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Structural Engineering and Mechanics Volume 76, Number 3, November10 2020 , pages 395-412 DOI: https://doi.org/10.12989/sem.2020.76.3.395 |
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Curved beam through matrices associated with support conditions |
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Faustino N. Gimena, Pedro Gonzaga, José V. Valdenebro, Mikel Goñi and Lorena S. Reyes-Rubiano
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| Abstract | ||
| In this article, the values of internal force and deformation of a curved beam under any action with the firm or elastic supports are determined by using structural matrices. The article presents the general differential formulation of a curved beam in global coordinates, which is solved in an orderly manner using simple integrals, thus obtaining the transfer matrix expression. The matrix expression of rigidity is obtained through reordering operations on the transfer notation. The support conditions, firm or elastic, provide twelve equations. The objective of this article is the construction of the algebraic system of order twenty-four, twelve transfer equations and twelve support equations, which relates the values of internal force and deformation associated with the two ends of the directrix of the curved beam. This final algebraic system, expressed in matrix form, is divided into two subsystems: twelve algebraic equations of internal force and twelve algebraic equations of deformation. The internal force and deformation values for any point in the curved beam directrix are determined from these values in the initial position. The five examples presented show how to apply the matrix procedures developed in this article, whether they are curved beams with the firm or elastic support. | ||
| Key Words | ||
| curved beam; stiffness matrix; transfer matrix; structures matrices; support conditions | ||
| Address | ||
| Faustino N. Gimena, Pedro Gonzaga, José V. Valdenebro, Mikel Goñi:Department of Engineering, Public University of Navarra, Campus Arrosadia, 31006 Pamplona, Spain Lorena S. Reyes-Rubiano: School of Economic and Administrative Sciences, University of La Sabana, 250001 Chia, Colombia | ||