Published

2014-05-01

A mathematical model for fixed-end moments for two types of loads for a parabolic shaped variable rectangular cross section

Un modelo matemático para momentos de empotramiento para dos tipos de cargas para sección transversal rectangular variable de forma parabólica

Keywords:

fixed-end moments, variable rectangular cross section, parabolic shape, consistent deformation method, Bernoulli-Euler theory (en)
Momentos de empotramiento, sección transversal rectangular variable, forma parabólica, método de deformación consistente, teoría de Bernoulli-Euler (es)

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Authors

  • Arnulfo Luévanos Rojas Universidad Juárez del Estado de Durango

This paper develops a mathematical model for fixed-end moments for two different types of loads on beams with a parabolic shaped variable rectangular cross section. The loads applied on beam are: 1) a uniformly distributed load and 2) a concentrated load located anywhere along the beam length. The properties of the rectangular cross section of the beam varies along its axis, i.e., the width "b" is constant and the height "h" varies along the beam, this variation follows a parabolic form. The consistent deformation method based on the superposition of the effects is used to solve these problems. The deformation anywhere along the beam is obtained by using the Bernoulli-Euler theory. Traditional methods used to obtain deflections of variable cross section members are any techniques that perform numerical integration, such as Simpson's rule. Tables presented by other authors are restricted to certain relationships. Beyond the effectiveness and accuracy of the developed model, a significant advantage of it is the moments are calculated at any cross section of the beam using the respective integral representations as mathematical formulas.

En este trabajo se desarrolla un modelo matemático para momentos de empotramiento para dos tipos diferentes de cargas en las vigas de sección transversal rectangular variable de forma parabólica. Las cargas aplicadas sobre la viga son: 1) carga uniformemente distribuida, 2) carga concentrada situada en cualquier parte de la longitud sobre la viga. Las propiedades de la sección transversal rectangular de la viga varían a lo largo de su eje, es decir, el ancho "b" es constante y la altura "h" varía a lo largo de la viga, esta variación es de tipo parabólico. El método de deformación consistente basado en la superposición de los efectos se utiliza para resolver tales problemas, y por medio de la teoría de Bernoulli-Euler se obtienen las deformaciones en cualquier parte de la viga. Los métodos tradicionales usados para obtener las deflexiones de miembros de sección transversal variable son por medio de la regla de Simpson, o alguna otra técnica para llevar a cabo la integración numérica y algunos autores presentan tablas que se limitan a ciertas relaciones. La eficacia y la precisión del modelo desarrollado, una ventaja significativa es que los momentos se calculan en cualquier sección transversal de la viga usando las representaciones integrales respectivas como fórmulas matemáticas.

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References

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Copyright (c) 2014 Arnulfo Luévanos Rojas

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