Automatic generation of statically admissible stress fields in masonry vaults

Chiara, E. De; Cennamo, Claudia; Gesualdo, Antonio; Montanino, Andrea; Olivieri, Carlo; Fortunato, Antonio

doi:10.2140/jomms.2019.14.719

Cited by 21 publications

(10 citation statements)

References 32 publications

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“…In MEA, the equilibrium of a vault is assessed through the search for a membrane surface, comprised inbetween the intrados and the extrados of a vault, capable to equilibriate the assigned load with a purely compressive membrane stress field [34,40,41].…”

Section: Membrane Equilibrium Analysismentioning

confidence: 99%

“…where the assumption of summation over repeated indices is implicit; moreover, a α is a curvilinear covariant basis vector, tangent to the membrane geometry, and T αβ is a contravariant component of the generalized stress. After some algebra, which is out of the scopes of this work, but is reported in [41,43], we reach the transversal equilibrium equation of the membrane…”

Section: Membrane Equilibrium Analysismentioning

confidence: 99%

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Graphical and Analytical Quantitative Comparison in the Domes Assessment: The Case of San Francesco di Paola

et al. 2021

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(1) Methods for checking the condition of monumental masonry structures can still be considered understudied. Among the different approaches available in the literature, the graphical ones have a special role, due to their simplicity and effectiveness. (2) In this work, a 2D method (Thrust Line Analysis (TLA)), the Modified Thrust Line Method (MTLM), and the 3D Membrane Equilibrium Analysis (MEA) method are compared. All methods have the same starting concept: no tensile strength, no sliding between the stone blocks, infinite compressive strength. (3) The methods are compared in terms of stress distribution (for the same—or similar—thrust line), and in terms of the Geometrical Safety Factor ensured. (4) The work shows that these theories, if properly conveyed in a scientific methodology (as many authors are doing currently and have done in the past) demonstrate the effectiveness and the advantages of graphical methods for simple structures.

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Section: Membrane Equilibrium Analysismentioning

confidence: 99%

Section: Membrane Equilibrium Analysismentioning

confidence: 99%

Graphical and Analytical Quantitative Comparison in the Domes Assessment: The Case of San Francesco di Paola

et al. 2021

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“…The search for admissible stress states in masonry structures has motivated several researchers to model internal forces in masonry structures as thrust lines (e.g., [9][10][11][12][13][14]), or as thrust surfaces (e.g., [15][16][17][18]) or thrust networks (e.g., [19][20][21]) to account for the full 3D mechanical responses of masonry vaults.…”

Section: Introductionmentioning

confidence: 99%

Parametric Stability Analysis of Groin Vaults

et al. 2021

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This paper presents a parametric stability study of groin, or cross vaults, a structural element widely used in old masonry construction, particularly in Gothic architecture. The vaults’ stability is measured using the geometric safety factor (GSF), computed by evaluating the structure’s minimum thickness through a thrust network analysis (TNA). This minimum thickness is obtained by formulating and solving a specific constrained nonlinear optimisation problem. The constraints of this optimisation enforce the limit analysis’s admissibility criteria, and the equilibrium is calculated using independent force densities on a fixed horizontal projection of the thrust network. The parametric description of the vault’s geometry is defined with respect to the radius of curvature of the vault and its springing angle. This detailed parametric study allows identifying optimal parameters which improve the vaults’ stability, and a comprehensive comparison of these results was performed with known results available for two-dimensional pointed arches. Moreover, an investigation of different force flows represented by different form diagrams was performed, providing a better understanding of the vaults’ structural behaviour, and possible collapse mechanisms were studied by observing the points where the thrust network touches the structural envelope in the limit states. Beyond evaluating the GSF, the groin vault’s stability domain was described to give additional insights into the structural robustness. Finally, this paper shows how advances in equilibrium methods can be useful to understand and assess masonry groin vaults.

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“…Three assumptions are at the base of his theory: (i) masonry has no tensile strength, (ii) stresses are so low that masonry has effectively an unlimited compressive strength and (iii) sliding failure does not occur. According to Heyman's work, the geometry assumes a crucial role in guaranteeing the equilibrium for masonry structures, and indeed his formulation provided the roots for thriving research (Varma and Ghosh 2016;De Chiara et al 2019;Iannuzzo et al 2019;Fraddosio et al 2020).…”

Section: Introductionmentioning

confidence: 99%

Graphical Modelling of Hoop Force Distribution for Equilibrium Analysis of Masonry Domes

2021

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The behaviour of axisymmetric masonry shells can be simulated by a system of forces constituted by meridian forces acting in the vertical planes, and by hoop forces acting circumferentially. A crucial component for the assessment of these structures using the Modified Thrust Line Method (MTLM) is the determination of hoop forces, whose computation is strenuous, limiting the practical application of MTLM. Working around this limitation, the current research introduces a strategy to manipulate the hoop forces by graphically implementing a function describing their distribution. The adaptiveness of this distribution function not only allows the application of MTLM for the analysis of a range of geometries, but also enables the simulation of membrane behaviour, arch behaviour and their combination, for considering partially cracked structures. Taking this into account, the approach is applied in the case studies illustrated within the current research.

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Automatic generation of statically admissible stress fields in masonry vaults

Cited by 21 publications

References 32 publications

Graphical and Analytical Quantitative Comparison in the Domes Assessment: The Case of San Francesco di Paola

Graphical and Analytical Quantitative Comparison in the Domes Assessment: The Case of San Francesco di Paola

Parametric Stability Analysis of Groin Vaults

Graphical Modelling of Hoop Force Distribution for Equilibrium Analysis of Masonry Domes

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