Reliable calibration of cyclic models for steel members

Accurate response predictions of steel structures subjected to earthquake loading involve the use of models able to simulate properly the cyclic behaviour of the regions where nonlinear phenomena take place. These include hardening, softening, strength and stiffness degradation, pinching and gap closure. In case of full-strength joints, all nonlinear effects appear in the members connected, and particular relevance is assumed by softening and strength degradation. Even though a number of phenomenological models have been developed in the last decades, their calibration seems to have received less attention. Usually, calibration is based on matching the experimental and numerical cyclic responses under loading protocols proposed by standards. These protocols have been developed to give a reliable estimate of the cyclic deformation demand of the considered structural system, since demand strongly depends on the loading history and the hysteretic behaviour when dealing with structural elements characterised by nonlinear behaviour. In general, the accuracy of a numerical model calibrated minimising the discrepancy between experimental and computed response is controlled by the sensitivity of the considered response on the parameters, and since the original aim of loading protocols is not the calibration of numerical models, investigation is needed to assess the predictive capability of so calibrated models. In this work, a calibration procedure based on the minimisation of response discrepancy is presented and critically discussed, with reference to an experimental programme carried out at the University of Salerno. In particular, cyclic, monotonic and pseudo-dynamic tests were carried out on a hollow square member, with the aim of calibrating an advanced phenomenological model. It is shown that a calibration based on cyclic response under ordinary loading protocols only is not robust, since its accuracy under different loading conditions may deteriorate. In particular, loading histories characterised by sudden strong impulses after small-amplitude cycles may involve parameters which are not well represented by ordinary cyclic loading protocols. The introduction of the monotonic test in a multi-objective framework may be effective, and its accuracy is confirmed by the results of pseudo-dynamic tests.