**1. Introduction**

Girder bridge decks are a structural typology commonly used in the design of road and railway bridges, and therefore, any optimization in their calculation has a depth impact on the project phase. As explained in [1], the design process relies solely on the designers' experience, intuition, and ingenuity resulting in a depth cost material, time, and human effort. It is very common to use structural grillage models [2–10] to calculate the cross-sectional distribution of live loads between the different beams that make up the cross section of the deck. Another way to deal with the design and calculation of such decks would be to apply different formulations contained in the bridge design standards that allow approximating the cross-sectional distribution of the bending moment and shear stress caused by live loads through what is known as

the load distribution factor "LDF" [11–23]. The "LDF" associated with each case study is conditioned by the type and number of beams, their spacing and length, as well as the existence or not of transverse diaphragms that bring transverse rigidity to the deck.

However, the LDF does not allow determining the distribution of bending stresses on all beams; therefore, the design is oversized. The need for a method to calculate the cross-sectional distribution across all types of beams, without resorting to complex structural grillage models or finite element models in specific structure calculation programs, or to approximate parametric methods based on the "LDF," is one of the authors' motivations for the development of the research work that has given rise to this article.
