Análise comparativa entre teorias de vigas de Euler–Bernoulli e de Timoshenko

Abstract

This paper seeks to analyze the structural behavior of Euler-Bernoulli and Timoshenko beams, with the main focus of comparing the transverse displacements for the two theories when applied to isostatic beams. The Euler-Bernoulli beam theory assumes that the cross-section remains flat after bending, and remains perpendicular to the longitudinal axis of the beam, while the Timoshenko beam theory considers both bending and shear deformation in the cross-section. For the comparison, the analytical formulations governing the two beam theories were described. With the formulations deduced, analytical results were obtained for Euler-Bernoulli and Timoshenko beams. The transverse displacement values of both theories were compared, analyzing parameters such as percentage difference and length to height ratio. It was found that in simple bi-axial beams with rectangular and T sections, the application of the Euler-Bernoulli theory is satisfactory when the L/h ratio is greater than 10, with percentage differences of 1.40% and 1.36% for each configuration. Similarly, for cantilevered beams, this ratio is limited to 7.58 and 9.09, with differences of 1.497% and 1.571%, respectively. In addition, two formulations of shear coefficients were taken into account when calculating the transverse displacements of the Timoshenko beam. The choice between the formulations depends on the desired accuracy of the displacements. For a deflection check, it is recommended to opt for the simplified coefficient, which has proven to be more conservative compared to the more elaborate coefficient.