A modal precise integration method for the calculation of footbridge vibration response

•A new modal precise integration method is proposed.•It is applied to vertical acceleration of pedestrian loaded bridges.•A closed-form approach for simply-supported bridges is determined.•The method is compared to Newmark-Beta method for the same problem.•It is shown to be computationally efficient and accurate for the problem.

This paper presents a computationally efficient methodology for determining footbridge vibration response when subject to pedestrian excitation suitable for use in a Monte Carlo framework. A general modal precise integration method is developed for moving force problems. A closed-form solution for the transition matrix for the important case of a simply-supported beam subject to harmonic moving loads is given. The proposed method is efficient and accurately estimates important statistics of response in pedestrian excitation problems. This method should therefore find value in assessing new or existing footbridges when subject to random pedestrian excitation.