Engenharia de petroleo

RCTVM

Novembro | 2010

VETOR CENTRO DE GRAVIDADE: UMA APLICAÇÃO DA ÁLGEBRA LINEAR NA ENGENHARIA CIVIL Dias, Magno B.1; Gouvea Junior, Hilton2; Louro, Jacqueson T.3; Silva, José R4, Subtil, Geraldo R. 5 Faculdade Presidente Antônio Carlos de Teófilo Otoni Departamento de Engenharia Civil [e-mail], [e-mail], [e-mail], [e-mail], [e-mail] Abstract. The objective of this study is to use the knowledge on linear algebra to determine the gravity center of a flat and polygonal structure. Therefore, a problem solver based on a physical model will be used in order to redraw, in terms, a linear algebra problem with its applications in vectors and matrices multiplications. In order to test the results, a model whose base is shaped like an equilateral triangle and which has three wooden lathes, will be built. The weights of these objects follow the same proportion as the weights of the proposed problem: 1:2:3:4. The gravity center, in this experiment, is obtained by result between the matrices of the weights and the matrices of the individual gravity centers. In conclusion, these results shall be compared to an experimental measurement, whose values are compatible to what had been theoretically thought of. This study is justified by the necessity of making the knowledge on linear algebra more meaningful, joining the theoretical nature of this subject with the practical dimension required in civil engineering.

Resumo. O Objetivo deste estudo é utilizar os conhecimentos de álgebra linear para a determinação do centro de gravidade de uma estrutura plana poligonal. Para tanto, utiliza-se um modelo físico de solução do problema e o reelabora em termos de um problema de Álgebra Linear com aplicações em vetores e multiplicação de matrizes. Para testar os resultados, confecciona-se uma maquete contendo uma base na forma de um triângulo equilátero e três tornos de madeira. Os pesos destes