Scan-to-BIM Process Versus 3D Procedural Modelling of Gothic Masonry Vaults

From Stress to Shape: Equilibrium of Cloister and Cross Vaults

Applied Sciences ◽

10.3390/app11093846 ◽

2021 ◽

Vol 11 (9) ◽

pp. 3846

Author(s):

Andrea Montanino ◽

Carlo Olivieri ◽

Giulio Zuccaro ◽

Maurizio Angelillo

Keyword(s):

Error Function ◽

Membrane Surface ◽

Equilibrium Analysis ◽

Test Cases ◽

Order Partial Differential Equation ◽

Negative Semidefinite ◽

Historical Heritage ◽

Masonry Vaults ◽

Membrane Shape ◽

The Given

The assessment of the equilibrium and the safety of masonry vaults is of high relevance for the conservation and restoration of historical heritage. In the literature many approaches have been proposed for this tasks, starting from the 17th century. In this work we focus on the Membrane Equilibrium Analysis, developed under the Heyman’s theory of Limit Analysis. Within this theory, the equilibrium of a vault is assessed if it is possible to find at least one membrane surface, between the volume of the vaults, being in equilibrium under the given loads through a purely compressive stress field. The equilibrium of membranes is described by a second order partial differential equation, which is definitely elliptic only when a negative semidefinite stress is assigned, and the shape is the unknown of the problem. The proposed algorithm aims at finding membrane shapes, entirely comprised between the geometry of the vault, in equilibrium with admissible stress fields, through the minimization of an error function with respect to shape parameters of the stress potential, and then, with respect to the boundary values of the membrane shape. The application to two test cases shows the viability of this tool for the assessment of the equilibrium of existing masonry vaults.

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Experimental Behavior of Masonry Vaults Strengthened with Thin Extradoxal or Intradoxal Layer of Fiber Reinforced Lime Mortar

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.747.274 ◽

2017 ◽

Vol 747 ◽

pp. 274-281 ◽

Cited By ~ 1

Author(s):

Natalino Gattesco ◽

Ingrid Boem ◽

Alessandra Gubana ◽

Davide Menegon ◽

Norman Bello ◽

...

Keyword(s):

Thin Layer ◽

Experimental Tests ◽

Horizontal Load ◽

Actual Behavior ◽

Cyclic Tests ◽

Lime Mortar ◽

Numerical Investigations ◽

The Third ◽

Loading Patterns ◽

Masonry Vaults

The results of a first experimental research program on masonry vaults strengthened by means of GFRP meshes embedded in a thin layer of lime mortar, are herein presented. The tests were designed to reproduce the pattern of a transversal horizontal load proportional to the vault self-weight. The typical simplified loading patterns generally used for the experimental tests concern concentrated vertical loads at the crown section or at 1/4 of the span, but some numerical investigations evidenced that these configurations are not able to reproduce the actual behavior and the effectiveness of the reinforcement. So a specific rig was designed to apply the horizontal load pattern.Solid brick masonry barrel vaults were considered (thickness 120 mm, arch span 4000 mm, arch rise/radius = 0.75). Three quasi-static cyclic tests were performed: the first concerned an unreinforced vault, the second a vault reinforced at the extrados through the application of a mortar coating reinforced with a GFRP mesh and the third reinforced at the intrados surface with the same technique. The experimental results demonstrated the technique effectiveness and the important increment of ductility of the vaults.

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