A combination of terrestrial laser-scanning point clouds and the thrust network analysis approach for structural modelling of masonry vaults

Terrestrial laser-scanning (TLS) is well suited to surveying the geometry of monumental complexes, often realised with highly irregular materials and forms. This paper addresses various issues related to the acquisition of point clouds via TLS and their elaboration aimed at developing structural models of masonry vaults. This structural system, which exists in numerous artifacts and historical buildings, has the advantages of good static and functional behaviour, reduced weight, good requisites of insulation, and aesthetic quality. Specifically, using TLS, we create a geometric model of the ancient masonry church, S. Maria della Libera, in Aquino, largely characterised by naves featuring cross vaults and previously used as a case study in the paper entitled ‘Terrestrial laser-scanning point-clouds for modeling masonry vaults’, presented at the 2019 IMEKO TC-4 International Conference on Metrology for Archaeology and Cultural Heritage. The results of the TLS survey are used as input for a structural analysis based on the thrust network analysis. This recent methodology is used for modelling masonry vaults as a discrete network of forces in equilibrium with gravitational loads. It is demonstrated that the proposed approach is both effective and robust in terms of assessing not only the safety conditions of existing masonry vaults, the actual geometry of which significantly influences the safety level, but also to design new ones.

Form-finding of pierced vaults and digital fabrication of scaled prototype

The new serious consideration to masonry and non-metallic structures evidenced their direct prospective to be, even in the present days, advanced architectural and engineering solutions. In the present paper, a form finding for a cement based tessellated pierced vault is studied. The multi-body rope approach (MRA) was used to define compression-only vault optimal shapes. Successively, the thrust network analysis (TNA) was implemented by Rhino-vault for a further validation of the shape and the definition of different tessellation meshes of the surfaces, according to different hole pattern configuration. Different piercing percentage of the vaults were considered and compared for the best solution identification. In addition, the geometrical solutions were analyzed by means of global stability analysis, taking into account the different positions of the holes. Furthermore, 3D printing with a Fuse Deposition Modeling (FDM) technique in polylactide (PLA) material (completely eco-friendly) is used for the construction of the formworks of the cement based blocks (dowels) useful for the assembly of a vault scaled prototype. The prototype of the vault, characterized by a certain piercing percentage was subjected to different loading conditions and monitored by a non-contact device based on the Digital Image Correlation (DIC) technique. The 3D-DIC was performed to recognize the structural behavior during the loading process of the model (prototype). DIC measurements were used to recognize in advance the critical condition of the vault under loading and the displacement measurements were correlated to the different loading phases up to the collapse condition.

ArchLab: a MATLAB tool for the Thrust Line Analysis of masonry arches

According to Heyman’s safe theorem of the limit analysis of masonry structures, the safety of masonry arches can be verified by finding at least one line of thrust entirely laying within the masonry and in equilibrium with external loads. If such a solution does exist, two extreme configurations of the thrust line can be determined, respectively referred to as solutions of minimum and maximum thrust. In this paper it is presented a numerical procedure for determining both these solutions with reference to masonry arches of general shape, subjected to both vertical and horizontal loads. The algorithm takes advantage of a simplification of the equations underlying the Thrust Network Analysis. Actually, for the case of planar lines of thrust, the horizontal components of the reference thrusts can be computed in closed form at each iteration and for any arbitrary loading condition. The heights of the points of the thrust line are then computed by solving a constrained linear optimization problem by means of the Dual-Simplex algorithm. The MATLAB implementation of presented algorithm is described in detail and made freely available to interested users (https://bit.ly/3krlVxH). Two numerical examples regarding a pointed and a lowered circular arch are presented in order to show the performance of the method.

Shell-supported footbridges

Architects and engineers have been always attracted by concrete shell structures due to their high efficiency and plastic shapes. In this paper the possibility to use concrete shells to support footbridges is explored. Starting from Musmeci’s fundamental research and work in shell bridge design, the use of numerical form-finding methods is analysed. The form-finding of a shell-supported footbridge shaped following Musmeci’s work is first introduced. Coupling Musmeci’s and Nervi’s experiences, an easy construction method using a stay-in-place ferrocement formwork is proposed. Moreover, the advantage of inserting holes in the shell through topology optimization to remove less exploited concrete has been considered. Curved shell-supported footbridges have been also studied, and the possibility of supporting the deck with the shell top edge, that is along a single curve only, has been investigated. The form-finding of curved shell-supported footbridges has been performed using a Particle-Spring System and Thrust Network Analysis. Finally, the form-finding of curved shell-supported footbridges subjected to both vertical and horizontal forces (i.e. earthquake action) has been implemented.