Various theories and analytical formulations were implemented and exploited in the 1980s and 1990s for the design of bridge beams or decks curved in the horizontal plane and subjected to out-of-plane loads. Nowadays, the Finite Element Method (FEM) is a valid tool for the analysis of structures with complex geometries and, therefore, the development of sophisticated analytical formulations is not needed anymore. However, they are still useful for the validation of FE models. This paper presents the case study of an existing viaduct built in North Italy, aiming to compare analytical approaches and numerical modelling. The bridge is characterized by an axis curved in two directions and a rectilinear segment. The global analysis of the viaduct is carried out with special attention to the attributes that cause torque action and bending moment. The theoretical developments focus on a deeper understanding of the torsional response under different constraint and loading conditions and aspire to raise awareness of the mutual interaction of flexural and torsional behaviour, that are always present in these complex curved systems. The examination of the case study is also obtained by comparing the response of isostatic and hyperstatic curvilinear steel box-girders.
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