Stiffness values

The use of an integral eentering spring damper eonfiguration allows preeise loeation of the damper journal and realization of the required stiffness value. To aehieve the low stiffness values while still maintaining lower stresses, the damper eonfiguration shown in Figure 6-25 was used. 

Stiction, in mercury thermometers, 24 465 Stiff differential equation, 25 285 Stiffness loss, in fatigue, 16 187-188 of fibers, 11 181, 182 Stiffness values, of paper, 18-101 Stilbene(s), 25 181... 

Standard geotechnical test reports address typical static properties of soil such as shear strength and bearing capacity but may not provide dynamic properties unless they are specifically requested. In these situations, it is necessary to use the static properties. Dynamic soil properties which are reported may be based on low strain amplitude tests which may or may not be applicable to the situation of interest. Soils reports will generally provide vertical and lateral stiffness values for the foundation type recommended. These can be used along with ultimate bearing capacities to perform a dynamic response calculation of the foundation for the applied blast load. 

Carbon-carbon (C-C) composites with a variety of unique properties can be fabricated by altering the combinations of the type and distribution of filaments and the bonding matrix used. Many engineering applications can be satisfied with a composite material whose density is just 70% that of aluminum and 25% that of steel, but for which the specific strength and stiffness values are four or five times those of steel. To attain the desired properties for such applications requires an understanding of the interrelationship of the fibers and the matrix that holds them. 

Therefore, the approximately-corrected complex stiffness value can be expressed as ... 

We have evaluated the effect of considering the fictitious joints as real joints on the equivalent stiffness tensor T,ju. We can notice that the terms of the equivalent stiffness tensor terms are smaller if we consider 3DEC fictitious joints are real. For the WP3 case (where high joint stiffness values are considered) the differences remain small. It increased up to 30 % for Kn = 4.34 lO Pa/m. 

The results is highly related to the choice of the fracture stiffness value. This invites us to investigate later on the effect of stress on the result considering stress dependent stiffness. 

The equivalent permeability tensor K j has been computed at 2 m scale considering the real length of the joint (we have shown the importance to avoid artificial joint prolongations). The REV could not be estimated due to code limitation reasons. The relation between permeability and stress (considering an isotropic state of stress) has been determined and is highly dependent on the joint stiffness value. 

This reduces to lirR Gt for a circular section tube of mean radius R. Figure 13.9 ranks the torsional stiffness of some beams of constant cross-sectional area. The preferred designs are hollow tubes the best has a circular section, as this includes the greatest area A for a given perimeter. The per cent stiffness values only apply to these specific dimensions. If the size of the section is increased, while the thickness t is kept at 2 mm, the advantage of the hollow tubes increases. 

The first assumption allows the development of averaged stiffness values for each ply, which depend on the individual stiffnesses of the fibers and matrix. The second and third assumptions are necessary for the development of the weighted stiffnesses for each ply and for each laminate. They can be relaxed when dealing with some failure modes such as fiber pull-out and delamination. The last two assumptions form the Kirchhoff hypothesis and ensure small deflections and rotations. 

The basic approach [1—4] starts with a single orthotropic ply. In the coordinate system of the ply, with one axis parallel to the fibers and one perpendicular to the fibers, in the plane of the ply, the stiffness properties are assumed known. These stiffness values may be obtained from analytical modelling at lower scales using micromechanics or may be obtained experimentally with 1 and 2 ply coordinates as opposed to the laminate coordinates x and y (see Figure 6.2). 

The above discussion was specific to the plane stress assumptions where no out-ofplane stresses are present. For a more general situation, the three-dimensional stiffness values of a laminate can be obtained as a thickness-weighted average of the ply compliances given by Eqn (6.12) ... 

In the general approach, the loads are applied incrementally until first-ply failure occurs. The type of failure, matrix or fiber, determines which properties of the failed plies must change to reflect the damage created. This is subjective and can cover a range of possibilities. The most conservative approach would completely discard affected properties for the failed plies. So for fiber failure, E would be set to zero. For matrix failure, E22 and G12 would be set to zero. Then, the loads would be incremented until another ply fails, and the procedure would be repeated to complete failure of the laminate. Less conservative approaches attempt to only partially discount stiffness values of the failed ply and even differentiate between tension and compression moduli. These methods can be reasonably accurate if they are accompanied by selected tests that help better define adjustment factors for the stiffness properties of failed plies. However, they are limited in applicability and accuracy because they are affected by the first-ply failure criterion used to trigger the failure sequence and because they do not correctly capture damage modes such as delamination and the interaction between them such as matrix cracks causing delaminations in adjacent ply interfaces. 

Thus, for metallic materials in many idealized practical situations, the design process is simplified to a stress (but not strain or displacement) analysis followed by comparison and optimization with critical stress values. When the problem is not statistically determinate, the stress analysis requires specification of material stiffness values, but the associated strain and deformation values are usually not required. Since the material behavior is usually represented adequately by linear isotropic elasticity, the stress analysis can be limited to that form, and there are many standard formulae available to aid the designer. 

The procedure initially developed by Lee (1974) and later refined by Chaney (1979,1980) and Makdisi et al. (1978) involved the concept that permanent seismic deformations of a slope may be computed by evaluating dynamic-induced softened pseudo slope stiffness values for soil elements with the resultant settling of the slope to a new condition being compatible with pseudo or apparent stress-strain properties of the soils comprising the slope. Figure 11.17 shows an example of the use of the permanent deformation method for evaluating the deformation of the continental slope off Flaifa, Israel, under earthquake loading from a transform fault on the Jordan rift valley. 

The nominal value of each story stiffness parameter is selected Ifom a uniform distribution over 2K to ik, where k is the actual interstory stiffness, so the nominal values O are significantly overestimated and the variation between the different interstory stiffness values is very substantial. Recall that the nominal stiffness values are taken as the initial values in the optimization to find the most probable values based on the modal data and it affects the prior distribution of the stiffness parameters. The subsystem stiffness matrices are given by Ko = 0i2x 12 since the problem is linear ... 

Consider next the incomplete mode shape measurements where only six sensors on the first, fourth, fifth, seventh, tenth and top floors are available. The results presented in Table 5.2 are based on five measured modes and show the initial values, final most probable values, standard deviations and COVs of the stiffness parameters, which are comparable to the COV of the modal data. Figure 5.1 shows the iterative history for the most probable values of the stiffness parameters, with convergence occurring in about 120 iterations. Again, the same set of nominal stiffness values is used so the nominal model overestimated the interstory stiffnesses by 100 to 200%. The parameters converge very quickly even for such an unsatisfactory set of initial values. The CPU time for 200 iterations is about 0.8 s with a conventional dual CPU 3.0 GHz personal computer under the MATLAB environment [171]. Figure 5.2 shows the comparison between the identified system mode shapes (solid lines) and the actual mode shapes (dashed lines) for the first five modes but the two sets of curves are on top of each other. Of course, it is no wonder that the mode shape components of the observed degrees of freedom are estimated better than the unobserved ones. 

Figure 2.1 Mechanical degradation with temperature for typical fibers (strength), polymers, and composites (stiffness), values normalized by those at 20°C. (Data reproduced from [1-4].)...

The breaking point practically corresponds to an equi-stiffness temperature a temperature at which the bitumen reaches critical stiffness that fractures. It has been shown that upon fracture, the bitumen has a stiffness value of 2.1 x 10 which approaches the maximum stiffness value of bitumen, 2.7 x 10 Pa (Thenoux et al. 1985). 

---