Flexural force

Note 8 Notes 3 and 6 show that the application of the defined sinusoidal flexural forces (i), (ii) and (iii) (note 1) to a Voigt-Kelvin solid of negligible mass, with or without added mass at the points of application of the forces, results in out-of-plane sinusoidal flexural oscillations of the same frequency. 

Deflection of a specimen subject to a forced flexural oscillation at the point of application of the flexural force. 

Note 1 For a Voigt-Kelvin solid of negligible mass, the absolute modulus can be evaluated from the ratio of the flexural force (/o) and the amplitude of the flexural deflection (y) with... 

For relatively small flexural forces, and after expanding the integrand of Eq. (17.184) in series, we can write... 

A. 5% reduction in maximum flexural force compared to zero overstrain (Method B2)... 

Czipott, P.V., M.D. Levine, C.A. Paulson, D. Menemenlis, D.M. Farmer, R.G. Williams, Ice flexure forced by internal wave packets in the Arctic Ocean, Science, 254, 832-835,1991. 

Hysteretic whirl. This type of whirl occurs in flexible rotors and results from shrink fits. When a radial deflection is imposed on a shaft, a neutralstrain axis is induced normal to the direction of flexure. From first-order considerations, the neutral-stress axis is coincident with the neutral-strain axis, and a restoring force is developed perpendicular to the neutral-stress axis. The restoring force is then parallel to and opposing the induced force. In actuality, internal friction exists in the shaft, which causes a phase shift in the stress. The result is that the neutral-strain axis and neutral-stress axis are displaced so that the resultant force is not parallel to the deflection. The... 

Flexural modulus is the force required to deform a material in the elastic bending region. It is essentially a way to characterize stiffness. Urethane elastomers and rigid foams are usually tested in flexural mode via three-point bending and tite flexural (or flex ) modulus is obtained from the initial, linear portion of the resultant stress-strain curve. 

The first group of tests is carried out on specimens generally fabricated into a dumb-bell shape, with forces applied uniaxially. The usual apparatus consists of a machine with a pair of jaws, which during the test are moved relative to each other, either together or apart, in a controlled manner. A chart recorder is employed to give a permanent record of the results obtained, so that the force at fracture can be determined. Whether this kind of set up measures tensile, compressive, or flexural strength depends on how the sample is oriented between the jaws, and on the direction that the jaws are set to travel relative to one another. 

Automated flexure tests are similar. The robot moves the bottom bar from the magazine to the measuring device where its width and thickness are determined, then it places the bar on the flexure test fixture. The PDP-11/44 begins the test by putting the crosshead in motion. Data collection begins when the first load is detected, and the test continues until the specimen bar breaks, the load cell maximum force is reached, or a specified maximum strain value is reached. Then the crosshead is stopped, the specimen is ejected from the fixture, and the crosshead is returned to its initial position. This process is repeated until the test series is complete. 

AB cements tend to be essentially brittle materials. This means that when subjected to mechanical loading, they tend to rupture suddenly with minimal deformation. There are a number of different types of strength which have been identified and have been determined for AB cements. These include compressive, tensile and flexural strengths. Which one is determined depends on the direction in which the fracturing force is applied. For full characterization, it is necessary to evaluate all of these parameters for a given material no one of them can be regarded as the sole criterion of strength. 

Flexural strength is determined using beam-shaped specimens that are supported longways between two rollers. The load is then applied by either one or two rollers. These variants are called the three-point bend test and the four-point bend test, respectively. The stresses set up in the beam are complex and include compressive, shear and tensile forces. However, at the convex surface of the beam, where maximum tension exists, the material is in a state of pure tension (Berenbaum Brodie, 1959). The disadvantage of the method appears to be one of sensitivity to the condition of the surface, which is not surprising since the maximum tensile forces occur in the convex surface layer. 

The mechanical properties of a polymer describe how it responds to deforming forces of various types, including tensile, compressive, flexural, and torsional forces. Given the wide range of polymer structures, it should be no surprise that there is a correspondingly wide... 

The classic way that we perform force versus deformation measurements is to deform a sample at a constant rate, while we record the force induced within it. We normally carry out such tests in one of three configurations tensile, compressive, or flexural, which are illustrated in Fig. 8.1. We can also test samples in torsion or in a combination of two or more loading configurations. For the sake of simplicity, most tests are uni-axial in nature, but we can employ bi-axial or multi-axial modes when needed,... 

Young s modulus is often measured by a flexural test. In one such test a beam of rectangullar cross section supported at two points separated by ia distance Lq is loaded at the midpoint by a force F, as illustrated in Figure 1.2. The resulting central deflection V is measured and the Young s modulus E is calculated as follows ... 

The mechanical properties of a material describe how it responds to the application of either a force or a load. When this is compared to an area, it is called stress, another term for pressure. Three types of mechanical stress can affect a material tension (pulling), compression (pushing), and shear (tearing). Figure 15.27 shows the direction of the forces for these stresses. The mechanical tests consider each of these forces individually or in some combination. For example, tensile, compression, and shear tests only measure those individual forces. Flexural, impact, and hardness tests involve two or more forces simultaneously. 

E is still the modulus of elasticity. The E is assumed to be independent of force, rate of rupture, and so on. It has been pointed out recently99 that the wedge, unless it advances extremely slowly, is likely to cause vibrations (flexure waves) in the specimen which would necessitate an alteration of Eq. (52). 

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