## 1 Introduction
The ratio of moment and cross-section rotation is the basis for deriving the value of the cross-section rotation parameter \(\varphi_{y}\) when the yield point is reached. Several expressions [14; 28; 29] can be found in the literature to calculate the approximate value of cross-sectional rotation during yielding. These expressions can be used to estimate the value of rotation when the yield point is reached for rectangular and circular sections. In bridge structures, we often use cross-sections of columns that differ from these two typical shapes, i.e., cross-sections for which a detailed \(\mathrm{M}/\varphi\) analysis is required to obtain information about their rotational capacity. Accurate data input (shape and dimensions of the cross-section, arrangement, and quantity of longitudinal and transverse reinforcement) and the properties of the materials used (stress and strain ratio) are crucial to obtain the most accurate ratio of moment to rotation of the cross-section. This refers primarily to the ratio between stress and strain, which should be considered as close as possible to the actual behavior of the material (non-linear diagrams). The accurate determination of the bending moment to rotation diagram of reinforced concrete sections is a reliable indicator of the bearing capacity of elements under seismic loads [30; 31]. In simplified calculations of reinforced concrete elements, the connection between the reinforcement and the concrete is considered completely fixed. This assumption can be applied in areas where very low stresses occur between concrete and reinforcement. In areas with high shear stresses, such as in sections around cracks, relative deformations between concrete and reinforcement occur. For this reason, the slip effect must be used as a parameter when analyzing the behavior of the structural element [32]. The low bond strength between reinforcement and concrete directly affects three main deformation mechanisms: Bending, shear, and end section rotation. The results of experimental research show an average 35% higher deformation capacity of elements made with smooth reinforcement compared to elements made with ribbed reinforcement [7]. Whilethe deformability of elements with smooth reinforcement is increased due to their better ductility properties, it simultaneously decreases due to the nonseismic detailing of such elements. Unconfined concrete has significantly lower properties in the region of plastic hinges than confined concrete. Tests have shown that the level of the rotational capacity is significantly affected by the amount of axial force applied and that the deformability of the elements decreases almost linearly under the influence of such a force [33]. An insufficient number of tests on elements with such properties suggests caution in assessing their deformability. In addition to rectangular, square, and circular cross-sections, which are all typical for columns in buildings, bridge columns often have cross-sections whose seismic resistance indicators cannot be analyzed using the previously mentioned expressions developed by individual researchers. The purpose of the research presented in this paper is to define the seismic resistance indicators of the columns of the existing bridge, which have an atypical cross-section with smooth reinforcement and without seismic details. The experimental part of this research extends the current base of the tested column thus providing the improvement and development of the standards for the seismic assessment of structures.