Determinação via critério dinâmico das cargas críticas em elementos de múltiplas camadas

Abstract

This paper proposes to analyze numerically the critical loads and the natural frequencies of multilayer beams and columns with partial interaction. The analytical solutions, however, are too complicated, and it is necessary to implement computationally numerical methods as an alternative solution, such as the finite element method. The main idea of this work is to analyze by dynamic criterion the critical loads of the multilayers elements, such as the composite steel-concrete beam, widely used in civil construction. The analysis is based on Euler beam theory, whose main hypothesis is the displacement of the structure in space keeping the sections flat and perpendicular to the axis without considering the effect of the shear stress. The dynamic analysis is characterized as an alternative and superior method to the static method, which manifests as a generalized eigenvalue problem between the tangent stiffness matrix and the elastic stiffness matrix. The dynamic method is, in turn, an eigenvalue problem between the mass matrix and tangent stiffness matrix. As the axial thrust load is forced into the structure, the fundamental frequency of the element decreases, ultimately causing the phenomenon of buckling. In the dynamic analysis it is possible to associate with each compression load an associated fundamental frequency, which does not occur with the static analysis. The present paper compared the results obtained with analytical solutions of 2 layers beams as a way of ascertaining the quality of the results to expand the analysis for cases of multilayer elements.