The Equivalent-Frame Method (EFM), a simplified procedure for structural modelling of masonry constructions, is having a great success for the good balance that it allows between the accuracy of the geometrical description and the simplicity of the mechanical calibration.\ud Despite the widespread use of EFM in scientific and professional field, some uncertainties affect its application to the specific problem of the existing unreinforced masonry (URM) buildings. For these structures, in fact, irregular geometries, the presence of deformable diaphragms and the interaction with other structures in aggregate configurations represent hard-to-model features that limit the accuracy of EFM.\ud The paper presents a comparative study in the linear field between EFM and the more accurate Finite Element Method (FEM), assumed as reference. The comparative analysis involves a wide set of geometrical schemes, characterized by both regular and irregular configurations, and it is aimed at providing a measure of the EFM modelling accuracy as a function of the geometry of the wall. Non-dimensional parameters allow exploring the limits of applicability of EFM for both regular and irregular walls.\ud Based on the parametric analyses, some recommendations are given for improving the effectiveness of the method and preserving the simplicity of application that makes EFM models so popular and widely used.Peer ReviewedPostprint (author's final draft
The accuracy of the Equivalent Frame Method (EFM) in modelling the seismic non-linear behaviour of unreinforced masonry (URM) buildings is investigated for regular walls (i.e. walls with regular openings' distribution) with different pier-to-spandrel geometrical relations. The developed EFM is composed of pier and spandrel elements with spread plasticity to simulate the flexural behaviour and lumped plasticity to simulate the shear behaviour. The investigation focuses on checking, by means of comparison with Finite Element Model (FEM) assumed as reference, the applicability of EFM to existing buildings. These structures are often characterised by geometrical schemes difficult to be represented by ideal frames. To point out the role of the geometrical configuration, the numerical results provided by the two modelling approaches are compared for different representative cases of regular walls characterized by pier-spandrel configurations rather typical in existing URM buildings. In addition to the innovative EFM approach, based on a fiber discretized beam element, also a more traditional approach, based on beam elements with lumped plasticity, is included in the comparative study. The two different EFM approaches were implemented in the software Midas GEN © [44], while an open source software was used to implement the FEM (Kratos Multiphysics [59-60]). All the models were used to perform static non-linear analyses under equivalent loading and boundary conditions. The evaluation of EFM and FEM is derived from a comparative simulation of a two-storey URM wall experimentally tested by other researchers. Two alternative approaches are assumed for the definition of piers' effective heights in the EFM, i.e. the models proposed by Dolce [1] and Augenti [2]. The results demonstrate that remarkable differences may be detected in EFM and FEM predictions of the shear capacity and damage mechanisms as a function of pier-spandrel geometrical configurations. This result highlights the need for a cautious application of EFM to existing URM structures.
In the last decades increasing attention has been devoted to masonry structures both from researchers and professionals. This is due to the awareness of the great importance of these structures in the historical urban context, together with the great risk that they suffer in seismic areas.Growing success has been obtained by a simplified approach that models masonry walls through "equivalent" plane frames, with concepts and procedures drawn from the study of reinforced concrete and steel frames. In this approach, known as Equivalent Frame Method (EFM), each masonry resisting wall is modelled as a system of linear (frame) elements representative of the behaviour of finite portions of the wall (pier and spandrel panels).Up to now EFM has proven to be effective in the case of new buildings characterized by regular geometrical configurations and with openings' dimensions for which the frame-like assumption is suitable. Critical issues emerge from existing buildings in European historical centres, where irregularities are almost always present and geometrical anomalies can be detected even in the case of regular walls.For the specific case of geometrically regular URM walls, this paper presents sample cases tested with linear and non-linear analyses, with the aim to explore the applicability of EF procedures and to identify its limits. A comparison between an EFM procedure with a fiber approach and a more detailed FEM method with plane elements, is adopted as a validation tool, to evaluate the accuracy of the results provided by the EFM for walls characterized by different geometrical configurations.
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