## 1 Introduction  
Historical masonry buildings represent the significant part of the Italian historical heritage. Since these buildings were originally designed to resist gravity loads only, they often suffered serious damage during earthquakes [1; 2; 3; 4]. The importance of protecting their historical and cultural value and the need to guarantee their structural safety to avoid loss of life during earthquakes has increased the interest of researchers and engineers in the study and assessment of their seismic behavior [5; 6; 7; 8; 9; 10; 11] in order to propose the most appropriate retrofitting interventions [12; 13; 14; 15; 16; 17]. Despite the great advancements in research made in the last years and the introduction in Italian design codes of specific guidelines for built heritage [18; 19; 20], the evaluation of the seismic vulnerability of masonry buildings is still a challenging issue. The main difficulties arise from the heterogeneity of the material and its low tensile strength, when compared with its compressive strength, that results in a complex constitutive behavior. Historical masonry towers are widespread in Italy and represent an important part of the built heritage to be preserved. The experience of past seismic events has proven how these structures are particularly vulnerable to earthquakes [21; 22; 23]. Indeed, their unique peculiar morphologic and typological features (e.g., high slenderness, presence of irregularities, leaning phenomena) might significantly affect their behavior under horizontal loads [24]. A realistic estimation of their structural behavior is fundamental to evaluate both the safety level and the most appropriate retrofitting interventions, but a compromise should always be found between required computational resources and accuracy of results. Different approaches to predict the masonry towers' seismic response were proposed in the scientific literature. The different methods can be grouped into two main categories: the continuum method and the discrete approach [25]. Continuum methods assume that stresses and strains over the structure are approximated by continuous functions. Among the continuum approaches, the finite element (FE) method proved to be a suitable tool to study the seismic behavior of towers [26; 27; 28; 29; 30], and the implementation of full nonlinear solid FE models is highly recommended to obtain accurate results. A macro-modeling strategy is usually adopted [31] together with sophisticated constitutive models (i.e., elasto-plastic with softening and damaging models) suitable for an insight into the nonlinear structural response. The main disadvantage of this approach is that it requires skilled users with strong mechanical backgrounds and powerful and expensive FE codes, which are different from the commercial ones commonly used in engineering practice. As alternative to 3D solid models, simplified approaches were formulated, as suggested in [18], in order to reduce the computational effort and to propose practice-oriented methods. The structure of the masonry tower, thanks to its simple geometry, can be represented by a continuous one-dimensional model (i.e., cantilever beam), and the main mechanical characteristics of the material in all the cross-sections along the height evaluated by means of a nonlinear elastic constitutive law formulated in terms of generalized stress and strain [32; 33]. This procedure gives more reliable results for slender towers with a predominant bending behavior. When the tower is not particularly slender, flexural damage is often associated to shear cracks, which cannot be taken into account by the cantilever model, leading to wrong evaluations and inadequate retrofitting interventions. In the discrete approach, the structure is considered as an assembly of distinct bodies, which interact along their boundaries [34].