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©2012 Civil-Comp Ltd |
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A. Baratta and O. Corbi
Department of Structural Engineering, University of Naples "Federico II", Italy
Keywords: masonry structures, tensile strength, no-tension material, brittle material, complementary energy, fracture fields, stress fields.
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The actual behaviour of masonry arches and walls can be well reproduced and structural assessment is successfully achieved, using the no-tension (NT) model. This model allows data to be ignored, e.g. the tensile strength and modulus, and to yield safe results, thus improving the reliability of the final conclusions. However masonry often has a low tensile strength and is randomly variable in the body of the structure. It is also poorly durable and has a brittle character. In other words, it is an unreliable parameter, describing the evolutionary character of the material strength, in that after fractures have produced, i.e. after crossing the first threshold of the limit domain on the tensile side, the strength is lost, and thereafter locally the material cannot resist anymore. So, there are reasons to neglect tensile stress in masonry. Despite this conclusion, the presence of some resistance, and the admissibility of tension somewhere in the structure, can alter the picture of the fracture distribution, so that the model may fail in interpreting this behaviour.
In the paper a procedure is set up to establish a relationship between the NT solution and the elastic-brittle (EB) stress field, which may be associated with different fracture fields. Four different materials are compared. The first one is fully elastic, and the solution stress field obeys the unconditioned minimum principle of complementary energy. The second one is equipped with a low (adequate for masonry) tensile strength, but with a ductile character, so outlining a perfectly plastic material, with the relevant solution obeying the minimum principle of the energy conditioned to the admissibility of the stress field. The third material corresponds to the NT model, obeying the minimum principle of the energy conditioned to the absence of tensile stresses in the equilibrium fields, and the fourth material is the EB model, equipped with the same tensile strength as the elastic-plastic model.
It is proved that the values of the relevant complementary energies in the solution are ordered according to the following increasing list as regards to the different modelling of the material: 1) the indefinitely elastic material; 2) the elastic-plastic material; 3) the elastic-brittle material; and 4) elastic-NT material. In the above, the "elastic" quality is referred to as the behaviour in compression. After this result, it is possible to conclude that the EB solution cannot be so far from the NT one, assuming metrics in the sense of the elastic energy. So, the stress fields correspond to similar values of the energy, and in this sense stress and fracture fields approximate each other in both cases.
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