Size optimization of the Van Beethoven footbridge in Mechelen (Belgium) under static and dynamic loading

The Van Beethoven footbridge in Mechelen (Belgium) is a steel structure with a variable L-shaped cross-section, composed of beams covered by plates. The bridge has a relatively short span of 29 meters, and its first bending mode exhibits a natural frequency of 3.2 Hz, which coincides with the frequency range of pedestrian excitation. As a result, a tuned mass damper (TMD) was installed to mitigate vibrations. This study presents the results of a gradient-based structural optimization of the Van Beethoven bridge, aiming to minimize its weight by optimizing the cross-sections. In the first scenario, the bridge’s weight is minimized without relying on TMDs for vibration control. Instead, the bridge design is modified to reduce sensitivity to pedestrian excitation, without deviating too much from the initial design concept. Both static and dynamic performance criteria are included as constraints in the formulation of the optimization problem. In the second optimization scenario, the bridge’s weight is minimized while allowing the use of TMDs. The damper parameters are included as additional design variables, and their mass is limited by an upper bound. A comparison of both results provides insight into how the inclusion or exclusion of TMDs affects the optimal structural design of the footbridge.