T-section beams with straight haunches under uniformly distributed load

Beams arc classified according to its cross section: prismatic beam whose cross section is constant along its entire length and non-prismatic beam whose cross section is not constant along its entire length. This paper shows a model for non-prismatic T-section beams with straight haunches under uniformly distributed load. Bending and shear deformations are considered to obtain the fixed-end moments and carry-over and stiffness factors, which are the main parts of this research. The superposition method is used to solve these types of beams, and the conjugate beam method by an exact integration is used to find the deformations at any location in the beams. The superposition method consists in splitting a statically indeterminate problem into separate statically determinate problems; that is, the slope or deflection at any point on the beam is equal to the resultant of the slopes or deflections at that point caused by each of the loads acting separately. The traditional model does not consider shear deformations; other authors consider the bending and shear deformations; thorough tables are presented but are limited to some parameters. Also a comparison of the proposed model against the traditional model is shown in Tables 1 and 2, and the main differences are presented in the parameters, d = 0.20L. For the fixed-end moments, in some cases the traditional model is greater and in others, the proposed model is greater, and for the carry-over and stiffness factors in all cases, the traditional model is greater. The proposed model is more suitable and exact for structural engineering analysis and also is adapted to the real conditions, since the shear forces and bending moments act at any structure type and thus the bending and shear deformations are presented. A significant advantage is that the fixed-end moments and carry-over and stiffness factors are calculated for every T-section using their mathematical equations.