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• 3D no-tension masonry-like structures are analysed using an energy-based approach. • The solving algorithm iteratively calls a finite element software for orthotropic solids. • A limited number of iterations is needed to solve the equilibrium for any compatible load. • Load paths are shown in cracked solids of general shapes, such as masonry vaults and domes. • The collapse load multiplier is computed with no a priori assumption on the mechanism. A new numerical procedure is presented to perform the analysis of three-dimensional linear elastic no-tension structures exploiting the application programming interface of a general purpose finite element analysis software. Masonry is replaced by an equivalent orthotropic material with spatially varying elastic properties and negligible stiffness in the case of cracking strain. A non-incremental algorithm is implemented to define the distribution of the equivalent material, minimizing the strain energy so as to achieve a compression-only state of stress for any given compatible load. Applications are shown for masonry-like solids of general shape visualizing load paths in walls subject to dead loads and out-of-plane live loads, circular domes under self-weight and a groin vault acted upon by both vertical and horizontal seismic loading. [ABSTRACT FROM AUTHOR]

The funicular analysis of curved masonry structures is addressed, considering the stereotomy of the voussoirs, a limited compressive strength, and a limited friction coefficient. The force density method is used to handle the equilibrium of the loaded nodes of the network, whose vertices lie along vertical lines passing through the centroids of the blocks. For the resulting grid with fixed plan projection, the minimization of the horizontal thrusts is formulated in terms of the height of the restrained nodes and of any set of independent force densities. Anti-funicular networks are sought by enforcing compression-only branches of the network. Local constraints are stated at each joint addressing the hypothesis of a limited compressive strength and a finite value of the friction coefficient between two adjacent voussoirs. To enforce no-tension blocks, lower and upper bounds for the vertical coordinates of the unrestrained vertices of the network are prescribed, as well. Sequential convex programming is used to solve the arising multi-constrained minimization problem. The algorithm, which can handle networks with general topology, is assessed by comparisons with results achieved with the Durand–Claye method, a semi-analytical method for the equilibrium analysis of symmetric masonry arches and domes that accounts for the limited compressive strength of masonry, the friction coefficient and the stereotomy of the voussoirs. Numerical examples concern arches, domes and a cloister vault, considering varying mechanical parameters. • Minimum thrust funicular networks are sought accounting for stereotomy aspects. • Joints with finite compressive strength and finite friction are dealt with in arches and vaults. • Statically admissible solutions are retrieved that are fully feasible with failure constraints. • An updated version of the stability area method is employed for algorithm validation. • Networks are remarkably sensitive to geometry and mechanical properties of the joints. [ABSTRACT FROM AUTHOR]

• Safety assessment of masonry domes. The solution method is based on the static theorem of limit analysis. • Domes are modelled as thin shells. Membrane forces and bending moments are suitably combined to find statically admissible internal forces. • The internal force distribution that maximizes the safety factor is searched by means of a constrained optimization method. The solution is pursued numerically by means of an expressly developed procedure that uses the collocation method. • The paper illustrates application of the method to the dome of Pisa cathedral. The present paper illustrates a methodology for the safety assessment of masonry domes. The dome is modelled as a thin shell made of a material satisfying Heyman's hypotheses. Based on the static theorem of limit analysis, the method searches for statically admissible distributions of internal forces within the shell, suitably combining membrane forces and bending moments, by solving a convex optimisation problem. The solution is pursued numerically by means of an expressly developed collocation method that enables obtaining the analytical expressions for each internal force component. In its present formulation the method can be applied to domes of any shape, as well as to arbitrary load distributions. After validation against the benchmark case of the spherical dome under its self-weight, the paper illustrates application of the method to the dome of Pisa Cathedral under vertical loads as a first real case study. [ABSTRACT FROM AUTHOR]

• Static and seismic behaviors of masonry domes with circular and octagonal drum and buttress. • Failure behaviours of masonry domes with circular and octagonal drum and buttress under strong earthquake shaking. • Failure angles of masonry domes with thickness-to-span ratios t/R = 0.092 under strong ground motions. General stability and failure behaviors of masonry domes under static loads have been investigated extensively in literature. However, a few studies have been done on the seismic failure behavior of masonry domes under strong ground shaking. This study aims to investigate the seismic failure behaviors and failure angles of masonry domes with support system including drum and buttresses using advanced 3D nonlinear numerical simulations. Four types of masonry domes with thickness-to-span ratios t/R = 0.092, such as a dome with circular drum (Dome A), a dome with circular drum and buttress (Dome B), a dome with dodecagon drum (Dome C), a dome with dodecagon drum and buttress (Dome D), built on historical structures are selected. Three-dimensional solid finite element models of the selected masonry domes are created using isotropic continuum macro modelling technique with homogenized properties. The finite element models are utilized to simulate the seismic behaviors of the masonry domes under three different strong ground motion acceleration records matched according to the target response spectrum with a return period of 475 years in the Turkish Building Earthquake Code. The seismic failure behaviors of four masonry dome models are evaluated by comparing mode shapes, displacements, maximum principal stresses, damage propagation patterns and failure angles. It is determined that the average angle intervals of hoop tension failure regions of Dome A, Dome B, Dome C and Dome D models under strong ground motions vary between 39, 25, 35 and 26 degrees, respectively. [ABSTRACT FROM AUTHOR]

