A novel framework for assessing the serviceability of footbridges under human-induced bending and torsional vibrations: from detailed formulation to simplified design method

Modern footbridges are highly susceptible to dynamic vibrations induced by pedestrians. While significant research has focused on vertical and lateral vibrations generated by walking, the effects of vertical forces on torsional vibrations remain insufficiently addressed. Traditional assessment methods generally overlook torsional dynamics, which can be limiting under eccentric pedestrian loading activating torsional modes. This oversight may lead to inaccuracies in evaluating structural performance, particularly for complex footbridges where torsional effects play a significant role. This paper presents a detailed numerical modelling approach incorporating both translational and rotational effects induced by pedestrian excitation, acknowledging the coupling between bending and torsion in vertical vibrations. Numerical analyses are conducted involving individuals walking with parametrically varied eccentricities and crowd flows simulated at the microscale, to evaluate the structural response under various loading scenarios. A simplified design-oriented method to account for coupled bending-torsional vibrations is also introduced, based on multiplication factors enabling traditional bending-only analyses to be easily adjusted to include torsional effects. The proposed method is validated through experimental testing conducted on a boomerang-shaped footbridge with asymmetrical cross-section, subjected to single pedestrians walking eccentrically. Results confirm the method accuracy and highlight the importance of considering bending and torsional dynamics for reliable serviceability assessments.