Considerations about the static response of masonry domes: a comparison between limit analysis and finite element method

Cusano, Concetta; Angjeliu, Grigor; Montanino, Andrea; Zuccaro, Giulio; Cennamo, Claudia

doi:10.1504/ijmri.2021.118835

Cited by 15 publications

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“…Structural analysis of masonry constructions can generally involve two alternative approaches: equilibrium-based methods and deformation-based methods. The complexity and appropriateness of each procedure is related to the peculiarity of masonry material, which exhibits an high strength under compression compared to its weak strength under tension, unilateral contact and friction, in-homogeneity, and anisotropy due to the presence of joints [33,34]. In order to illustrate the equations that will be used in Section 3.2 and the parameters that will be employed in the discussion of the results, in this Section the basic elements of the Linear Arch Static Analysis (LASA) are presented in some detail.…”

Section: Methodsmentioning

confidence: 99%

Masonry Spiral Stairs: A Comparison between Analytical and Numerical Approaches

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The present paper applies the Linear Arch Static Analysis (LASA), which models the masonry material as unilateral, i.e., No-Tension material in the sense of Heyman, and the Safe Theorem of the Limit Analysis to the study of masonry spiral stairs. A comparison is made with a refined FE analysis of the same problem, obtained by means of the ANSYS Parametric Design Language (APDL). The objective is to prove that LASA can be a valid alternative to other more complex numerical methods, such as FE, especially when the modeling parameters, such as the boundary conditions, cannot be exactly defined. The case study of a small spiral staircase placed in the tower of Nisida, a small island close to Naples, Italy is taken into consideration. The results show that the LASA analysis provides results that fall within two limit FE cases in terms of stress and overall thrust, providing at the same time a meaningful insight into the equilibrium state of the structure.

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Section: Methodsmentioning

confidence: 99%

Masonry Spiral Stairs: A Comparison between Analytical and Numerical Approaches

et al. 2022

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“…While a more sophisticated method for three-dimensional geometries has been developed, TLA has remained a first, straightforward starting point for the assessment of domes, and as such, it has been adopted to assess the domes of San Francesco di Paola [2,7] under statics and dynamic loads. It has recently been applied in [11] to study of the doubleshell dome of Santa Maria alla Sanitá and the single-shell dome of San Gregorio Armeno, in Naples.…”

Section: Previous Applications Of the Methodsmentioning

confidence: 99%

“…The advantage is that it can be applied to a large variety of vaults, disregarding the symmetries of geometries and loads, such as cloister vaults, cross vaults, and others. Some comparative studies between TLA and MEA were recently developed in [11].…”

Section: A Few Initial Remarksmentioning

confidence: 99%

“…Out of the authors' knowledge, there are few works comparing different methodologies applied to masonry structures. TLA and MEA have been used in [5] to assess the seismic vulnerability of San Francesco di Paola; in [11], some differences between TLA and MEA have been highlighted, and both methods are discussed together with the Finite Element Method, following the idea proposed in [12].…”

Section: Introductionmentioning

confidence: 99%

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

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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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“…MEA has been adopted mainly for the assessment of the equilibrium of masonry constructions [20][21][22][23][24], but it is a general tool for computing the stress field on curved membrane surfaces. For example, it has been used for the evaluation of the stress field of soft tissues, such as the human cornea [25].…”

Section: Introductionmentioning

confidence: 99%

From Stress to Shape: Equilibrium of Cloister and Cross Vaults

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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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Considerations about the static response of masonry domes: a comparison between limit analysis and finite element method

Cited by 15 publications

References 0 publications

Masonry Spiral Stairs: A Comparison between Analytical and Numerical Approaches

Masonry Spiral Stairs: A Comparison between Analytical and Numerical Approaches

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

From Stress to Shape: Equilibrium of Cloister and Cross Vaults

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