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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Data
2020-12-16
Autores
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Universidade Federal de Goiás
Resumo
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.
Descrição
Palavras-chave
Método das forças, Elementos finitos, Concreto protendido, Análise não linear, Forces method, Finite elements, Prestressed concrete, Nonlinear analysis
Citação
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.