Looking at the collapse modes of circular and pointed masonry arches through the lens of Durand-Claye’s stability area method

Analytical and numerical analysis on the collapse modes of least-thickness circular masonry arches at decreasing friction

“…", as handled in the present case. These outcomes have also been confirmed by the recent analysis by Aita et al [23]. Despite, further, general analytical and numerical formulations shall investigate the subject, in inspecting if friction reduction effect may induce a resulting non-uniqueness in the prediction of the least-thickness condition, as instead still recorded in the present setting devoted to the analysis of symmetric masonry arches under self-weight, for more unspecific configurations and loading conditions.…”

“…Arches of a general half-angle of embrace 0 <  <  (including for undercomplete and over-complete, horseshoe circular masonry arches) have been systematically analysed in analytical terms. Different solutions have been explicitly derived, and numerically explored, which appeared fully consistent with updated outcomes from a re-discussion by Heyman [4], and prior developments by Ochsendorf [11][12], as well as with classical earlier work by Milankovitch [13] (see Foce [14]), and several most recent attempts that meanwhile have appeared [15][16][17][18][19][20][21][22][23][24]. An earlier account on these developments was provided in SAHC10 conference paper [5]; later, a comprehensive analytical treatment with unprecedented closed-form explicit representations was provided in [6], while in [8], consistent comparisons were developed by a Discrete Element Method implementation, in the form of a Discontinuous Deformation Analysis (DDA) tool.…”

“…Specifically, Fig. 7 first reports a main outcome of the derivation, as the limit curve in the (,  ) plane, in the sort of typical representation pointed out by Gilbert et al [25] and Sinopoli et al [26][27][28], and recently by Aita et al [23], there generalised to masonry arches of various typologies and shapes. On the hierarchy of the collapse modes at variable (decreasing) friction coefficient , it may be resumed that for  > rm the collapse mode in the least-thickness condition is purely-rotational (Fig.…”

The role of different sliding resistances in limit analysis of hemispherical masonry domes

“…The curve "Heyman's cracked model" [17] represents the classical solution of a dome already cracked along the meridians (zero hoop forces) but satisfying the meridional sliding constraint according to Eqn. (14). In fact, this model yields a constant value of the t/R ratio of 0.0425 if the friction coefficient  is greater than 0.25.…”

“…In the literature, 2D thrust-line, membrane, and 3D thrust-network [4,5], along with convex and concave contact models [3,6,7], have been developed within the limit analysis framework to find the ultimate load factor (or the minimum thickness) for the feasible models of masonry structures. Referring to basic geometries, 2D thrust-line and membrane were applied to find the limit equilibrium of semi-circular arches [8][9][10][11][12][13][14][15][16], hemispherical domes [17][18][19][20] and vaults of given geometries including skew arches, and pavilion, cross and groin vaults [21][22][23][24][25][26]. Finding the ultimate load factor, together with the stress state and failure mechanisms for models with basic geometries, is a classical problem also solved through other structural analysis methods such as Finite Element (FE) analysis, including detailed and simplified finite element micro models [27][28][29], and Discrete Element (DE) analysis [30][31][32].…”