnesses of a laminate. The laminate is presumed to consist of per-... 

Verify for a single layer of isotropic material with material properties E and v and thickness t that the extensional and bending stiffnesses are... 

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