Modello costitutivo di Bouc e Wen con interazione P-M per la linearizzazione stocastica delle intelaiature piane

Randomness of the ground motion and uncertainty of the plastic structural behavior make the assessment of seismic performance doubtful. Among the probabilistic methods of seismic structural analysis, the stochastic equivalent linearization is a sound alternative to Monte Carlo simulation. Assuming the Bouc-Wen hysteresis model in particular, gives a closed-form equivalent linear system, which is fundamental to the computation economy. An extension of this model is proposed in order to introduce the dependency between the axial force and bending moment of framed structures in the plastic stage. A second-degree parabola is assumed as such a relationship, within the lumped plasticity approach with linear beam elements and hysteretic springs at their ends. The formulation of the expected values and covariance of the response quantities is developed for the non-zero mean stationary problem with Gaussian processes. Non-zero mean values may come from either deterministic load or asymmetric strength; dispersion is due to the ground motion modelled as a filtered white noise. A qualitative validation of the model is presented comparing two portal frames in which the importance of the axial force variation is different. The results are reasonable and encourage to further verification and, finally, to the model application to case studies.