Deflections in Beams of Rectangular Cross Section with Parabolic Haunches Subjected to a Uniformly Distributed Load

Abstract

This work shows the equations for a rectangular section beam with parabolic haunches subjected to a moment at each support and a uniformly distributed load taking into account the shear and bending deformations to obtain the rotations and the perpendicular displacements to the longitudinal axis at any point of the beam, which is the main contribution of this research. The current model considers only the bending deformations to obtain the rotations and the perpendicular displacements to the longitudinal axis of the beam. The methodology is developed under the concept that the integral of the moment is the slope or rotation and the second integration of the moment is the vertical displacement of the beam. Also, a comparison is made between the proposed model and the current model for beams fixed at both ends with respect to the maximum vertical displacement and its location on the beam. Results show that the proposed model is greater for beams fixed at both ends in the maximum vertical displacement with respect to the current model. Therefore, the proposed model is safer and more suitable with respect to the current model for structural analysis, since shear forces and bending moments are present in all structures and deformations due to bending and shear occur.