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Smart Structures and Systems Volume 22, Number 6, December 2018 , pages 689-697 DOI: https://doi.org/10.12989/sss.2018.22.6.689 |
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Deflections and rotations in rectangular beams with straight haunches under uniformly distributed load considering the shear deformations |
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José Daniel Barquero-Cabrero, Arnulfo Luévanos-Rojas, Sandra López-Chavarría,
Manuel Medina-Elizondo, Francisco Velázquez-Santillán and Ricardo Sandoval-Rivas
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| Abstract | ||
| This paper presents a model of the elastic curve for rectangular beams with straight haunches under uniformly distributed load and moments in the ends considering the bending and shear deformations (Timoshenko Theory) to obtain the deflections and rotations on the beam, which is the main part of this research. The traditional model of the elastic curve for rectangular beams under uniformly distributed load considers only the bending deformations (Euler-Bernoulli Theory). Also, a comparison is made between the proposed and traditional model of simply supported beams with respect to the rotations in two supports and the maximum deflection of the beam. Also, another comparison is made for beams fixed at both ends with respect to the moments and reactions in the support A, and the maximum deflection of the beam. Results show that the proposed model is greater for simply supported beams in the maximum deflection and the traditional model is greater for beams fixed at both ends in the maximum deflection. Then, the proposed model is more appropriate and safe with respect the traditional model for structural analysis, because the shear forces and bending moments are present in any type of structure and the bending and shear deformations appear. | ||
| Key Words | ||
| elastic curve; rectangular beams; straight haunches; uniformly distributed load; moments in the ends; bending and shear deformations; Timoshenko Theory; Euler-Bernoulli Theory; deflections and rotations on the beam | ||
| Address | ||
| José Daniel Barquero-Cabrero: Institute of Multidisciplinary Researches, Autonomous University of Coahuila, Blvd. Revolución No, 151 Ote, CP 27000, Torreón, Coahuila, México; Institute for Long Life Learning IL3, University of Barcelona, Street Girona No, 24, CP 08010, Barcelona, Spain Arnulfo Luévanos-Rojas, Sandra López-Chavarría, Manuel Medina-Elizondo, Francisco Velázquez-Santillán and Ricardo Sandoval-Rivas: Institute of Multidisciplinary Researches, Autonomous University of Coahuila, Blvd. Revolución No, 151 Ote, CP 27000, Torreón, Coahuila, México | ||