The seismic assessment of masonry buildings, both modern unreinforced masonry (URM) buildings and historical heritage constructions, is a complex task, characterised by a several sources of uncertainty, which regard the appropriate modelling of strategy the problem, the model parameters, and the seismic input. In order to properly account for all sources of uncertainty and provide a robust risk estimate, simple models to be run under different conditions are necessary.

In this regard, equivalent frame modelling of masonry buildings is a modelling approach which can produce reliable estimates of the seismic demands, in terms of displacement and accelerati, for buildings showing a predominant in-plane failure mode. The simplicity of the approach allows performing multiple simulations at a reasonable computational cost.

This thesis concentrates on the extension of the equivalent frame approach for the modelling of both the in-plane and the out-of-plane response of masonry buildings. Making use of the computational simplicity of equivalent frame models, it further proposes an approach for the probabilistic assessment of buildings, which aims at being potentially applicable also outside the research domain, to which probabilistic methods are mainly confined at the state of the art.

In order collect information on the uncertainties related to the assessment of the in-plane behaviour of masonry, with a particular regard to stone masonry, a database of 128 shear compression tests on walls was collected and analysed. Distributions and median values of the most relevant material properties were derived, including the displacement capacities at cracking, yielding, maximum force capacity, significant damage and collapse limit states. Moreover, the uncertainty on the determination of force capacity and stiffness was discussed.

This data was then used to apply to a case study a simplified approach for the explicit introduction of uncertainty in a seismic assessment of a stone masonry building. The method was compared to established approaches of similar complexity and a reference Monte Carlo simulation. From the analysis, the relative impact of all sources of uncertainty on the total model uncertainty could be evaluated, showing the major relevance of the displacement capacity in determining the seismic performance.

Secondly, a formulation of a macro-element model for the simulation of the in-plane and out-of-plane response of masonry walls is proposed. Its use in simulating from small element tests to shaking table tests on entire buildings is shown. The proposed macro-element is able to describe the out-of-plane dynamic response of buildings, showing the major sources of vulnerability and simulating the effect of the quality of connections on the global response, both in terms of displacement demands and failure modes.