Unreinforced masonry (URM) buildings, a common structural typology worldwide, are highly vulnerable to earthquake loading, making their seismic assessment essential and their numerical modelling particularly challenging. This complexity is further amplified in heritage buildings, where retrofit interventions must balance structural improvements with strict conservation guidelines, ensuring the preservation of the authenticity of the structure.

A distinctive feature of masonry heritage is the presence of arches, structural forms inspired by nature that have been integral to architecture since ancient times. These elements efficiently span large spaces, deriving strength from their geometry while also contributing to the aesthetic value of historic buildings. However, being primarily designed to resist static loads through compression, arches are particularly susceptible to seismic forces.

Therefore, simplified models capable of providing reliable predictions of the structural response of buildings under dynamic loading are needed. To achieve this, equivalent frame models of masonry buildings are employed, offering a computationally efficient approach for accurately evaluating structural behaviour. Recent advancements in this modelling strategy have enabled the representation of both in-plane and out-of-plane failure mechanisms of masonry panels. Building on this foundation, this thesis introduces two main contributions to the equivalent frame modelling approach: (1) the implementation of a method for modelling the strengthening of masonry walls using fibre-reinforced polymers (FRPs), and (2) the development of a new element specifically designed to model curved components, such as arches, commonly found in patrimony.

The first part of the work focuses on developing efficient numerical models capable of capturing the impact of FRP strengthening on masonry walls. This is accomplished by extending an existing macro-element, where longitudinal FRP strips are modelled as additional fibres within the section to improve flexural capacity, while transverse FRP strips are represented by increased cohesion, effectively enhancing shear strength.

Secondly, a new macro-element is proposed for simulating the behaviour of masonry arches in their actual geometry and validated against experimental data from literature. This model adopts a variational rigid-block approach combined with an optimisation-based algorithm to calculate displacements and forces. Fully integrated into OpenSees software as a beam-like element, it ensures complete compatibility with other components and analysis procedures. Leveraging the computational efficiency of equivalent frame models, a sensitivity analysis is performed to evaluate the impact of various numerical uncertainties, with a primary focus on damping. The potential of the model is further demonstrated on a section of an arched arcade, both in its unstrengthened state and in a retrofitted configuration using tie rods.