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

Abstrak
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 (fT) is generally lower than the vertical frequency (fV), 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 (δT) 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 (fV, fT), static (δV, δT), 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 fT=207L−1.12 and δT=7.28fT−1.64. Approximately 15% of the bridges, particularly those with spans '100 m, are at risk of exceeding comfort limits. The resulting guidance curves provide a practical framework for the initial design, condition assessment, and maintenance prioritization of long-span steel arch bridges in tropical environments.