MODELLING FOR MECHANICAL ELEMENTS OF RECTANGULAR MEMBERS WITH STRAIGHT HAUNCHES USING SOFTWARE: PART 1

This paper presents a mathematical model for mechanical elements of rectangular members with straight haunches for the general case (symmetrical and/or non symmetrical) subjected to a uniformly distributed load considering the bending and shear deformations to obtain the fixed-end moments, carry-over factors and stiffness factors, which is novelty of this research. The properties of rectangular cross section the member are: the width "b" is constant and the height "h" varies along beam, this variation is linear type. The superposition method is used to obtain the solution of such problems, and the deformations anywhere of beam are found by the conjugate beam method through exact integrations using the software "Derive" to obtain sonic results. The traditional model takes into account only bending deformations. Also a comparison is made between proposed model (bending and shear deformations are considered), and traditional model (bending deformations are taken into account) to show the differences. Besides the effectiveness and accuracy of the developed model, a significant advantage is that fixed-end moments, carry-over factors and stiffness factors are obtained for any rectangular cross section of beam using the mathematical equations.