This paper addresses the long-standing problem of the equilibrium of the circular, pointed, and elliptical arches commonly found in historical masonry buildings and bridges that are subjected to their own weight and the weight of superimposed masonry walls. The equilibrium problem is studied by applying two different complementary methods: the first is a simple extension and analytical re-reading of the Durand-Claye stability area method; the second is based on the application of a nonlinear elastic one-dimensional model, already used by the authors in previous studies. It is assumed that the arch’s constituent material has limited compressive strength and null tensile strength. In addition, the load transferred to the arch by the wall is determined under the common assumption that each vertical strip of wall bears directly down on the underlying arch element. The study focuses on the maximum height that the superimposed wall can reach under equilibrium conditions while maintaining acceptable valu...

Keywords: Structural analysis, Laser scanning, Photogrammetry, Cultural Heritage, Dome This paper aims to illustrate the preliminary results of a research project on the dome of Pisa Cathedral (Italy). The final objective of the present research is to achieve a deep understanding of the structural behaviour of the dome, through a detailed knowledge of its geometry and constituent materials, and by taking into account historical and architectural aspects as well. A reliable survey of the dome is the essential starting point for any further investigation and adequate structural modelling. Examination of the status quo on the surveys of the Cathedral dome shows that a detailed survey suitable for structural analysis is in fact lacking. For this reason, high-density and high-precision surveys have been planned, by considering that a different survey output is needed, according both to the type of structural model chosen and purposes to be achieved. Thus, both range-based (laser scanning) and image-based (3D Photogrammetry) survey methodologies have been used. This contribution introduces the first results concerning the shape of the dome derived from surveys. Furthermore, a comparison is made between such survey outputs and those available in the literature.

This paper aims to illustrate and compare different approaches for the limit analysis of masonry domes of revolution with an oculus at the top. It specifically focuses on the influence of the limited compressive and tensile strength of masonry on the bearing capacity of the dome. The first assessment is conducted through a semi-analytical formulation that revisits Durand-Claye’s method within the framework of the lower bound theorem of limit analysis. The second investigation is performed using a kinematic approach, which allows for closed-form solutions by exploiting the upper bound theorem of limit analysis and the virtual work theorem. These approaches are applied to a case study that was experimentally tested, involving a hemispherical dome with an oculus. The dome is subjected to its self-weight and a vertical load at the crown. Parametric investigations are presented to compare the results obtained through the proposed methods with those derived from the classical limit analysis of masonry structures, based on Heyman’s hypotheses.

This study, framed within the context of the lower bound theorem of limit analysis, aims to assess the anti-funicular equilibrium of masonry arches and domes using a computational approach based on the constrained force density method. In contrast to the commonly adopted classical Heyman’s assumptions, the approach proposed here considers the effects of finite compressive strength in the material. Assuming a fixed plan projection for a network with independent sets of branches, a suitable set of local constraints is enforced at each joint to account for the limit bending moment resulting from the material’s assumptions, including limited compressive strength and zero tensile strength. Additionally, the stereotomy of the voussoirs is considered by assigning a geometric law to the joint inclination. The collapse load is determined by formulating a multi-constrained maximization problem. The method is validated using a modern version of the semi-analytical Durand-Claye’s method. For benchmark case studies, such as symmetric masonry arches and domes with specific stereotomies subjected to axi-symmetrical load conditions, the set of statically admissible solutions compatible with equilibrium and strength requirements is graphically determined in terms of the horizontal thrust and its eccentricity at the crown, examining the shape of the stability area. Assuming an infinite value for the friction coefficient, the collapse condition is reached when the stability area shrinks to a single point. The results obtained from both of these methods are in excellent agreement. The influence of compressive strength on the bearing capacity of the structures is also discussed.