MATHEMATICAL MODEL FOR RECTANGULAR BEAMS OF VARIABLE CROSS SECTION OF SYMMETRICAL LINEAR SHAPE FOR CONCENTRATED LOAD

摘要

This paper presents a mathematical model for rectangular beams subjected to a concentrated load localized at any point on beam of variable cross section of symmetric linear shape 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 linear type. The consistent deformation method is used to solve such problems; a method based on the superposition of effects and by means of the Bernoulli-Euler theory obtains the deformations at any point of the beam. Traditional methods to obtain deflections of variable section members are Simpson's rule, or any other technique to perform numerical integration and others authors present tables which are restricted to certain relationships. Besides the effectiveness and accuracy of the developed method, a significant advantage is that the displacement and moments are calculated at any cross section of the beam using the respective integral representations as mathematical formulas.