The inadequacy of member models in D as a limitation of nonlinear modelling

It is natural to expect that a sophisticated method (in this case non-linear seismic response analysis) will be at least as good at tackling general design situations in their full complexity as simplified approaches (in the present case, linear seismic response analysis). However, as already noted, the non-linear static (pushover) analysis method has been developed for analysis of seismic response in 2D (regardless of whether a 3D structural model is used), and its application in cases of truly 3D response (due to torsional effects) still raises certain questions. Although it has also been developed primarily for 2D analysis, the non-linear dynamic method can, in principle, be applied equally well to seismic response analysis in 3D. It is presumed that, for such an extension to 3D, appropriate models of the behaviour of members under 3D loading are available. However, the lack of reliable yet simple models for the (monotonic or cyclic) post-elastic behaviour of vertical members in two orthogonal transverse directions (in biaxial bending and shear with axial load) is currently the single most important challenge to the achievement of full-fledged non-linear seismic response analysis, static or dynamic, in 3D.

Fibre models of members can, in principle, represent well the (monotonic or cyclic) post-elastic flexural behaviour of prismatic members in the two orthogonal directions of bending. However, due to the requirements of such models in computer time and memory and the exponential increase of the risk of numerical problems with the amount of calculations, fibre models cannot be used practically for the non-linear seismic response analysis in 3D of full-sized buildings. Moreover, fibre models need careful tuning of their input properties and parameters, in order to reproduce the intended behaviour pattern of a member, including its connections - be it a pattern consistent with the fundamental assumptions and rules specified in Eurocode 8 for member modelling, or experimental behaviour: such tuning requires specialized knowledge and experience, which is far beyond the current capabilities of design professionals. Lumped inelasticity (point hinge) models are not capable of representing well the (monotonic or cyclic) post-elastic behaviour of members in two orthogonal transverse directions, without sacrificing their simplicity, flexibility and - most importantly - their reliability and numerical stability, i.e. all the attributes that made them the workhorse of member modelling for non-linear analysis in 2D. Currently, non-linear seismic response analysis in 3D often uses one independent model of this type in each one of the two orthogonal directions of bending. Coupling of the response between these two directions is normally ignored, or taken into account only as far as the value of the yield moment and the failure criteria in terms of plastic hinge rotations in the two orthogonal directions of bending. Such an approximation is usually acceptable if the non-linear response is primarily in one of the two directions of bending, as is often the case in fairly symmetric buildings subjected to a single horizontal component of the seismic action. It may be insufficient - and certainly in the unconservative direction - for simultaneous application of the two horizontal components of the seismic action and/or when the building develops a strongly torsional response due to irregularity in plan.

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