Singular stress fields in masonry structures: Derand was right

Abstract

The idea of a no-tension (NT) material underlies the design of masonry structures since antiquity. Based on the NT model, the safety of the structure is a problem of geometry rather than of strength materials, in the same spirit of the “rules of proportion” of the medieval building tradition. The use of singular stress fields for equilibrium problems of NT materials in 2d, has been recently proposed by Lucchesi et al. to produce statically admissible stress fields; here we introduce a simple way to construct singular stresses, based on the Airy’s stress formulation. We interpret the singular part of such stress fields as axial contact forces acting on ideal 1d structures arising inside the body, in the same spirit of Strut and Tie methods. A number of simple problems of equilibrium concerning typical walls, arches and portals, is solved in terms of stress fields having regular and singular parts, by adopting the direct and the stress function formulation. The validity of the rules of proportion described by Derand and Gil is also verified

Static Analysis of Cross Vaults: The Case of the Cathedral of Casertavecchia

“…Indeed the more efficient tool that can be introduced for applying the unilateral No-Tension model to masonry structures is the systematic use of singular stress and strain fields, within the framework defined by the two theorems of Limit Analysis (see Angelillo et al [21] for applications of the safe theorem and Fortunato et al [27] for applications of the kinematic theorem to walls).…”

“…The concept of compatible loads and distortions, and the validity of the two theorems of Limit Analysis, admitting singular stresses and discontinuous displacements, are discussed in Angelillo et al [21,26,27]. The use of singular equilibrated stresses for approximating plane equilibrium problems can be traced to the work of Fraternali et al [28], and for vaults to the more recent paper by Block & Ochsendorf [29].…”

Closed form solution for predicting the horizontal capacity of masonry portal frames through limit analysis and comparison with experimental test results

“…In this contest, in 1993 Angelillo [34], used the no-tension material model for studying URM walls via FEM according to the Heyman's assumptions; recently Angelillo [35] have introduced a simple way to construct singular stresses, based on the Airy's stress formulation, and have solved, in terms of stress fields, a number of simple problems of equilibrium concerning typical walls, arches and portals.…”

“…have been calculated using the closed form equations (21)-(24),(34) and(35), by varying the area of the steel ties A t from 50mm 2 to 400mm 2 .Two different portal frames with the same thickness (s=0.5m) and global aspect ratio (=H/D=1) have been examined; the first one is a slender portal, characterized by pier slenderness =B/D=0.3 and spandrel slenderness =t/H=0.4; the second one is a stocky portal, characterized by pier slenderness =B/D=0.4 and by spandrel slenderness =t/H=0.5.The portal frames are made of tuff19 masonry material (f v0 =0.026MPa; f m =1.5MPa; =16KN/m 3 ) and no external gravity loads have been applied (=0).Steel grade S235 (f y =235MPa)has been adopted for the tie rods.The results of the parametric analysis have been summarized in the diagrams of Figures 13, where the load multiplier () calculated for each strengthening scheme is depicted as a function of tie area (A t ). The curves refer to the Case 0 of un-strengthened portal frame (i.e.…”

Advanced Models for the Limit Analysis of Masonry Structures

“…The analysis of masonry-like materials can be conducted within the frame of limit analysis, specifically by applying the static and kinematic theorems on the basis of admissible stress and strain fields (see [18]). The first tool that can be introduced for applying the unilateral No-Tension model to masonry structures is the systematic use of singular stress and strain fields, within the framework defined by the two theorems of Limit Analysis [19,20]. The use of singular equilibrated stresses for approximating plane equilibrium problems can be traced in [17,[21][22][23].…”