Desenvolvimento de uma ferramenta computacional para determinação de propriedades geométricas e cálculo de tensões normais na flexão geral

Abstract

The aim of this work was to develop a computational tool that allows the automated calculation of the geometric properties of generic symmetrical and asymmetrical cross-sections of one or more materials and the application of normal stress calculations in general bending. To this end, a study of the formulations related to the calculation of the geometric properties of plane crosssections and normal stresses in general bending for one or more materials was carried out, followed by a bibliographic survey of articles, books, theses, and dissertations for foundational analysis. Subsequently, formulas for the geometric properties were deduced through the resolution of contour integrals of the area based on Green's Theorem, so that the automated calculation of these properties is possible. Furthermore, based on the bibliographic review, the calculation of normal stresses was directly applied to the general bending formulas. Thus, the entire calculation routine was organized into algorithms for computational implementation in Fortran. Therefore, data analysis and results were performed using spreadsheets, as well as free post-processing software. Initially, after the computational implementation for polygonal crosssections of a single material, several tests were conducted with examples of problems from the literature focused on geometric properties to ensure the correct functioning of the program and its validation. However, finally, the computational program encompassed not only polygonal cross-sections but also circular and partial circular cross-sections, both with one or more materials, in addition to the calculation of normal stresses in general bending. Therefore, examples were performed to demonstrate the applicability of the program, which will be developed for more general cross-sectional situations with loads. Finally, it was concluded that the results obtained were satisfactory, with no relevant differences observed in the results when compared to the literature.