Single variable shear deformation model for bending analysis of thick beams

Salima Abdelbari, Lemya Hanifi Hachemi Amar, Abdelhakim Kaci and Abdelouahed Tounsi

Abstract

In this work, a new trigonometry theory of shear deformation is developed for the static analysis of thick isotropic beams. The number of variables used in this theory is identical to that required in the theory of Euler-Bernoulli, sine function is used in the displacement field in terms of the coordinates of the thickness to represent the effects of shear deformation. The advantage of this theory is that shear stresses can be obtained directly from the relationships constitute, while respecting the boundary conditions at the free surface level of the beam. Therefore, this theory avoids the use of shear correction coefficients. The differential equilibrium equations are obtained using the principle of virtual works. A thick isotropic beam is considered, whose numerical study to show the effectiveness of this theory.

Key Words

thick beam; high order theory; virtual working principle; bending

Address

Salima Abdelbari: 1) Departement de Genie Civil, Institut des Sciences et de la Technologie, Centre Universitaire de Ain Temouchent, Algeria 2) Civil Engineering Department, Faculty of Technology, Material and Hydrology Laboratory, University of Sidi Bel Abbes, Algeria Lemya Hanifi Hachemi Amar: 1) Departement de Genie Civil et Hydraulique, Faculte de Technologie, Universite Dr Tahar Moulay, BP 138 Cite En-Nasr 20000 Saida, Algerie 2) Laboratoire des Ressources Hydriques et Environnement, Universite Dr Tahar Moulay, BP 138 Cite En-Nasr 20000 Saida, Algerie Abdelhakim Kaci: 1) Civil Engineering Department, Faculty of Technology, Material and Hydrology Laboratory, University of Sidi Bel Abbes, Algeria 2) Departement de Genie Civil et Hydraulique, Faculte de Technologie, Universite Dr Tahar Moulay, BP 138 Cite En-Nasr 20000 Saida, Algerie Abdelouahed Tounsi: 1) Civil Engineering Department, Faculty of Technology, Material and Hydrology Laboratory, University of Sidi Bel Abbes, Algeria 2) Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia

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