Proper material constitutive models for concrete-filled tube ͑CFT͒ columns are proposed and verified by the nonlinear finite element program ABAQUS against experimental data. The cross sections of the CFT columns in the numerical analysis are categorized into three groups, i.e., circular section, square section, and square section stiffened by reinforcing ties. Via the numerical analyses, it is shown that for circular CFT columns, the tubes can provide a good confining effect to the concrete especially when the width-to-thickness ratio D/t is small ͑say D/tϽ40). For square CFT columns, the tubes do not provide a large confining effect to the concrete especially when the width-to-thickness ratio B/t is large ͑say B/tϾ30). The confining effect of square CFT columns with reinforcing ties is enhanced by the use of reinforcing ties especially when the tie spacing is small and the tie number ͑or tie diameter͒ is large.

BackgroundFinite element analysis results will show significant differences if the model used is performed under various material properties, geometries, loading modes or other conditions. This study adopted an FE model, taking into account the possible asymmetry inherently existing in the spine with respect to the sagittal plane, with a more geometrically realistic outline to analyze and compare the biomechanical behaviour of the lumbar spine with regard to the facet force and intradiscal pressure, which are associated with low back pain symptoms and other spinal disorders. Dealing carefully with the contact surfaces of the facet joints at various levels of the lumbar spine can potentially help us further ascertain physiological behaviour concerning the frictional effects of facet joints under separate loadings or the responses to the compressive loads in the discs.MethodsA lumbar spine model was constructed from processes including smoothing the bony outline of each scan image, stacking the boundary lines into a smooth surface model, and subsequent further processing in order to conform with the purpose of effective finite element analysis performance. For simplicity, most spinal components were modelled as isotropic and linear materials with the exception of spinal ligaments (bilinear). The contact behaviour of the facet joints and changes of the intradiscal pressure with different postures were analyzed.ResultsThe results revealed that asymmetric responses of the facet joint forces exist in various postures and that such effect is amplified with larger loadings. In axial rotation, the facet joint forces were relatively larger in the contralateral facet joints than in the ipsilateral ones at the same level. Although the effect of the preloads on facet joint forces was not apparent, intradiscal pressure did increase with preload, and its magnitude increased more markedly in flexion than in extension and axial rotation.ConclusionsDisc pressures showed a significant increase with preload and changed more noticeably in flexion than in extension or in axial rotation. Compared with the applied preloads, the postures played a more important role, especially in axial rotation; the facet joint forces were increased in the contralateral facet joints as compared to the ipsilateral ones at the same level of the lumbar spine.

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