Static Analysis of Isotropic Beams Resting on Elastic Foundations of the Winkler-Pasternak Type

Larissa Oliveira Santos; Fabio  Carlos da Rocha; Leslie Darien Pérez Fernández

doi:10.14295/vetor.v33i1.15133

Authors

Larissa Oliveira Santos Universidade Federal de Sergipe
Fabio Carlos da Rocha Universidade Federal de Sergipe
Leslie Darien Pérez Fernández Universidade Federal de Pelotas https://orcid.org/0000-0002-4452-264X

DOI:

https://doi.org/10.14295/vetor.v33i1.15133

Keywords:

Isotropic Beams, Euler-Bernoulli Theory, Winkler-Pasternak Foundations

Abstract

Beams resting on elastic foundations are widely used in engineering projects, so analyzing their displacement fields is very important. The present work presents solutions for the deflection of isotropic beams resting on elastic foundations of the Winkler-Pasternak type. The proposed formulation is based on the Euler-Bernoulli beam theory, and the governing equations and the boundary conditions are derived from the principle of virtual work. The direct integration method can decouple the deflections from axial displacement and twists. The system of deflection equations decouples into two principal directions and is transformed into a first-order system. The solution of this system of equations is obtained through the method of variation of parameters. When analyzing the results of the maximal deflections, it is observed that increasing values of the foundation stiffness provide decreasing deflections and that the influence of the Pasternak parameter is more significant on the results than that of the Winkler parameter.

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