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Euler stress

Fv = vertical seismic force, lb F), = horizontal seismic factor, see Procedure 3-3 F i = allowable axial stress, psi F, = allowable bending stress, psi F( = seismic force applied at top of vessel, lb F(. = Euler stress divided by safety factor, psi f] = miiximum eccentric load, lb = horizontal load on leg, lb F,i = maximum axial load, lb... [Pg.125]

Since the first Piola-Kirchhoff stress II is not symmetric as understood by (2.110), we introduce a symmetrized tensor T, called the second Piola-Kirchhoff stress, and the Euler stress t, which is the transformed tensor of T, into the deformed body using the rotation tensor R ... [Pg.34]

As mentioned in Sect. 3.4.3, only the isotropic material body can form the rate of internal energy d Ua t, s) together with the rate e of the generalized Eulerian strain measure and its energy-conjugate corotational Euler stress =... [Pg.120]

Equation (74) shows that continuity (43) is automatically satisfied by any LB model. The Navier-Stokes equation (44) will be satisfied, if we succeed in ensuring that the Euler stress pc Sap + pUaUp, the Newtonian viscous sbess, a p (45), and the fluctuating sbess (47) are given correctly by the sum of the momentum fluxes in (75). Since depends only on p and j, it must be identified with the Euler sbess ... [Pg.110]

While the general form of the generalized Euler s equation (equation 9.9) allows for dissipation (through the term Hifc) expression for the momentum flux density as yet contains no explicit terms describing dissipation. Viscous stress forces may be added to our system of equations by appending to a (momentarily unspecified) tensor [Pg.467]

Precisely owing to the continuum description of the dispersed phase, in Euler-Euler models, particle size is not an issue in relation to selecting grid cell size. Particle size only occurs in the constitutive relations used for modeling the phase interaction force and the dispersed-phase turbulent stresses. [Pg.170]

Equation 7.2-22 indicates that the separating force is proportional to the local shear stress (fiy) in the liquid, it is a sensitive function of the Euler angles of orientation, and is proportional to the projection of the cross-sectional are (S = nc2). The angular velocities of rotation of the freely suspended spheroid particle were given by Zia, Cox, and Mason (46)... [Pg.351]

M. Moreau, B. Bedat, and O. Simonin. A priori testing of subgrid stress models for euler-euler two-phase LES from euler-lagrange simulations of gas-particle turbulent flow. In 18th Ann. Conf. on Liquid Atomization and Spray Systems. ILASS Americas, 2005. [Pg.323]

Alternatively, by substituting the strain in Eq. (11.66) sls a. linear function of the stress, the free energy can be represented as a quadratic function of Uy. Applying once more the Euler theorem, the corresponding counterpart of Eq. (17.64) in terms of the stress is obtained as... [Pg.785]

Finally, the Hooke equations in a crystallite can be written by using the eomponents of the strain and stress tensors in the sample reference system. Denoting by g the triplet of Euler angles (q>i, Oq, q>2) and using Equations (64-66) we have ... [Pg.352]

To find the stress tensor in the same system we place Equation (87) into Equation (73a) and one obtains an expression similar to Equation (84b). To obtain the macroscopic stress we must integrate this expression over the Euler space. The integral acts only on the single-crystal stiffness tensor elements Equation (74a) and can be calculated analytically. The macroscopic stress is ... [Pg.357]

To calculate the macroscopic strains and stresses. Equations (112) are averaged over the Euler space. The average acts only on the matrix P and, presuming isotropic polycrystals, one obtains ... [Pg.363]

Since we have just verified that both the viscous stresses and the heat conduction terms vanish for equilibrium flows, the constitutive stress tensor and heat flux relations required to close the governing equations are determined. That is, substituting (2.233) and (2.234) into the conservation equations (2.202), (2.207) and (2.213), we obtain the Euler equations for isentropic flow ... [Pg.258]

