Análise de matriz tangente de treliças planas: uma verificação da contribuição do componente [?K0]

Abstract

The primary role of Civil Engineering is to guarantee, through technique, solutions to real problems in civil construction, with results that enable the best proportion between safety, economy and efficiency. In this context, considering that in practice the models are not ideal, the structural analysis fits in the light of the simplified second order theory, considering the rheological linearity (respect for Hooke's law) and the geometric non-linearity of plane reticulated structures. This work focuses on the matrix analysis of plane trusses by the displacement method (MMD), evaluating the contribution or not of the stiffness correction term due to changes in nodal coordinates [ΔK_0] as a component of the matrix of tangent stiffness of the bars [k_t] and, consequently, of the structure [K_T]. To this end, literature and scientific articles were reviewed to support and exemplify the theory, and the reasoning was organized as follows: firstly, a theoretical review was developed about the method of displacements and its matrix formulation considering the structural analyzes of first and second order, presenting the deduction of the matrices that govern such systems for plane trusses and their efficiency in verifying structural stability; later, based on calculation examples, an evaluation was made of the possibility of disregarding the component [ΔK_0] in the calculation of the tangent matrix of plane trusses. Finally, the results and conclusions were presented.