Determination of the efforts in two-way slabs of concrete through the finite difference method

Palabras clave: Concrete, Elastic method, Finite differences method, Two-way slabs

Resumen

From the implementation of analytical solutions for thin rectangular slabs using the Finite Difference Method, the present paper was developed with the purpose of comparing the determined efforts in a concrete plate with those that would be found using the tables originated from the plates theory of authors established in the literature. For this, the programming language Python was used, taking as a case study, a slab with dimensions of 5 meters long by 3 meters wide and thickness equal to 0.10 meters. In the analysis of the efforts, several support conditions were considered, in which the internal efforts and displacements obtained by the Finite Difference Method were compared with the results obtained through the tables proposed in literature. It was verified that the Finite Difference Method constitutes a good alternative for the resolution of thin solid plates, since the results were similar to the classic solution proposed in literature. The implemented program allows the visualization of the efforts through of spectrums of zone which facilitates the understanding of the distribution of the efforts along the slab, differing slightly from the uniform distribution adopted in the tables consulted.

Referencias bibliográficas

R. Bares. Tablas para el cálculo de placas y vigas parede. Barcelona: Editora Gusta-vo Gili S/A, 1972.

R. C. Carvalho and J. R. F. Filho. Cálculo e detalhamento de estruturas usuais de concreto armado. 3th ed. São Carlos: Edi-tora UFSCar, 2012.

J. N. Reddy. Theory and analysis of elastic plates and shells. CRC Press, Taylor and Francis, 2007.

Associação Brasileira de Normas Técnicas - ABNT: NBR 6118 “Projeto de estruturas de concreto Procedimento”. Rio de Ja-neiro, 2014.

J. D. Hoffman and S. Frankel. Numerical methods for engineers and scientists. CRC Press, Boca Raton, 2001.

G. D. Smith. Numerical solution of partial differential equations: finite difference methods. 3rd ed. Oxford University Press, 1985.

J. Biezuner. Class notes. (2016, November 24) [Online]. Available: http://www.mat.ufmg.br/~rodney/notas_de_aula/df.pdf.

J. M. Araújo. Curso de concreto armado. 4th ed. v. 2. Rio Grande, Dunas, 2014.

D. A. O. Martinelli, I. Montanari and W. Savassi. “Placas Elásticas”. EESC-USP, São Carlos, Brazil, Publicação 018/93, 1986.

S. D. C. Júnior. “Elaboração de um pro-grama computacional para o cálculo e dimensionamento de lajes maciças”. Final year project, Faculdade de Engenharia, Universidade Federal de Juiz de Fora, Juiz de Fora, 2008.

J. V. Guttag. Introduction to Computation and Programming Using Python: With Application to Understanding Data. 2nd ed. Cambridge, MIT Press, 2016.

Associação Brasileira de Normas Técnicas - ABNT: NBR 6120 “Cargas para o cálculo de estruturas de edificações”. Rio de Janeiro, 1980.

Cómo citar
dos Santos Araújo, C. V., Matos Xavier, J. P., & Lopes Pereira, R. (2021). Determination of the efforts in two-way slabs of concrete through the finite difference method. Revista Ingenio, 18(1), 25-32. https://doi.org/10.22463/2011642X.2662

Descargas

La descarga de datos todavía no está disponible.
Publicado
2021-01-01
Sección
Artículos de Investigación

Más sobre este tema