Barrel vault

Abstract: This paper describes a new technique for the limit state analysis of arcuate masonry vaults. The technique involves modelling the principal stresses in a masonry vault as a discrete network of forces. This network of forces is constrained to lie within the masonry vault and be in equilibrium with the loads applied to the vault. Optimization techniques are used to select the optimum forces within the network and the optimum network shape. The network model can be optimized to calculate either the geometric factor of safety for a set of known loads, or the collapse load factor for a given pattern of imposed loading. The application of the force network model is demonstrated by applying it to calculate the collapse load factor of a masonry barrel vault carrying a single imposed point load.

Abstract: Coated woven fabrics have been used in state-of-the-art structures for over 40 years yet their design is not codified and relies heavily on experience and precedent. The mechanical behaviour of fabrics is non-linear and time dependent, with assumed or highly simplified material properties commonly used for analysis. The shape of a tensile fabric canopy is fundamental to its ability to resist all applied loads in tension. Increasingly Architects are moving away from conventional fabric forms, utilising lower levels of curvature and new materials. This paper considers the importance of material properties and structural geometry in the design and analysis of tensile fabric structures. Three typical tensile forms are examined: the conic, hyperbolic paraboloid (‘hypar’) and barrel vault. Whilst the barrel vault demonstrates the expected result that minimally curved structures are inefficient and highly sensitive to changes in materials properties, the hypar exhibits more complex behaviour with the structural action varying dramatically with changes in geometry, material properties and patterning (fabrication) direction. For conic structures the feasible geometries that can be attained using ‘soap film’ form-finding is established, which combined with checks for ponding provide a range of geometric parameters for the efficient design of conic structures.

Abstract: Grid shells exhibit different modes of stability failure. This paper explains some parameters influencing the failure load of domes and barrel vaults and makes suggestions for the imperfection shape which has to be assumed in an analysis. All computations are carried out with a commercial FE-program.

Abstract: Some different procedures for the evaluation of the non-linear behavior of masonry arch bridges are here proposed. In particular, the Venice trans-lagoon masonry arch bridge is numerically analyzed by means of several 3D FE numerical strategies. The three dimensional behavior of the structure when subjected to train loads and pile foundation settlement is investigated. Focus is also posed to the stabilizing role played by the backfill. Both a non-commercial code and a standard commercial FE software are utilized. The non-commercial code properly takes into account for the orthotropic behavior of the barrel vaults and the stone arches, and allows performing non-linear static and limit analyses on complex 3D structures. Within the non-commercial FE approach, each material of the bridge (barrel vault, external stone arches, spandrels, piers, backfill) is suitably modeled using rigid parallelepiped elements and quadrilateral interfaces exhibiting an orthotropic constitutive law with either softening or rigid-plastic behavior in the non-linear and limit analysis version respectively. In both FE codes, mechanical properties of each material of the bridge (barrel vault, external stone arches, spandrels, piers, backfill) are modeled starting from suitable homogenization procedures in the elastic range (commercial software) and also beyond the linear limit (non-commercial FEM). The bridge is studied under service loads and up to failure for the passage of a standard train on either a single or both tracks. In the analyses, the stabilizing role played by the backfill, the strength increase obtained with stiff lateral stone arches on the barrel vault and the 3D effects induced by both load configurations are discussed. Results obtained with the incremental non-linear procedures are always compared with limit analysis predictions of collapse loads and failure mechanisms. Finally a uniform foundation settlement of one of the piles is simulated.

Abstract: Composite materials made with textile fibers both with polymeric and cementitious matrices are often adopted for the retrofitting of masonry arches and vaults. A specific project that analyzes the performance of ancient masonry arches and vaults strengthened with composite systems has been recently concluded at Politecnico of Milan. The project involves the experimental evaluation and the development of numerical and analytical simulations. In this paper the experimental campaign is described, whereas the numerical validation is provided in an accompanying paper (Bertolesi et al., 2017). The tests were performed in situ on ancient masonry arches and vault elements. In particular, three barrel vaults and two arches either unreinforced or reinforced with Steel Reinforced Grout (SRG), Textile Reinforced Mortar (TRM) and Fiber Reinforced Polymer (FRP) were tested. The arches had a span equal to 3.30 m, a rise equal to 0.83 m and were built with common Italian bricks regularly spacing out two bricks laid edge on (thickness of the arch 12 cm) with two bricks (one over the other) disposed in single leaf. Barrel vaults had the same geometry of the arches but were made with a single leaf. In all cases, an eccentric vertical load was applied at 1/4 of the span and was increased up to failure. The experimental results on unreinforced structures are compared with those obtained on the strengthened ones in terms of failure mode, maximum load, stiffness and ductility.