Abstract
In the present paper, the ultimate load of the reinforced concrete slabs [16] is determined using the finite element method and mathematical programming. The acting efforts and displacements in the slab are obtained by a perfect elasto-plastic analysis developed by finite element method. In the perfect elasto-plastic analysis the Newton-Raphson method [20] is used to solve the equilibrium equations at the global level of the structure. The relations of the plasticity theory [18] are resolved at local level. The return mapping problem in the perfect elasto-plastic analysis is formulated as a problem of mathematical programming [12]. The Feasible Arch Interior Points Algorithm proposed by Herskovits [8] is used as a return mapping algorithm in the perfect elasto-plastic analysis. The proposed algorithm uses Newton's method for solving nonlinear equations obtained from the Karush-Kuhn-Tucker conditions [11] of the mathematical programming problem. At the end of this paper, it is analyzed six reinforced concrete slabs and the results are compared with available ones in literature.
Highlights
Reinforced concrete slabs [16] are among the most common structural elements
In this paper will be presented: the strength criterion proposed by Johansen, the elastoplastic analysis of plates using finite element method and mathematical programming, the Feasible Arc Interior Point Algorithm and six examples of reinforced concrete slabs whose results are compared with results available in literature
In all the examples presented in this paper the stress distribution in the ultimate configuration determined using the perfect elasto-plastic analysis is according to the collapse mechanism predicted by the yield line theory
Summary
Reinforced concrete slabs [16] are among the most common structural elements. Despite of the large number of slabs designed and built, the details of their elastic and plastic behavior are not fully appreciated or properly taken into account. The acting efforts and displacements in the slab are obtained by a perfect elasto-plastic analysis developed by finite element method. A.M. Mont’Alverne et al / Determination of the reinforced concrete slabs ultimate load using FEM and programming 71 ming problems [12] with nonlinear objective function and nonlinear constraints quickly and efficiently. The Feasible Arc Interior Point Algorithm is a new technique for nonlinear inequality and equality constrained optimization and was first developed by Herskovits [8]. In this paper will be presented: the strength criterion proposed by Johansen, the elastoplastic analysis of plates using finite element method and mathematical programming, the Feasible Arc Interior Point Algorithm and six examples of reinforced concrete slabs whose results are compared with results available in literature
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