## 1 Introduction  
Damage due to earthquakes can have a significant impact on transportation networks, in particular on bridges that represent the weakest component of those networks. Structural and non-structural damage in bridges can, indeed, produce significant losses both in terms of a prolonged traffic disruption and in terms of the repairs required for assure again the viability of the damaged bridges [1, 2]. In order to prevent those nefarious outcomes, in recent decades, great effort has been made for the assessment of the seismic vulnerability of bridges, specifically on reinforced concrete (RC) bridges constructed before the adoption modern seismic codes.  
Modern bridge structures are able to resist the seismic action with a response that assures high levels of dissipation of energy thanks to an inelastic behavior characterized by large ductile deformation cycles. To achieve this performance objective, modern design codes have implemented in their provisions plastic design principles aimed at preventing the activation of brittle damage mechanisms.  
On the other hand, existing bridge structures have been designed when many sites were not classified as seismically prone and adopting older construction standards, relying on the admissible stress method, with levels of seismic demand (if any) much lower than the ones currently adopted. Therefore, the resulting structures where conceived to respond in the elastic range, leaving a false sense of security that the actual resistances (well beyond the nominal ones considered in the design process) would be assured by the adopted safety coefficients and by the inelastic behavior of materials and structures. On the contrary, the lack of a hierarchy of strengths that would be lately assured by the implementation, in modern codes, of capacity design principles, would not prevent the occurrence of non-ductile failure modes reducing the extent of the inelastic response [3; 4; 5; 6].  
A typical characteristic of existing bridge piers is the presence of a low percentage of transversal reinforcement, usually represented by poorly detailed and highly spaced stirrups, that would be considered substandard according the construction practice adopted today [7].  
According to the experimental evidence, structures with such a characteristic can show a premature shear failure, limiting the capacity to undergo inelastic deformation and therefore dissipate energy. In fact, several researches and studies on shear strength have evidenced that, even in the case those piers have been initially designed with nominal shear capacity exceeding the shear in equilibrium with flexural yielding, those piers could still fail early in shear due to the detrimental action of inelastic flexural deformations on the shear strength [8; 9].  
Indeed, the widening of flexural-shear cracks due to cyclic inelastic deformations, especially in the plastic-hinge region, reduce the ability of concrete to transfer the shear action through mechanisms relying on aggregate interlock. As a consequence, there is a sectional shear capacity reduction, showing that under cyclic loading the shear strength of columns can be heavily dependent on the inelastic deformations and that shear strength degrades with ductility more quickly than flexural strength. Thus, it is important, when assessing the seismic response of existing structures to take into consideration in the numerical model the insurgence of those complex interaction phenomena affecting the overall response of the bridge structures.  
In past decades different attempts have been made to propose computational models able to couple flexural and shear effects. Those models offer a huge variety of solutions depending on the complexity and the sophistication of the numerical procedure adopted to represent the physical problem, from a relatively simple approach in which a translational spring, representing the shear behavior, is added [10; 11; 12] to frame models where sophisticated, multi-dimensional, constitutive laws are employed [13; 14; 15; 16; 17].