Avaliação de soluções ótimas de lajes nervuradas: análise por elementos finitos de grelha

Abstract

Waffle slabs are quite applied to housing, commercial and industrial buildings because their economy when compared to traditional solutions, such as reinforced concrete slabs for non-prestressed structures. However, an economy provided by reduction of concrete and possibly steel, is often badly endorsed by the misuse of the materials in their resistance limits. As an aggravating factor for this reality, a new project perspective was created, as a result of the ABNT NBR 15575 revision, as well as the ABNT NBR 6118, which imposed more attention on the performance of reinforced concrete structures in fire situations. In this way, the search for new structural solutions or the improvement of current systems is a pertinent reality. Changes in standard of performance implied in the design of ribbed slabs, mainly in minimum dimensions of cover, thickness and width of rib, making various dimensions of plastic forms impossible to apply. In this situation, the optimization of the waffle slab system is great interest, using as an objective function the cost production of the story of ribbed slabs. Several models of structural analyses are available for evaluation of slab stresses, like analytical and numerical analyses. Analytical methods are less representative of the reality design, however, they require little computational effort and, therefore, are widely used for optimizations problems. Nevertheless, optimization by analytical analyses could results in false optimum solutions, given by limitations on load, geometry and boundary. Thus, numerical methods, such as the Finite Element Method, could be used for validation of results from the optimization process. Therefore, it is studied how a more fidelity model of representation could affect optimum solutions obtained through simplified structural analyses. Samples of ribbed slabs ranging from 7 to 8 meters were optimized for both square and rectangular slabs by analytical e numerical methods. Results show that Finite Grid Analyses generate both larger displacements and stresses, mainly for square slabs, making increase of cost of the optimal solutions obtained through analytical method.