## 1 Introduction  
The assessment of the condition of existing bridges and their appropriate and optimal maintenance plan is certainly an issue that will take priority over the design of new transport infrastructure in the near future. To be more precise, the construction of much of today's European transport infrastructure began in the 1960s and more and more European bridges are approaching their planned lifetime [1, 2]. This hot topic is further accentuated by exceptional events and the increasing failure of bridges in recent years, which, in addition to material damage [3, 4], also has tragic consequences. It is also worth mentioning that these structures are often located in areas of extreme seismicity. The current design approach for new structures implies that it is uneconomic to design structures that provide a fully elastic response to the design value of seismic actions. An alternative is the widely accepted structural design approach for smaller seismic design loads, while at the same time detailing them according to the rules of ductile behavior so that they can withstand significant seismic loads due to inelastic deformation. There are many existing bridges that were designed according to now outdated norms which did not contain guidelines for the design of elements for ductile behavior. Some even older bridges do not even take earthquake loads into account. The degree of ductility of these bridges is unknown. Therefore, the question of the correct seismic assessment of bridges is still open for research. Several previous studies [5; 6; 7; 8; 9] indicate that structures that are not designed and detailed for seismic actions may still have some degree of seismic resistance. The loss of bond strength between concrete and smooth reinforcement, but also the better ductility of such reinforcement allows for greater deformability of the elements. In general, previous research on structural elements has focused on elements typical of high-rise buildings (beams, columns), which are produced with ribbed reinforcement [10; 11; 12; 13; 14] while a smaller number of studies evaluate the seismic resistance of bridges, especially girders [15; 16; 17] and arches [18; 19; 20; 21]. By analyzing the main parameters of the seismic resistance indicators [22; 23; 24], selecting a suitable evaluation method [25], and using the currently available guidelines for the evaluation of structures [26] and recent research in this field [10; 11; 12; 13; 14], it is possible to determine seismic resistance reserves of bridges that have not been previously designed and detailed for such actions. Nonlinear methods are mainly used to assess the seismic load-bearing capacity of existing bridges [25; 26; 27]. The application of such methods requires the knowledge of the actual behavior of the structure, either the actual rotational capacity of the elements under static load, if non-linear static analyses are used, or under cyclic load, if non-linear dynamic analyses are used. The ductility of reinforced concrete elements in the cracked state is estimated based on of the effective stiffness when the yield strength is reached. A review of the literature shows two approaches in defining effective stiffness [11]. First approach is the theoretical effective stiffness obtained from the relationship between the bending moment \(\mathrm{M}_{y}\) and the chord rotation \(\theta_{y}\) when the yield point is reached. This approach is more suitable for assessing the state of existing structures. The second approach is empirical formulation which is more suitable for designing new structures. The chord rotation at the yield point depends on the sum of the rotations of all cross-sections along the height of the element. The rotation of the end section is dominant. The end section of columns fixed to the foundation, arch, or superstructure is the key component in assessing the seismic resistance of bridges.