1 INTRODUCTION The analysis of the bridge decks through a grillage model is a technique diffused in the second half of the past century, after that some authors, Hrennikoff and Absì particularly, suggest the idea to study the elastic problems modelling the continuous systems through a finite number of elementary frameworks. This type of approach, first applied to the beam and slab decks, spreads widely and its application is ex- tended to the case of much more complex structures, such as cellular decks, skew and curve bridges, and to the case of particular loading conditions, such us the temperature and pre-stress loads. The fundamental principle lies on the bases of this modelling is clearly expressed in a Hrennikoff’s note, referred to the case of bi-dimensional elastic continuous elements but generalizable to the one of three-dimensional structures: ”The basic idea of the method consists in replac- ing the continuous material of the elastic body under investigation by a framework of bars, arranged ac- cording to a definite pattern whose elements are en- dowed with elastic properties suitable to the type of problem, in analyzing the framework and in spread- ing the bar stresses over the tributary areas in order to obtained stresses in the original body. The framework so formed is given the same external out- line and the boundary restraints, and is subjected to the same loads as the solid body, the loads being all applied at the joints” (Hrennikoff 1941). Hrennikoff imposes the equivalence between con- tinuous structure and grillage model through a kine- matics principle, according to the two models are equivalent if, subjected to the same loading condi- tions, present equal strains. This technique is taken again by Absì after the spread of the Finite Element Method, and it is re-proposed in a different key; Absì, in fact, supposes continuous structure and gril- lage model are equivalent if, subjected to the same loading conditions, present equal total potential en- ergy (Absi). The imposition of the equivalence lets to the equations which define the axial, flectional, torsional rigidities of the grillage beams. The two approaches practically let to the same results. 2 DEFORMATIVE MODES OF BRIDGE DECK 2.1 The problem In a bridge deck analysis through the use of a gril- lage model, the assignment of rigidities to the gril- lage members is certainly the main phase of this pat- tern. The expression of the rigidities must be assigned to the beams are given by various manuals for more common types of deck. These estimations of the equivalent rigidities derive from theoretical considerations and experimental observations re- ferred to only “principal” deformation modes, or flections and torsion of deck in longitudinal and transverse directions. As for cellular decks, these principal modes are accompanied by “secondary” Bridge deck analysis through the use of grillage models G. Battaglia Structural Engineer, Milan, Italy P.G. Malerba Technical university of Milan, Milan, Italy L. Sgambi University of Rome “La Sapienza”, Rome, Italy ABSTRACT: The object of the paper is the study of the representativity of the grillage models with which different types of bridge decks are schematized. First, the theoretical principles on which this kind of model- ling is based are recalled; the equivalent condition between bi-dimensional continuous elements and corre- sponding grillage models are imposed through the use of a kinematics and an energetic criterion. Secondly, the same technique is generalized to three-dimensional structures and specialized to the case of cellular decks. For this kind of deck, structural behaviours usually neglected by the current technical approaches, like shear lag, distortion and warping, are considered. The paper presents some methods introducing these effects in a grillage analysis; these methods provide a series of criteria with which it’s possible to define the rigidities of the equivalent model. These criteria are applied and compared with finite element solutions. Finally, a series of applications are executed in order to verify the efficiency and the accuracy of this kind of approach.