Resumen de Análisis no lineal de placas de hormigón postesado
An unprecedented calculation model for slabs of post-tensioned concrete is proposed, based on the general theory of thin plate analysis, using the finite element method, taking into account the degradation of the most critical sections of the slabs, which are usually located on their supports. The main objective of the model is to review the amount of passive reinforcement required in the construction of the post-tensioned slabs in the abacus areas (on the supports), with the primary idea being that of identifying economic savings.
Although the problem of thin slabs is at the root of the matter, the shell or membrane problem posed by the effect of the post- casting treatment is considered at the same time, especially when studying the degradation of the critical or most critical sections. The consideration of the said degradation of the sections results in the loss of proportionality in the relation between action and response or, in other words, in the nonlinearity of the problem. The nonlinearity of a post-cast slab, when a higher stress level is accepted than a conventional calculation, presents very particular characteristics, which are studied and presented in the proposed thesis. These characteristics condition the way the slabs can be analysed, when a more precise answer is sought.
The proposed model starts from a very extensive iterative calculation procedure in the nonlinear analysis of structural problems of diverse nature that, adapted properly, allows the specific study of the post-tensioned slabs including the particular effects of degradation of its sections. The approach involves, therefore, a detailed study of the evolution of the behavior of the sections of post-tensioned concrete, from the beginning of its service until its rupture.
Once the proposed procedures have been validated, through the corresponding problems of contrast and due analysis, we proceed to the study of three problems representative of the situations that are most commonly solved by post-tensioned slabs in buildings. The study of these cases develops in a very detailed way, controlling both the evolution of their deformations and the evolution of all the types of tensions that a laminar structure presents, as it is, in the end, a post-tensioned slab.
With the support of this model, it is demonstrated, preliminarily and in an exclusively analytical way, that it seems possible to project or revise the post-tensioned slabs by substantially moderating the amount of steel required in the most affected regions of the problem, without identifying major problems, although it is certain that other aspects must be studied in later work in order to extend the concepts proposed in the thesis to daily professional practice. In the final part of the paper, the solutions obtained in the case studies considered as representative are compared with those that would be obtained in a calculation or normal professional procedure, clearly showing that the savings in the amount of passive reinforcement to be used on the supports can easily be between 35% and 50%.
The methodology followed could be extremely useful in the revision of buildings already built, for example, because of the need for an increase in load due to change of use, or for whatever reason. In these cases, the complexity and cost of a nonlinear calculation, such as the one proposed, is well below the cost of any reinforcement of the building in question, at least if it is finished and in full use.
