Study of the Vibratory Behavior of the Bridge under the Passage of Mobile Loads Convoys: Comparative Study between Uni-dimensional and Three-dimensional Modeling

Meriem Ouchenane

doi:10.28991/cej-0309145

Abstract

In order to understand the dynamic behavior of bridges under the passage of convoys of moving vehicles, it was necessary to start with the example of a single moving force, however, this study was deemed insufficient because the bridge is under several vehicle forces simultaneously. As a result, this study focuses on the vibration of bridges subjected to convoys of several mobile loads. Based on the analysis of the equation of motion that manage this behavior for the case of a simply-supported unamortized thin beam, subjected to convoys of one, two, and three forces at constant speed. In order to verify the solution obtained for a convoy of n forces through the superposition of solutions of single force with a time offset, see the influence of the spacing ‘e’ between the forces of the convoy on the dynamic amplification factor and compare the results of the analytical study with those derived from the real model established by the software Csi Bridge.

Highlights

Research on the dynamic response of bridges due to moving loads has received particular attention in recent years
We note that the dynamic amplification decreases in increasing the number of loads in the convoy (Table 3, Figure 9 and 10); the displacement increases by 82.16% but the amplification decreases by 9.95% for the case of two loads in the convoy compared to that of one load in the convoy
For the case where we have three loads in the convoy, the displacement increases by 29.80% but the amplification decreases by 13.39% compared to that when we have two loads in the convoy, the displacement increases by 136.44% and the amplification decreases by 22% with respect to one load. This decrease in the dynamic amplification is justified because a single mobile load on the bridge causes a punching effect on the deck, whereas increasing the number of loads in the convoy causes a decrease in this punching effect despite the increase in the value of the resulting load of the deck

Summary

Introduction

Research on the dynamic response of bridges due to moving loads has received particular attention in recent years. [11] presents a study describing an analytical resolution of vibration eigen waves for a rail structure under the influence of a mobile source, the rail is modelled as an infinite Euler beam placed on elastic and periodic supports. [16] study considered the vibratory behavior of bridge decks under the effect of a mobile source, the structure of the deck has been modelled in 3D under the software SAP 2000 and. The second model is a uni-dimensional beam model using the Euler-Bernoulli theory and solving the differential equation that governs the motion, it is an analytical approach, based on the method of modal superposition, and the overall solution is obtained by evaluating the generalized functions by the convolution integral

Analytical Approach of a Beam Behavior through by Convoys Mobile Loads

CSI Bridge Model

Case Study

Effect of the Spacing between the Convoy Loads on the Bridge Behavior

Real Model by CSI Bridge

Comparison of Analytical Results with Those of CSI Bridge

Conclusion