Axial stiffness

API 617 recognizes the need for the compressor thrust design to take into account peripheral factors such as the coupling. Gear couplings can transmit thrust to the compressor because of tooth friction. The standard uses an arbitrary friction coefficient of, 25, which can be a design basis. Flexible element couplings transmit less thrust because of the lower flex ing element axial stiffness. 

Another approach is to recognise that initially for a flat sheet, the axial stiffness is high but the transverse stiffness is relatively low. As the corrugation depth increases then the transverse stiffness increases but at the expense of the axial stiffness. It is readily shown that the axial deflection per unit load for the corrugations for the new geometry compared with the flat sheet is given by... 

If this is then divided into the previous enhancement ratio, q, it is possible to observe the way in which one stiffness increases at the expense of the other. Fig. 2.32 shows this transverse/axial stiffness ratio as a function of the depth of the corrugations. It may be seen that when the depth is less than four times the wall thickness then the axial stiffness ratio is better than the transverse stiffness ratio. However, when the depth is greater than four times the wall thickness then the transverse stiffness ratio dominates. 

Suppose we replace the 90° layers with a laminae in an attempt to increase the axial stiffness and to increase the first-ply failure load as in Figure 7-61. The load-deflection curve slope after first-ply failure also increases when a laminae replace the 90° layers. However, the energy absorption decreases with such a stacking sequence change. The associated fatigue lives are not known unless both laminates are made and subjected to fatigue loading. 

Space frames are structures made up of nodes and struts. When the struts that connect the nodes together are slender, the axial stiffness of the strut becomes the dominant form of stiffness, and the bending stiffness that might be achieved in the attachment of a strut to a node is usually very much smaller, and can often be ignored. 

Individually, the silk molecules will adopt a shape and conformation dictated by the competition to hydrate polar and nonpolar moieties (Hossain et al., 2003 Jin and Kaplan, 2003). In addition, to achieve fiber formation and optimal axial stiffness, the system must organize and lock the molecules in their extended configuration (Donald and Windle, 1992)... 

Deviations of the delamination from the mid-plane imply mixed-mode conditions, i.e., a deviation from a pure Mode I opening load. The degree of mode mixity will depend on the relative stiffness of the two unequal beams. In the cross-ply laminates, this stiffness difference will be small , as long as the unidirectional plies that essentially provide the axial stiffness are equal in both beams. This is a rational justification for a validity criterion for cross-ply laminates that allows deviations from the mid-plane, as long as the delamination does not show a transition into the unidirectional plies. 

Calculation of the residual in-plane axial stiffness 0 using Eq. (5) and transformation formulae [3] yields the strain energy release rate associated with local delamination in terms of IDEFs and 0/. as... 

The motility appears to be due to a passive piezoelectric behavior of the ceU plasma membrane [Kahnec and colleagues, 1992]. Iwasa and Chadwick [1992] measured the deformation of a ceU under pressure loading and voltage clamping and computed the elastic properties of the wall, assuming isotropy. It appears that for agreement with both the pressure and axial stiffness measurements, the ceU wall must be... 

Here, A is the greater of the axial stiffnesses An and A22 for the sublaminate and e is the applied strain. By comparing the difference in energies to Gic, the SERR required to cause Mode I failure of the resin, it is possible to approximately predict the threshold strain below which propagation of a delamination will not occur. 

Due to the positioning face and the larger supporting diameter associated with it, the HSK achieves higher radial and axial stiffnesses compared to the SK. Even the repeat fitting accuracy is reproducible and lies at < 1 pm. In the case of the SK, by contrast, the tolerances alone lead to deviations within the tenth-millimeter range (Week and Reinartz 1999). 

The lateral bending stifihess ofthe plate girder bridge is quite small in comparison to the axial stiffness (1 x EA = 3.255 GNm ) or the Euler buckling load of each span. So when the piers try to rotate about their cross-sectional axis, the superstructure i.e. bridge deck offers least resistance. 

For the calculations, the length of IPMC was varied from 0 to 5.5 mm (see Fig. 2.48 for the definition of IPMC length). If the length is 5.5mm, then the unit consists of only IPMC, i.e. the sides are not of Nation. Conversely, the simulations show that the axial stiffness of an elementary unit... 

Continuous efforts are being made to improve the manufacturing process. Wright Laboratory s Materials Directorate sponsored work by Aerotherm Corp., Kaiser Aerotech and Lockheed Missile Space Co. to investigate an alternative approach for products with improved stiffness, but which would be cheaper. The approach used a pitch matrix and provided added axial stiffness to 345 GPa with reduced production time from months to hours. 

The fibres of the AKIOOO blade are orientated along its length to provide an axial stiffness at its root of 24 and 15 GPa in the chord. At the junction between the main hydrodynamic profile and the root, the fibres are aligned to give an axial laminate modulus of 29 and 13 GPa in the chord. 

Using finite element analysis on a representative 0.1 m wide strut, radial and axial displacements of the bulkhead and the strut-rock interface are calculated and shown in Fig. 2. The effect of the large induced moment can be seen in the radial displacements, U ,-. For all three materials, the displacements at the rock-strut interface are the same. The radial stiffnesses are nearly the same however, the axial stiffness, or resistance to shear deformation, of the cloth/epoxy or cloth/polyester is considerably less than that of the variable angle composite. 

The Geogrid was modeled as linearly elastic-perfectly plastic material with Mohr-Coulomb failure criterion. The axial stiffness (J) and the tensile strength (T) were needed in the program and taken J = 620 kN/m and T = 70 kN/m, respectively. The interaction coefficient between the geogrid and cohesive backfill was taken 0.7. 

For small deflections (i.e., elastic behavior), a bellows can be simplified by only half a convolution (Fig. 42.9b). The axial and transverse stiffness from such an analysis can be regarded as a reference base for the verification of any later more detailed, and therefore necessarily less refined, FE model. An analysis using 2688 eight-node isoparametric 2D symmetric elements, PLANE82, with 8753 nodes, resulted in a determined axial stiffness, axiai of 403.8 kN/m (2,306 Ibf/in) with a transverse stiffness, of 5,558 kN/m... 

With large transverse deflections, contacts between adjacent convolutions occur and the whole bellows must be modeled. The shape of the beUows is asymmetric, i.e., the overall shape of the deformed stmcture possesses 180° rotational symmetry about the midpoint of the neutral axis. Three-dimensional shell elements (SHELL43) are thus necessary (Fig. 42.9c). An element size of 12 X 12 mm yields 11,760 elements and 11,979 nodes to mesh only one half a bellows. The computational requirements for this are large. Increases in element size result in an increase in axial stiffness. 

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