Uncertainty-based approaches for the lateral vibration serviceability assessment of slender footbridges

Slender footbridges with long spans and light materials may lead to serviceability problems in lateral vibrations due to walking pedestrians. The phenomenon, known as the "lock-in effect" occurs when the number of pedestrians on the footbridge reaches the "critical number". Considering the mode of vibration in which the instability is more likely to develop, the footbridge response depends on the structural natural frequency and modal damping ratio. These parameters may not have a fixed value during the footbridge overall life cycle due to environmental and operational changes. Therefore, lateral vibration serviceability procedures should include the uncertainty in the footbridge modal parameters in the most simple and applicable way, as the dynamic response of slender footbridges is very sensitive to these uncertainties. Hence, this paper proposes a simple approach, useful for practical engineering applications, to assess the lateral vibration serviceability of slender footbridges, considering the uncertainties in natural frequency and modal damping ratio. The uncertainty is considered by two approaches: probability theory and possibility theory (fuzzy sets). As a result, the study allows checking the vibration serviceability criteria over a range of levels of uncertainty, suggesting that the external factors that affect the modal parameters are more significant when the crowd density exceeds the critical number. The study also shows the simplicity and effectiveness of the possibility theory to deal with the uncertainty in modal parameters, although for similar level of uncertainty, the dynamic response is slightly higher than using the probability theory. Finally, the proposal is applied in two real footbridges, showing a good agreement with the experimental data.