### Modeling for Beams of Rectangular Cross Section with Parabolic Haunches: Part 1

#### Abstract

This paper presents a mathematical model for rectangular beams with parabolic variation in the height (work object) under a uniformly distributed load taking into account the bending and shear deformations to obtain the fixed-end moments, carry-over factors and stiffness factors. The properties of the rectangular cross section of the beam vary along its axis “x”, i.e., the width “b” is constant and the height “h” varies along the beam, this variation is parabolic type. The compatibility equations and equilibrium are used to solve such problems, and the deformations anywhere of beam are found by means of the virtual work principle through exact integrations using the software “Derive” to obtain some results. The traditional model considers only bending deformations. Besides the effectiveness and accuracy of the developed models, a significant advantage is that fixed-end moments, carry-over factors and stiffness factors are calculated for any rectangular cross section of the beam using the mathematical equation presented in this paper, which is the main part of this research.

#### Keywords

Rectangular members, parabolic haunches, bending and shear deformations, fixed-end moments, carry-over and stiffness factors