Force, body

Typical correlation between the magnetic characteristic and the body force measured on the head of 85 mm long M24 Friedberg 10.9 bolts where the thickness off the plates screwed together is more than 40mm. 

Several types of experiments have been carried out to investigate the stress state in the head of the bolt created by the body forces. The results of the finite element model experiment can be seen in Fig. 2, and those of the optical plane model experiment are presented in Fig. 3. 

Correlation between the body forces and the stress state in the head was investigated both by the strain gauge method and the optical coat work stress examination method, and the magnetic measurements were performed at the same time. 

At nominal body forces the same compressive stress of 100 -110 Mpa was calculated in all directions in the middle of the head of the examined bolts... 

The torque to obtain the specified body force under construction conditions and on bolts removed from the bridge. 

Distribution of the relativ body force (RF) on 1127 bolts determined by the magnetic method and 42 bolts out of this number found faulty by the DIN method. 

Fig. 7 shows the torque necessary to obtain the specified body force under construction conditions and in tbe state when removed from the bridge. It can well be seen that the change of the friction coefficient causes a very big scattering, and the necessary torque is much bigger than specified. The distribution of the results of a measurement performed on 1,127 bolts is presented in Figure 8. An average of 80% of nominal body force was found by the new method. The traditional method found the nuts could be swivelled much further than specified on 42 bolts, these bolts were found to have 40 - 60 % body force by the new method. 

The traditional method for investigating the forces originating in the body of the bolt, which is based on measuring the torque of the nut, can detect only the bolts with a very great lack of body force since tbe friction coefficient worsens with time. 

Equations II-12 and 11-13 illustrate that the shape of a liquid surface obeying the Young-Laplace equation with a body force is governed by differential equations requiring boundary conditions. It is through these boundary conditions describing the interaction between the liquid and solid wall that the contact angle enters. 

The first finite element schemes for differential viscoelastic models that yielded numerically stable results for non-zero Weissenberg numbers appeared less than two decades ago. These schemes were later improved and shown that for some benchmark viscoelastic problems, such as flow through a two-dimensional section with an abrupt contraction (usually a width reduction of four to one), they can generate simulations that were qualitatively comparable with the experimental evidence. A notable example was the coupled scheme developed by Marchal and Crochet (1987) for the solution of Maxwell and Oldroyd constitutive equations. To achieve stability they used element subdivision for the stress approximations and applied inconsistent streamline upwinding to the stress terms in the discretized equations. In another attempt, Luo and Tanner (1989) developed a typical decoupled scheme that started with the solution of the constitutive equation for a fixed-flow field (e.g. obtained by initially assuming non-elastic fluid behaviour). The extra stress found at this step was subsequently inserted into the equation of motion as a pseudo-body force and the flow field was updated. These authors also used inconsistent streamline upwinding to maintain the stability of the scheme. 

In the absence of body force, the dimensionless form of the governing model equations for two-dimensional steady-state incompressible creeping flow of a viscoelastic fluid are written as... 

The majority of polymer flow processes are characterized as low Reynolds number Stokes (i.e. creeping) flow regimes. Therefore in the formulation of finite element models for polymeric flow systems the inertia terms in the equation of motion are usually neglected. In addition, highly viscous polymer flow systems are, in general, dominated by stress and pressure variations and in comparison the body forces acting upon them are small and can be safely ignored. 

In the absence of body force the equations of continuity and motion representing Stokes flow in a two-dimensional Cartesian system are written, on the basis of Equations (1.1) and (1.4), as... 

Similarly in the absence of body forces the Stokes flow equations for a generalized Newtonian fluid in a two-dimensional (r, 8) coordinate system are written as... 

The creation terms embody the changes in momentum arising from external forces in accordance with Newton s second law (F = ma). The body forces arise from gravitational, electrostatic, and magnetic fields. The surface forces are the shear and normal forces acting on the fluid diffusion of momentum, as manifested in viscosity, is included in these terms. In practice the vector equation is usually resolved into its Cartesian components and the normal stresses are set equal to the pressures over those surfaces through which fluid is flowing. 

To illustrate the use of the momentum balance, consider the situation shown in Figure 21c in which the control volume is bounded by the pipe wall and the cross sections 1 and 2. The forces acting on the fluid in the x-direction are the pressure forces acting on cross sections 1 and 2, the shear forces acting along the walls, and the body force arising from gravity. The overall momentum balance is... 

Assuming that the current in the gas is carried mostly by electrons, the induced electric field uB causes transverse electron motion (electron drift), which, being itself orthogonal to the magnetic field, induces an axial electric field, known as the Hall field, and an axial body force, F, given by... 

The composite conductor is typically wound in the form of a cable, which can be cooled either internally by a forced belium flow or externally by immersion in a pool of belium. Large electromagnetic body forces, up to 500 t/m, are experienced by the conductor during operation. These are contained by a massive external stmcture, although designs have been proposed in which the conductor itself serves as its own force containment stmcture (126). 

Electrokinetics. The first mathematical description of electrophoresis balanced the electrical body force on the charge in the diffuse layer with the viscous forces in the diffuse layer that work against motion (6). Using this force balance, an equation for the velocity, U, of a particle in an electric field... 

Natural convection occurs when a solid surface is in contact with a fluid of different temperature from the surface. Density differences provide the body force required to move the flmd. Theoretical analyses of natural convection require the simultaneous solution of the coupled equations of motion and energy. Details of theoretical studies are available in several general references (Brown and Marco, Introduction to Heat Transfer, 3d ed., McGraw-HiU, New York, 1958 and Jakob, Heat Transfer, Wiley, New York, vol. 1, 1949 vol. 2, 1957) but have generally been applied successfully to the simple case of a vertical plate. Solution of the motion and energy equations gives temperature and velocity fields from which heat-transfer coefficients may be derived. The general type of equation obtained is the so-called Nusselt equation hL I L p gp At cjl... 

Momentum Balance Since momentum is a vector quantity, the momentum balance is a vector equation. Where gravity is the only body force acting on the fluid, the hnear momentum principle, apphed to the arbitraiy control volume of Fig. 6-3, results in the following expression (Whitaker, ibid.). 

Centripetal and Centrifugal Acceleration A centripetal body force is required to sustain a body of mass moving along a curve tra-jec tory. The force acts perpendicular to the direction of motion and is directed radially inward. The centripetal acceleration, which follows the same direction as the force, is given by the kinematic relationship ... 

Several additional studies [Winitzer, Sep. ScL, 8(1), 45 (1973) ibid., 8(6), 647 (1973) Maru, Wasan, and Kintner, Chem. Eng. Set., 26, 1615 (1971) and Rapacchietta and Neumann, J. Colloid Inteiface ScL, 59(3), 555 (1977)] which include body forces such as gravitational acceleration and buoyancy have been made. A typical example of a force balance describing suen a system (Fig. 22-39) is summarized in Eq. (22-41). 

If a motion is specified with satisfies the continuity condition, the velocity, strain, and density at each material particle are determined at each time t throughout the motion. Given the constitutive functions (e, k), c(e, k), b( , k), and a s,k) with suitable initial conditions, the constitutive equations (5.1), (5.4), and (5.11) may be integrated along the strain history of each material particle to determine its stress history. If the density, velocity, and stress histories are substituted into (5.32), the history of the body force at each particle may be calculated, which is required to sustain the motion. Any such motion is termed an admissible motion, although all admissible motions may not be attainable in practice. 

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