Self-standing Bearing Capacity of Symmetric Circular Masonry Arches at Finite Friction

The present research investigation concerns the issue of finite friction, in ruling self-standing bearing capacity and collapse modes of (symmetric circular) continuous masonry arches, with ideal inherent radial stereotomy. With primary reference, and as an enhancement, to classical “Couplet-Heyman problem” of least-thickness form optimization, in the realm of purely-rotational collapse solutions, finite (Coulomb) friction is herein set, among the theoretical joints of the arch, and systematically explored, in implying possible manifestations of sliding failure. The configuration of uniform self-weight distribution is considered, for both Heyman-like distribution along geometrical centreline and true Milankovitch-like distribution accounting for the real centres of gravity of the ideal wedge-shaped chunks of the circular arch. The governing mechanical equations are outlined, and resolved, by a full analytical approach, by deriving all physical domains and collapse states of the masonry arch. Diverse key aspects are newly outlined, as for instance per: the complete representation maps of all characteristic solution variables as a function of geometrical and friction parameters; the peculiar extremal conditions for intrinsic non-dimensional horizontal thrust and inner failure joint angular positions; the kinematical multiplicity of the collapse modes at the interfaces of the various failure domains. Analytical outcomes are eventually validated, and widely illustrated, by a separate dedicated Complementarity Problem/Mathematical Programming formulation, and consistent numerical self-implementation, by fully conformal results. The analytical-numerical achievements shall allow for a full understanding of the problem at hand, in the Mechanics (statics) of masonry arches, and specific related role of finite friction, in providing crucial self-bearing structural capacity.