**2. Traditional methods for girder bridge deck analysis**

Structural grillage models began to be used for the analysis of cross-sectional distribution on beams in the 1960s. These models divide the beam deck into longitudinal and transverse beams (**Figure 1**). Longitudinal beams are responsible for providing the longitudinal bending stiffness of the deck, considering as many longitudinal beams as beams conform to the analyzed beam deck. The structural section of each of the longitudinal beams shall be the result of the section composed of the beam analyzed and the effective depth of the contributing deck with that beam [24, 25]. The cross-sectional distribution of the structural model is provided by the cross-beams and the torsional stiffness of the longitudinal beams. The structural section of the cross-beams corresponds to a rectangular section with an equivalent depth to the slab thickness and a depth according to the discretization used in the grillage models. The analysis of such structural models involves the use of specific structure calculation programs that provide the computing power necessary for the resolution of the proposed matrix problem.

*Perspective Chapter: Simplified Matrix Calculation for Analysis of Girder-Deck Bridge… DOI: http://dx.doi.org/10.5772/intechopen.102362*

The use of structural grillage models allows obtaining the structural response of girder bridge decks to live loads, adequately manifesting the cross-sectional distortion of the girder bridge deck and the distribution of stresses on each of the longitudinal beams that make up the deck. However, such models involve complex, timeconsuming analysis that involves the need to use specific structure calculation programs, making it necessary to use simplified methods for the start of the design process.

The concept of LDF was first introduced using empirical formulas at the American Association of State Depthway Officials (AASHO) in 1931 [26]; these methods propose calculating the cross-sectional distribution on beam bridge decks roughly. The LDF is calculated from a series of formulations that parametrically treat the calculation of the percentage of bending moment and shear stress supported by the most requested longitudinal beam. The parameters that condition the calculation of the LDF are the depth of the beam, the span length, the spacing, the number of beams, the position of the load, and the beam position. This method provides an approximate value of the maximum bending stresses on the beams but is not able to reproduce the cross-sectional distribution of longitudinal bending between all the beams that make up the deck.
