Modeling for fixed-end moments of I-sections with straight haunches under concentrated load

This paper presents a mathematical model for fixed-end moments of I-sections with straight haunches for the general case (symmetrical and/or non-symmetrical) subjected to a concentrated load localized anywhere on beam taking into account the bending deformations and shear, which is the novelty of this research. The properties of the cross section of the beam vary along its axis &#34;<i>x</i>&#34;, i.e., the flange width &#34;<i>b</i>&#34;, the flange thickness &#34;<i>t</i>&#34;, the web thickness &#34; <i>e</i&#34;> are constant and the height &#34;<i>d</i>&#34;v aries along of the beam, this variation is linear type. The compatibility equations and equilibrium are used to solve such problems, and the deformations anywhere of beam are found by the virtual work principle through exact integrations using the software &#34;Derive&#34; to obtain some results. The traditional model takes into account only bending deformations, and others authors present tables considering the bending deformations and shear, but are restricted. A comparison between the traditional model and the proposed model is made to observe differences, and an example of structural analysis of a continuous highway bridge under live load is resolved. Besides the effectiveness and accuracy of the developed models, a significant advantage is that fixed-end moments are calculated for any cross section of the beam &#34;I&#34; using the mathematical formulas.