Dynamic analyses and seismic assessments of multi-storey buildings at the urban level require large-scale simulations and computational procedures based on simplified but accurate numerical models. For this aim, the present paper proposes an equivalent non-uniform beam-like model, suitable for the dynamic analysis of buildings with an asymmetric plan and non-uniform vertical distribution of mass and stiffness. The equations of motion of this beam-like model, which presents only shear and torsional deformability, were derived through the application of Hamilton’s principle. The linear dynamic behaviour was evaluated by discretizing the continuous non-uniform model according to a Rayleigh–Ritz approach based on a suitable number of modal shapes of the uniform shear-torsional beam. In spite of its simplicity, the model is able to reproduce the dynamic behaviour of low- and mid-rise buildings with a significant reduction of the computational burden with respect to that required by more general models. The efficacy of the proposed approach was tested, by means of comparisons with linear Finite Element Model (FEM) simulations, on three multi-storey buildings characterized by different irregularities. The satisfactory agreement, in terms of natural frequencies, modes of vibration and seismic response, proves the capability of the proposed approach to reproduce the dynamic response of complex spatial multi-storey frames.

The paper presents the comparison of the results obtained on a masonry building by nonlinear static analysis using different software operating in the field of continuum and discrete-macroelement modeling. The structure is inspired by an actual building, the "P. Capuzi" school in Visso (Macerata, Italy), seriously damaged following the seismic events that affected Central Italy from August 2016 to January 2017. The activity described is part of a wider research program carried out by various units involved in the ReLUIS 2017/2108—Masonry Structures project and having as its object the analysis of benchmark structures for the evaluation of the reliability of software packages. The comparison of analysis was carried out in relation to: global parameters (concerning the dynamic properties, capacity curves and, equivalent bilinear curves), synthetic parameters of structural safety (such as, for example, the maximum acceleration compatible with the life safety limit state) and the response in terms of simulated damage. The results allow for some insights on the use of continuum and discrete-macroelement modeling, with respect to the dispersion of the results and on the potential repercussions in the professional field. This response was also analyzed considering different approaches for the application of loads.