Keywords: low-cycle fatigue, hysteretic behaviour, degradation, composite member, smeared crack formulation, mixed formulation, damage, Bouc-Wen model.

New performance-based seismic design guidelines require that steel-concrete composite buildings be analysed by using non-linear static push-over analyses or non-linear dynamic analyses in order to control global and local demands. For this reason, designers need robust and computationally efficient models of members and joints for performing frame analyses in a reasonable amount of time.

The partial interaction between concrete slab and steel beam of composite systems in earthquake-prone zones as well as the use of partial strength beam-to- column joints provide more choice for the designer and reduce costs. However, the characterization of the partial shear connection and the deformability of beam-to- column joints is not an easy task. As a result, mathematical models and formulations of structural finite elements become more complex when the behaviour of members with partial shear connection needs to be traced.

Frame analyses with three- and two-dimensional finite elements are very expensive from a computational standpoint. So we formulated and implemented several one-dimensional composite beam elements based on the assumption of plane cross sections in each component, to reduce the computational expense. To improve the accuracy of numerical results in the case of highly non-linear curvature distributions, layered composite beam elements based on force (flexibility) formulations under small displacements were developed. The two beam-column components were connected by a continuous interface that approximated the shear force. Composite beam elements based on a displacement formulation were also developed demonstrating clearly the superiority of force over displacement formulations in the non-linear case. A two-field mixed beam element exhibiting a superior performance in the non-linear case was formulated too. At the current stage, models based on fibre concepts provide the best compromise between accuracy and computational expense, especially in the non-linear case.

Although there are many studies dealing with computational aspects of composite members and joints under seismic loading, there are few publications devoted to practical modelling and analysis issues as well as to the implications of low-cycle fatigue. In detail, we are interested in the seismic performance of composite beams with partial shear connection and partial strength joints with bolted extended end plate connections, which represent an alternative to fully welded connection for use in moment frames. Moreover, the shear lag and the flexible shear connection have not yet been incorporated in beam elements in view of linear and non-linear analyses. All together, they represent basic aspects of the analysis of composite systems and are the issues that the paper explores further.

In a greater detail, the objective of this paper is to survey some recent research and development results in the endeavour toward the seismic modelling of steel- concrete composite members and joints under cyclic loading. High ductile, composite steel-concrete moment frame structures are considered in which the global mechanisms are obtained by localizing dissipative phenomena in composite beam ends and beam-to-column joints.

The finite element analyses of composite substructures with partial composite action and partial-strength joints allow the comprehension of some inelastic phenomena characterizing their behaviour, such as the distribution of longitudinal stresses in the composite slab as well as the distribution of stresses in the column web panel and column flanges. Moreover, the analyses demonstrate the adequacy of three-dimensional finite element models based on the smeared crack approach and of one-dimensional models based on fibre concepts to the prediction of steel- concrete substructure behaviour. However, one-dimensional models require finite elements capable of embodying both the shear lag phenomenon and proper constitutive force-slip laws for headed stud shear connectors including stiffness deterioration and strength degradation.

With regard to the understanding of the low-cycle fracture behaviour of bolted steel connection, analyses under monotonic and cyclic loading provide insight in order to develop joint details able to reduce loading-induced toughness demands in connection components.

The development of composite beams with shear lag and force-slip constitutive laws for connectors embodying stiffness deterioration and strength degradation clearly imposes further work.

In this study, the parameter identification of the hysteresis models is performed by means of a trial and error method as the parameters have a clear physical meaning. Nonetheless, the adoption of a genetic algorithm might be a very interesting solution in view of an optimization of the parameter estimate of hysteresis models.

The simulation and implementation of the deteriorating behaviour of dissipative components of beam-to-column joints and composite members by means of hysteretic models in finite element codes deserves further studies.

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