Análise estrutural de placas retangulares submetidas a carregamentos estáticos trapezoidais

Abstract

One of the fundamental steps in structural design is the internal force analysis and initial displacements of a given element when it is subject to an external loading. In the case of surface structural elements, this analysis becomes more complex due to the two-dimensional effect on bending forces, requiring the use of methods that describe the structure behavior in a simplified manner. One of the methods commonly used in plates is the static plate analysis according to Kirchoff's theory for thin plates, where, by solving the differential plate equation (also called the Sophie-Germain-Lagrange equation), tables are generated for the calculations of internal forces and deflections. One of the crucial parameters of differential stress and transverse displacement equations is the Poisson's ratio, which is commonly set at a value of 0.20 for concrete slabs. This study presents an analysis of the influence of Poisson’s ratio variation on internal forces and deflection of simply supported plates, subjected to linearly distributed loads (trapezoidal shape). For this, from the resolution of the Sophie-Germain-Lagrange differential equation by the Navier method, calculation tables were generated for constant and triangular loads, with the Poisson’s ratio ranging from 0.00 to 0.40. These tables were validated by comparative analysis of the results with established bibliographies and the ANSYS Student 2019 R1 software, obtaining percentage differences of up to 3.19% and 7.12% for constant and triangular loading, respectively. From the results, it was verified that the increase in Poisson’s ratio values resulted in larger bending moments and in the reduction of torsional moments and shear forces.