Resistance of flat vaults taking their stereotomy into account

Fantin, Mathias; Ciblac, Thierry; Brocato, Maurizio

doi:10.2140/jomms.2018.13.657

Cited by 9 publications

(3 citation statements)

References 27 publications

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“…Unlike the previously mentioned contributions, the numerical method presented here stands out for its ability to rigorously account for the limited compressive strength of masonry and the stereotomy of the voussoirs. In contrast to the advancements in this area proposed by [24,25], the current approach tackles this challenge through mathematical programming, enabling the management of networks with various topologies, building upon the procedure introduced by [14]. A comprehensive description of this funicular method is available in [3], with a specific emphasis on identifying the funicular networks corresponding to the minimum thrust and exploring a range of statically admissible solutions.…”

Section: Collapse Behavior: Funicular Versus Stability Area Methodsmentioning

confidence: 99%

Limit analysis of masonry arches and domes with finite strength: funicular analysis versus stability area method

Aita,

Bruggi,

Taliercio

2024

Meccanica

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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.

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Section: Collapse Behavior: Funicular Versus Stability Area Methodsmentioning

confidence: 99%

Limit analysis of masonry arches and domes with finite strength: funicular analysis versus stability area method

Aita,

Bruggi,

Taliercio

2024

Meccanica

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“…Dans le logiciel RhinoVault (Rippmann, Lachauer, & Block, 2012) la dualité est mobilisée pour interagir à la fois sur les réseaux de forces et sur les polygones des forces pendant la conception de voutes. La prise en compte de l'évaluation des critères de résistance aux joints des maçonneries et la visualisation des lignes de pression a donné lieu à des développements spécifiques de la méthode des réseaux de forces en 2D par (Ciblac & Morel, 2014) et en 3D (Fantin & Ciblac, 2016) (Fantin, Ciblac, & Brocato, 2018). Ces développements visent à permettre une analyse à la rupture d'édifices patrimoniaux et à une étude plus fine pendant la conception de maçonneries.…”

Section: Maçonneriesunclassified

Les théories de la statique graphique revisitées par les approches numériques. De l’évaluation structurale paramétrique à la morphogénèse

Ciblac

2020

SHS Web Conf.

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Au-delà de son caractère calculatoire qui l’a initialement popularisée, la statique graphique présente des potentialités diverses pouvant être valorisées par l’usage de l’informatique, dans les domaines de la pédagogie et de la conception de structures. L’objectif de cet article est de montrer comment la statique graphique est ou pourrait être revisitée par des transpositions numériques, dont certaines sont proposées par l’auteur. Dans une première partie, nous présentons les théories de la statique graphique des plus classiques aux moins utilisées que des transpositions numériques peuvent mobiliser. La deuxième partie vise à caractériser les objectifs des transpositions numériques effectives ou potentielles et leurs apports spécifiques.

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“…Conversely, in [12] sliding is allowed, and the minimum thickness analysis of circular and elliptical masonry arches is conducted by re-interpreting the effect of finite friction as a geometric constraint on stereotomy. Finally, the research reported in [13,14] aims at refining the three-dimensional thrust network analysis by considering not only the equilibrium conditions at the nodes, but also strength criteria at the joints that take friction into account. From the studies quoted above, the effect of stereotomy on the stability of arches turns out to be significant when friction is assumed to be finite, and mixed or sliding collapse modes can occur.…”

Section: Introductionmentioning

confidence: 99%

Funicular analysis of symmetric arches with finite friction accounting for stereotomy

Aita,

Bruggi,

Taliercio

Proceedings of the Seventeenth International Conference On Civil, Structural and Environmental Engineering Computing

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In this contribution the funicular analysis of symmetric masonry arches is performed by accounting for stereotomy, as well as for the presence of Coulomb's friction at the interfaces between the voussoirs. The classical thrust network analysis approach is then enhanced by removing the hypothesis that the friction coefficient is infinite. The procedure presented here handles networks with any topology, fixed plane projection and loads applied at the nodes, whose equilibrium conditions are managed by exploiting the force density method. At each joint, a set of local constraints is enforced to restrain the shear-to-normal component ratio of the force between two adjacent voussoirs. The minimization/maximization of the horizontal thrusts, formulated in terms of applicate of the restrained nodes, is achieved by solving the corresponding multi-constrained minimization/maximization problem through sequential convex programming. The results obtained via this funicular method are validated by means of a graphical procedure based on the lower bound theorem of limit analysis, known as Durand-Claye method, by considering a masonry arch with nonconventional stereotomy.

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Resistance of flat vaults taking their stereotomy into account

Cited by 9 publications

References 27 publications

Limit analysis of masonry arches and domes with finite strength: funicular analysis versus stability area method

Limit analysis of masonry arches and domes with finite strength: funicular analysis versus stability area method

Les théories de la statique graphique revisitées par les approches numériques. De l’évaluation structurale paramétrique à la morphogénèse

Funicular analysis of symmetric arches with finite friction accounting for stereotomy

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