Uma abordagem não linear ao estudo de modelos de deformação via elementos finitos para viga 2d de concreto protendido com cordoalha aderente

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Universidade Federal de Goiás


The purpose of this work is to develop the nonlinear analysis of prestressed beams and obtain their load/displacement curves, the formulation of a finite element of the bar type will be presented for non-linear physical and geometric analysis based on the method of forces. Geometric nonlinearity is considered using the Euler-Bernoulli beam strain theory, with simplification for moderate rotations. In physical non-linearity, non-linear stress / strain relationships provided by the models constituting the materials are allowed. The contribution to concrete in compression uses the model developed by Hognestad (1951), and when subjected to traction the model developed by Bergan and Holand (1973), for the steel of active reinforcement, the model developed by Menegotto and Pinto (1973) and for the passive reinforcement the bi-linear model with perfect elastoplastic behavior is considered. In the coupling between the constituent materials of the structure, perfect adherence between its elements is considered, that is, there is no relative movement between them. The problem is formulated through the balance of nodal forces. For this, the forces and moments are calculated as a function of the stress/strain relationship. To solve the equations, the finite element method is employed. The methodology presented here proposes to achieve the balance of forces directly at the nodal points of the structure using differential equations instead of integral equations. The concept of generalized forces and moments at nodal points is introduced. Finally, numerical simulations are used to compare the results obtained with experimental results. The novelty in the present work resides in the fact that the modeling is done through the coupling between three elements, namely: the displacement of the concrete, the prestressing strand and passive reinforcement. It is also observed that prestressing is responsible for applying axial and shear forces; while the passive reinforcement only contributes to axial displacement. The incorporation of axial displacements is necessary, since the prestressing force is considered to be external, causing, in addition to axial forces, moment reactions due to the eccentricity between the position of the strand and the neutral line of the structure. Using appropriates theory of strain to, concrete, prestressing and reinforcement steel the stiffness matrix is obtained.



Método das forças, Elementos finitos, Concreto protendido, Análise não linear, Forces method, Finite elements, Prestressed concrete, Nonlinear analysis


SILVA, W. R. Uma abordagem não linear ao estudo de modelos de deformação via elementos finitos para viga 2d de concreto protendido com cordoalha aderente. 2020. 133 f. Dissertação (Mestrado em Engenharia de Produção) - Universidade Federal de Goiás, Catalão, 2020.