Abstract
A numerical-computational model for static analysis of plane frames with semirigid connections and geometric nonlinear behavior is presented. The set of nonlinear equations governing the structural system is solved by the Potra–Pták method in an incremental procedure, with order of cubic convergence, combined with the linear arc-length path-following technique. The algorithm pseudo-code is presented, and the finite element corotational method is used for the discretization of the structures. The equilibrium paths with load and displacement limit points are obtained. The semirigidity is simulated by a linear connection element of null length, which considers the axial, tangential, and rotational stiffness. Nonlinear analyses of 2D frame structures are carried out with the free Scilab program. The results show that the Potra–Pták procedure can decrease the number of iterations and the computing time in comparison with the standard and modified Newton–Raphson iterative schemes. Also, the simulations show that the connection flexibility has a strong influence on the nonlinear behavior and stability of the structural systems.
Highlights
IntroductionStructural analysis/design methodologies undergo a paradigm shift, in which linear analyses (with adaptations for consideration of nonlinear effects) are being progressively replaced by analyses capable of encompassing various nonlinear effects, such as second-order, material inelasticity, rigidity of the connections, soil-structure interaction, dynamic effects, among others [1]
Structural analysis/design methodologies undergo a paradigm shift, in which linear analyses are being progressively replaced by analyses capable of encompassing various nonlinear effects, such as second-order, material inelasticity, rigidity of the connections, soil-structure interaction, dynamic effects, among others [1]
This paper aims to present a numerical-computational model for static analysis of plane frames considering the geometric nonlinearity and the semirigidity in the connections between structural members
Summary
Structural analysis/design methodologies undergo a paradigm shift, in which linear analyses (with adaptations for consideration of nonlinear effects) are being progressively replaced by analyses capable of encompassing various nonlinear effects, such as second-order, material inelasticity, rigidity of the connections, soil-structure interaction, dynamic effects, among others [1]. Connections between members of these structures can affect critical loading and postbuckling behavior [4]. In steel structure designs, the frames are analyzed with the simplification that the beam-column connection behavior can be idealized by two extreme cases: ideally flexible, where no moment is transmitted between the column and the beam and these elements behave independently, and perfectly rigid, in which the total transmission of the moment occurs [5]. Pinheiro and Silveira [8] discussed numerical and computational strategies for nonlinear analysis of frames with semirigid connections. Lignos and Krawinkler [10] discussed the development of a database of experimental data of steel components and the use of this database for quantification of important parameters that affect the cyclic
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