2019-04-032019-04-032016-12SILVA, William Taylor Matias; GUTIÉRREZ, María Paz Duque; SILVA, Wellington Andrade da. Uma abordagem analítica para detecção de pontos limites e de bifurcação. Revista Eletrônica de Engenharia Civil, Goiânia, v. 12, n. 3, 2015/16. Disponível em: <https://www.revistas.ufg.br/reec/article/view/39506/pdf>.http://repositorio.bc.ufg.br/handle/ri/17358Using an analytical this paper describes in detail the detection and classification of critical points in the primary equilibrium path of structural systems. The Total Lagrangian formulation is employed to describe the kinematics of a 2D bar element. With this formulation, the internal force vector and the tangent stiffness matrix including the geometric nonlinearity effects are obtained. An elastic linear constitutive model is assumed for the uniaxial stress-strain state. Such model uses the Green-Lagrange strain tensor and the second Piola-Kirchhoff axial stress tensor which are energetically conjugate tensors. As a study case, the article presents a statically inderminate plane truss discretized with three 2D bar elements. Finally, the geometrical and physical conditions for the coalescence between limit and bifurcation points are determined. The main contribution of this work is to demonstrate the need to better understanding the non linear phenomena. Such understanding is necessary for designing safer structural systems.porAcesso AbertoDescrição lagrangiana totalAnálise não linear geométricaPontos de bifurcaçãoPontos limiteElementos de treliça planaTotal lagrangian formulationGeometrical nonlineartyBifurcation pointsLimit pointsPlane truss elementArtigo10.5216/reec.v12i3.39506