The relationship between natural frequency–span and deflection–span (Vertical and Transverse) as guiding parameters for the design and assessment of long-span steel arch bridges

Long-span steel bridges have high span-to-capacity efficiency; however, increased structural flexibility reduces natural frequencies and increases deflections. In steel arch bridges, the first transverse natural frequency ( f T ) is generally lower than the vertical frequency ( f V ), making the transverse response the controlling parameter in evaluating serviceability and user comfort. However, to date, no empirical relationship specifically linking transverse frequency, span length (L), and transverse deflection ( δ T ) including frequency–deflection coupling relationships is available, particularly for the population of long-span bridges in tropical regions. This study aims to develop typology-specific empirical relationships that integrate dynamic parameters ( f V , f T ), static ( δ V , δ T ), and comfort criteria in the form of practical guide curves. The analysis is based on a primary dataset of 27 steel arch bridges with spans of 50–300 m, compiled from FEM-based design documents and full-scale static and dynamic load test results prior to operation. The f–L and δ–L relationships were modelled using power-law regression based on log–log transformations and interpreted within a serviceability framework in accordance with CHBDC. The results indicate that the power-law model represents the dataset well, with transverse response being the dominant factor in serviceability performance, yielding the typology-specific relationships f T = 207 L − 1.12 and δ T = 7.28 f T − 1.64 . Approximately 15% of the bridges, particularly those with spans