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1 Drastic changes in distribution coef cients: The two theories based on idealization of composite deck and girder action are: The simpli ed beam theory, using transverse distribution factor The bridge deck is idealized as a series of T-beams (line girders composite with deck slab) in the longitudinal

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direction With the use of diaphragms in the transverse direction, a load distribution factor is applied The longitudinal beam is assumed stiffer than the transverse diaphragm This approach is commonly used in the US The primary mode of deformation is by bending and torsion The simpli ed beam theory uses AASHTO LRFD design code for two or more design lanes loaded (AASHTO Table 46222b-1) A set of tables for distribution coef cients for computing bending moments are given in AASHTO 2007 The distribution formula Eq (46a), takes into account spacing, span, and beam stiffness such as: DF 0075 (S/95)06 (S/L)02 (Kg /12 L ts3)01 (46a) where: S beam spacing, L span, ts thickness of slab In older AASHTO codes, the distribution of loads in the transverse direction was based on a simpler equation for the distribution factor The model used for original analysis was a typical longitudinal interior girder, which was generally simply supported between abutments or not fully continuous (with two lines of bearings over the piers), namely DF Girder spacing/55 (46b) Spacing generally varied between 6 and 12 ft and the empriicaldistribution factor variation differed widely for each spacing A similar approach is used for DF of timber bridges (AASHTO Table 46222a-1) In the grid or grillage theory in which the transverse spanning deck strips (and diaphragms) allow full two-way bending action Transverse diaphragms are idealized as truss members The bridge deck is idealized as a grid in plan (line girders in longitudinal directions and line diaphragms in transverse directions) The grid or grillage theory is commonly used in European countries 2 Comparison between the simpli ed beam theory and grillage theory With a longer span and small spacing, longitudinal girder bending will be controlled For small spans and wider spacing, transverse distribution of moments and forces will be higher (approaching a grillage type bending) A nite element analysis for the bridge deck using the grillage model will give a more accurate estimate of girder de ection, moment, shear distribution, and diaphragm forces In both the girder and grillage theories, deck slabs are analyzed as a thin plate However, for lower L/d ratios, such as a 9-inch thick deck slab with a continuous span of 6 feet, for example, it is likely to behave as a thick plate Due to composite action between girders and the deck slab, arching action may result, thereby increasing the compressive forces in the top ange of girders 3 Compact rolled steel joists (compactness de ned by Iyc/Iyy) have proven to perform better transverse stress distribution than the fabricated plate girders Use of non-compact plate girder sections will only allow partial moment and shear distributions compared to girders with compact sections Due to the relative thickness of the web and the gentle transition between the rolling of ange and web pro le, there are fewer instances of rolled steel joist failures than those of plate girders resulting from local web or ange buckling 4 Basic assumptions for analysis: Diaphragms can be modeled as co-existing beam or truss in the transverse direction Truss action is by X-frame, and K-frame con gurations of the diaphragm need to be considered The concrete deck may be assumed isotropic, ie, having equal strength in all directions Certain types of grid decks may be orthotropic Poisson s ratio for the slab and beam system for one-way action is neglected in the longitudinal beam theory Vertical shear deformation in the deck slab is considered negligible Wheel loads may be approximated as an equivalent patch load acting under the wheel width A 45 degree distribution in both directions may be assumed, located away from the.

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