Finite-friction least-thickness self-standing domains of symmetric circular masonry arches. Part II: Milankovitch-like self-weight distribution

Abstract

The present paper constitutes a sort of compendium to a recent analysis considering the role of finite (Coulomb) friction in the mechanics of (symmetric circular) masonry arches, towards addressing least-thickness self-standing states and collapse modes possibly including sliding. Thereby, a classical Heyman-like uniform self-weight distribution along geometrical centreline was considered, and all characteristic features delivered, by a comprehensive analytical approach, corroborated by consistent outcomes from a self-made numerical Complementarity Problem/Mathematical Programming implementation. The same is now updated, for the real Milankovitch-like uniform self-weight distribution, considering the true positions of the centres of gravity of the ideal wedged-shaped chunks of the arch, with radial stereotomy. The main achieved result is that the specific conceived distribution does not alter, conceptually, the salient recorded characteristic features, in terms of types of self-standing/collapse states, though some differences are displayed, in the details of the final analytical-numerical findings, with few physical implications. However, the main implant, put to light from the previous, simpler to be mathematically handled, classical self-weight distribution, is confirmed, showing definite reference, in methodological terms, discovered features and first-order amount of technical results. In general sense, the present true Milankovitch-like self-weight distribution leads to more precise results, which support further bearing capacity for the real arch, thus anyway with conservative estimates arising from the previous approximate Heyman-like self-weight distribution, quite simpler in the underlying mechanical and mathematical treatment.