(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.
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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