We present a tensegrity approach to the strengthening of masonry vaults and domes performed by bonding grids of fiber reinforced composites to the masonry substrate. A topology optimization of such a reinforcement technique is formulated, on accounting for a tensegrity model of the reinforced structure; a minimal mass design strategy; different yield strengths of the masonry struts and tensile composite reinforcements; and multiple loading conditions. We show that the given optimization strategy can be profitably employed to rationally design fiber-reinforced composite material reinforcements of existing or new masonry vaults and domes, making use of the safe theorem of limit analysis. A wide collection of numerical examples dealing with real-life masonry domes and vaults highlight the technical potential of the proposed approach. [ABSTRACT FROM AUTHOR]

We employ a r -adaptive finite element model to search for a ‘safe’ thrust surface of a masonry dome, which minimizes the maximum tensile stress carried by the unreinforced portion of the material. A numerical procedure based on a Breeder Genetic Algorithm is employed to drive the movement of the nodes of a membrane model within a suitable design domain, which coincides with the region comprised in between the intrados and extrados of the dome in correspondence with the unreinforced portion of the structure. The presence of externally bonded Fiber Reinforced Polymer and/or Fabric Reinforced Cementitious Mortar reinforcements is accounted for by allowing the thrust surface to move outside the physical domain of the structure in correspondence with the reinforced regions. A benchmark example shows that the proposed procedure leads to detect if a masonry dome is safe or not, according to the master ‘safe’ theorem of the masonry vault theory. In addition it allows to optimally design reinforcement strategies that are aimed at preventing or mitigating crack damage, and increasing the load carrying capacity of the structure. [ABSTRACT FROM AUTHOR]

The research synthesized in this paper focused on ultimate strength, structural safety assessment, and collapse of masonry domes. Activity was directed at analyzing the relationships between safety factor and geometry, and carrying out research targeted at reducing the incidence and severity of structural failures in cultural buildings. This paper shows that the resisting system of a masonry dome is not the two-dimensional shell, but a one-dimensional mechanism that derives from the splitting of the shell and drum. The resisting system, whose geometry depends on the dome shape and brick or stone pattern, may include the lantern and/or the masonry constructions around the drum. Well-known domes taken from architectural cultural heritage are used to exemplify the pivotal role of geometry and construction techniques in providing ultimate strength. These examples also show the importance of considering the architectural design of the time, in structural analyses. The results found in the paper suggest how to provide masonry domes with adequate safety, using the minimal level of structural intervention; in particular, without altering the way the building reacts to applied loads. Hence, the paper helps understand how to reduce the amount of structural work, which, in turn, guarantees conservation and restoration, as well as safeguarding. The conclusions are devoted to analyzing which observations are valid for seismic assessment and how the other observations have to be modified for seismic actions. [ABSTRACT FROM AUTHOR]

Highlights: [•] Assessment of masonry domes through: Limit Analysis more readable than FEM models. [•] Dome and drum are a structural system. [•] Hoop ties increase safety of the dome, may be used as retrofitting tools. [•] Cracks in domes are unlikely to be related foundation settlement or material creep. [Copyright &y& Elsevier]

Abstract: This study establishes a semi-empirical relationship to estimate the reduction in the load carrying capacity due to damage by exploiting the experimentally detected deviations in the natural frequencies for a tile dome. Finite element model developed to analyze the dome is calibrated against both non-destructive vibration measurements and destructive load–displacement measurements up to failure. The model is then executed to simulate incremental development of cracks. The first natural frequency and remaining load carrying capacity of the dome are monitored to define the desired empirical relationship, which is ultimately generalized for spherical domes with varying span-to-height ratios. [Copyright &y& Elsevier]

• Behavior of masonry domes under seismic loads through a procedure of adaptive limit analysis. • Adaptive kinematic limit analysis based on NURBS and metaheuristic algorithm. • Analysis of different geometries and load configurations. • Collapse behavior of three meaningful case studies, one made by Roman concrete. • Comparison of PGAs and damage pattern obtained with adaptive limit analysis and FEs. The ultimate limit state behavior of masonry domes under axisymmetric gravity loads is nowadays well known and it has been proved how a generalization of the thrush line method used successfully for arches is quite effective also in this case. However, the behavior of a dome under horizontal loads, which is important in case of seismic action, becomes incredibly hard to tackle and still remains an open issue. The present paper aims at presenting a fast and reliable automatized kinematic limit analysis approach able to accurately predict the actual behavior of masonry domes subjected to horizontal static loads. The model uses a rough discretization of the dome obtained by means of few rigid-infinitely resistant NURBS generated elements, adapting step by step the initial mesh in order to progressively overlap the element edges (where all dissipation is lumped) with the hinges forming the failure mechanism. The adoption of a rough mesh makes the code extremely fast, much more competitive than a standard FE model, allowing at the same time to approximate the actual geometry and load distributions in an extremely accurate way. The utilization of geometries obtained with laser scanner acquisitions is straightforward and the presence of pre-existing cracks can be accounted for as well. Three complex case studies are analyzed in detail to benchmark the approach proposed, relying into existing domes belonging to the Italian cultural heritage. The first example has the geometrical parameters of a typical late Renaissance dome, the Cathedral of Montepulciano, the second is the dome of Anime Sante church (collapsed during the L'Aquila 2009 earthquake with a paradigmatic failure mechanism) and the last is the dome of Caracalla baths, whose causes of collapse remain still unknown. In all cases inspected, the approach proposed quickly provides collapse accelerations and active failure mechanisms at a fraction of the time needed by non-linear FE analyses, providing interesting hints into the actual behavior of such kind of structures under horizontal loads. [ABSTRACT FROM AUTHOR]