Pedestrian-induced footbridge vibration response based on a simple beam analytical method

Abstract

This article aims to study the quantitative calculation of pedestrian-induced footbridge vibration comfort. Firstly, the analytical expression for the vibration response was derived. In addition, the simplified formula of the vibration response under resonance condition was put forward. The proposed analytical solution was compared with the numerical solution and the experimental result. Secondly, the analytical method was used to calculate the acceleration response under different crowd densities. The peak acceleration distribution and cumulative probability were analyzed. Finally, the cumulative probability that exceeded the acceleration limit was proposed as the comfort evaluation index, and the improved annoyance rate model was used to verify the proposed evaluation method. The results demonstrate that the analytical method can efficiently calculate the dynamic response of footbridges. Errors between the analytical results and the experimental results are less than 6.2%. Vibration comfort is negatively correlated with crowd density and walking speed. Furthermore, the errors between the proposed discomfort probability values and the calculated annoyance rate results are within 6%.