Sul comportamento fino a collasso di elementi strutturali ad arco con limitata resistenza a trazione: analisi numeriche e confronti teorico-sperimentali

The aim of this paper is to study the behaviour of no-tensile material arches and vaults (plane concrete, masonry) in the elastic-plastic domain and up to failure. The basic assumptions of the classic limit analysis are briefly reviewed. As it is well known, limit analysis gives only information concerning the ultimate load bearing capacity of the structure, but cannot describe the stress evolution. Two finite element models have been developed, suitable to the description of the behaviour of continuous or voussoir beams and arches: the former is a two noded “contact” element; the latter is a plane, isoparametric, six-noded “beam” element. The “contact” element, modeling joint sections, is advantageous in block structures, in which the joints are preferential failure sections; the model allows to concentrate the plastic deformations in the joints and to consider blocks as indefinitely elastic. The six-noded element is particularly fit to the study of continuous beams and arches. The elastic matrix is formulated so as to take into account the basic assumptions of De Saint Venant theory. For structures having preferential failure sections, the first model is particularly appropriate. but. the second model becomes advantageous when it is necessary to verify the yield condition in terms of local "stress" variables. The results obtained by means of the numerical analysis up to failure of two structures are shown. The former is a voussoir arch, whose joints are modeled by means of “contact" elements; the latter is a masonry vault, reinforced with a plane concrete shell, discretized with six-noded elements. The experimental results for both structures are compared with the numerical results obtained by the authors. The voussoir arch exhibits discrepancies between numerical and experimental results: this fact is critically discussed and partially justified. The authors stress that the joint compressive strength should not be taken as unlimited (as commonly assumed in limit analysis of block structures), because this assumption often leads to unsafe results. The agreement between the numerical and the experimental results for the reinforced vault is very satisfactory. The use of isoparametric, six-noded elements, and of a nonlinear computer program, solving the elastic-plastic incremental problem by means of an algorithm of Mathematical Programming, enables the authors to obtain (at a lower computational cost) more accurate results than those of the original research program.