Keywords: static analysis, push-over, three-dimensional structures, masonry, holonomic-plastic behaviour, no tension model.

For masonry structures, the proneness to degradation or collapse is much more dependent on the activation of cracking mechanisms than on the probability of masonry crushing. Thus masonry material models should include fracture as an intrinsic feature for the stress-strain relationships which in turn pushes researchers to develop structural mechanics for no-tension (NT) materials.

The formulation of analysis tools for NT bodies stands on the possibility of performing some extension of the plastic theory to masonry gravity structures such as arches and panels, provided certain assumptions are made. The underlying premise is that masonry structures can conceptually be considered as possessing an overall 'ductile' capacity; this viewpoint point is largely supported by the experimental evidence. Some clear advantages can be immediately observed, such as an example, that in the extension of the plastic limit analysis methods, the structure can be considered solely in relation to its ultimate state, simplifying matters considerably. This also implies that few material parameters and no prior knowledge of the initial stress state are required. Therefore, structural analysis under ordinary loading conditions as well as for collapse load evaluation can be performed by means of suitable extensions to the NT structures of the theoretical approaches for elastic-plastic structures.

By implementing the mechanical model and following solution paths based on the constrained optimisation of suitably defined energetic functionals, practical applications may be successfully developed not only with reference to the single masonry monads such as panels, arches and vaults, but also for analysing the entire masonry building under static loads, and to perform, for example, push-over analyses. Extensions may be provided for the analysis for quasi-static seismic-type actions, when the masonry structure exhibits some overall ductility properties, possibly entering a kind of plastic phase and developing hysteretic cycles. The method proposed in this paper performs a full holonomic plastic analysis of the structure, starting from the treatment of the single structural panel using the NT theory. The approach offers some clear advantages with respect to the POR method, since the initially performed NT analyses of the walls allows their treatment as a whole, including elements such as architraves possibly present on the doorways or openings, which, on the contrary are not considered in the POR method. Moreover some strength in the cross direction of the wall can also be accounted for by the assumption of an elliptical resistance domain. Finally collapse mechanism related to the overturning of the wall can also be considered, which are absent in the POR method. One should also emphasise that, as mentioned in the above, the method may be extended for considering seismic-type loads, thus allowing some evaluations of the behaviour of the masonry spatial structure subject to dynamic actions.

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