By choosing a small representative molecular dynamics sample of the shocked material, application of the Euler equations requires that macroscopic stress, thermal, and density gradients in the actual shock wave are negligible on the length scale of the molecular dynamics computational cell size. While the thermal energy is assumed to be evenly spatially distributed throughout the sample by the shock, thermal equilibrium within the internal degrees of freedom computational cell is not required. [Pg.302]

The response of a sinusoidal stress signal applied to a material will depend on the viscoelastic nature of that material, hence a sample of spring steel will be almost totally elastic, whereas a tub of grease or honey will be predominantly viscous. Hooke s "True theory of elasticity" said. The power of any spring is in the same proportion with the tension thereof, i.e. if one power stretch will bend it one space, two will bend it two. three will bend it three and so forth." Hence force F = A(A.v). where delta v is the displacement. Euler refined this to include the cross-sectional area A and the original length Z, but it was not until about 1800 that Thomas Young published it more widely as ... [Pg.504]

For short and intermediate cylinders the critical stress is independent of length. For long cylinders the length of the cylinder is a key factor. The range of cylinders whose slenderness ratios are less than Euler s critical value are called short or intermediate columns. [Pg.85]

Before proceeding, some definitions are useful. Stress is the ratio of the force on a body to the cross-sectional area of the body. The true stress refers to the infinitesimal force per (instantaneous) area, while the engineering stress is the force per initial area. Strain is a measure of the extent of the deformation. Normal strains change the dimensions, whereas shear strains change the angle between two initially perpendicular lines. In correspondence with the true stress, the Cauchy (or Euler) strain is measured with respect to the deformed state, while the Green s (or Lagrange) strain is with respect to the undeformed state. [Pg.287]

The Euler s formula developed by Leonard Euler (Swiss mathematician, 1707 to 1783) is used in product designs and also in designs using columns in molds and dies that process plastic. Euler s formula assumes that the failure of a column is due solely to the stresses induced by sidewise bending. This assumption is not true for short columns that fidl mainly by direct compression, nor is it true for columns of medium length. The failure in such cases is by a combination of direct compression and bending. [Pg.705]

Euler s formula is strictly applicable to long and slender columns, for which the buckling action predominates over the direct compression action and thus makes no allowance for compressive stress. The slenderness ratio is defined as the ratio of length i to the radius of gyration represented as t/k. [Pg.706]

For columns with value of t/k less than about 150, Euler s formula gives results distinctly higher than those observed in tests. Euler s formula is used for long members and as a basis for the analysis of the stresses in some types of structural parts. It always gives an ultimate and never an allowable load. [Pg.707]

No assumption regarding the flow field is required for the floating shear stress sensor. The displacement (5) of the floating element sensor as a function of shear stress (x ) can be derived from Euler-Bemoulli beam theory as... [Pg.2967]

F7 /8 y = Oij in the form of Euler-Lagrange equations (ojk is the stress tensor) along with the boundary conditions (see e.g. Refs. [47, 58, 59]). This system of differential equations should be solved along with the equations of mechanical equilibrium daij x) /9x, = 0 and compatibility equations equivalent to the mechanical displacement vector , continuity [100]. [Pg.245]

The ultimate axial force Ni in the most compressed member was determined from the strain measurements. The corresponding mean stress was far lower than the strength h, which indicated an elastic buckling phenomenon. Thus, the ultimate load N could be compared with the critical Euler s value, based on the buckling length I, which is related to the distance I between two successive nodes I, 0.78 I for the short trusses Ic 0-911 for the long truss. [Pg.598]


See other pages where Euler stress is mentioned: [Pg.87]    [Pg.406]    [Pg.406]    [Pg.136]    [Pg.87]    [Pg.406]    [Pg.406]    [Pg.136]    [Pg.834]    [Pg.92]    [Pg.54]    [Pg.54]    [Pg.95]    [Pg.142]    [Pg.167]    [Pg.380]    [Pg.406]    [Pg.831]    [Pg.260]    [Pg.1003]    [Pg.41]    [Pg.370]    [Pg.109]    [Pg.157]    [Pg.322]    [Pg.358]    [Pg.178]    [Pg.291]    [Pg.227]   
See also in sourсe #XX -- [ Pg.34 ]




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