Vibrations of a Bridge with Random Structural Irregularities Under Random Traffic Load and a Probabilistic Structural Degradation Assessment Approach

Abstract

Purpose Dynamic loads like traffic make bridges vibrate. Especially for bridges with a large span, vibrations have a significant impact on their structural stability and durability. Due to material defects, fatigue and other influences, a bridge typically has random structural irregularities, which affect its dynamic response. In this work, an effective mathematical approach is presented to study the dynamic response of a model single span slender beam bridge, in the presence of random structural irregularities. In addition, an approach to assess the structural degradation of a bridge is presented. Methods The slender beam bridge is modelled as an Euler-Bernoulli beam and the random structural irregularities are considered by random fields in the bending stiffness and the mass per unit length. As an illustrative example, the vibrations of a model road bridge are investigated for randomly crossing vehicles. After Monte Carlo experiments with and without random structural irregularities the vibrations and mechanical stresses of the bridge are determined and analysed. Results The study shows statistically significant variations in the most dominant frequencies with and without random structural irregularities. Conclusion The influence of the random irregularities on the structural stability status of a bridge may not be negligible. The probability of a serious structural degradation in the bridge can be assessed by means of a binomial logistic model. The developed approach enables a better understanding of the vibrations and structural status of bridges, taking into account random structural irregularities and random traffic.

Analysis of Train–Track–Bridge Coupling Vibration Characteristics for Heavy-Haul Railway Based on Virtual Work Principle

“…The equation of motion for the rear bogie is derived by considering the virtual work contributions of the inertia force acting on the rear bogie, the interaction between the car body and the rear bogie, the contact between the wheelsets and the rail, as well as gravity. The virtual work of the rear bogie can be expressed by: (7) where the subscripts "w3" and "w4" are the front and rear wheelsets of the rear bogie.…”

“…The mass matrix M vv , stiffness matrix K vv and damping matrix C vv of the heavy-haul train can be derived from the virtual work Equations ( 5)- (7). The mass matrix M vv with the order n v × n v can be expressed by:…”

“…The track system, consisting of rails, sleepers, and ballast, serves as a conduit for transferring the dynamic load of heavy-haul trains to the bridge deck. At the same time, the vibration of bridges and tracks exerts an adverse impact on running trains, thereby compromising the stability and safety of train operation [7]. The dynamic responses of the heavy-haul train, track, and bridge subsystems can be obtained through the establishment of a train-trackbridge coupling system.…”