Transverse stiffness

The obvious question is Ts there an optimum design for the corrugations Unfortunately the answer is No because if one wishes to increase transverse stiffness then the obvious thing to do is to increase D up to the point where buckling problems start to be a concern. Usually this is when D/h = 10, for short-term loading and less than this for long term loading because of the decrease in modulus of viscoelastic materials. 

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. 

Extensive experimental testing was performed on IM6/3100 to obtain longitudinal and transverse stiffnesses and major Poisson s ratio as a function of degree of cure. A detailed explanation of the test procedure can be found in [5], The model predictions and experimental results for this material system are shown in Figures 8.11-8.13. From these relations the lamina stiffnesses Qy can be obtained from... 

Nyland, L.R., Maughan, D.W. (2000). Morphology and transverse stiffness of Drosophila myofibrils measured by atomic force microscopy. Biophysical Journal, 78, 1490-1497. 

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... 

Moreover, MMCs also exhibit better performances compared with other composites, especially polymer matrix composites, because they possess a higher temperature capability along with fire resistance and low outgassing, a greater transverse stiffness and strength. 

For seismic analysis in bridge transverse direction, since the backfill soil is usually slopping away from abutment wingwall and there is a relatively weak connection between the abutment wingwaU and the stem, the displacement coefficient shall not be applied directly in the analysis. Reduced Rf or fully released abutment cases shall be studied. In order to increase the transverse stiffness of the abutment, interior supplemental shear walls may be attached to the abutment or the wingwall thickness may be increased, as shown in Figure 6.4. 

The purpose of applying a factor of 0.75 to the design of abutment shear keys is to reduce the possible damage to the abutment piles. For all transverse cases, if the design transverse earthquake force exceeds the sum of the capacities of the wingwalls and piles, the transverse stiffness for the analysis should equal to zero (EQj = 0). Therefore, a released condition that usually results in a larger lateral displacement at adjacent bents should be studied. 

For transversely stiff fibers (for fiber glass, E yi. E m T)), the temperature dependence is controlled by the matrix. For transversely weak fibers (for carbon or Kevlar, E y T) > E yiiT)), an additional temperature dependence arises. 

Adding 40% by volume of reinforcing fibers to the matrix for the cases plotted would result in only about 50% increase in transverse stiffness of the composite, but would increase longitudinal stiffness by 400% (Figure 8.6). Hence, the addition of fiber reinforcement to a polymer matrix can have a very pronounced effect on its stiffness and directional properties, particularly in the liber direction. 

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