Performance-Based Optimal Design of MTMDs for Human-Induced Vibration Serviceability of Glulam Footbridges

Abstract

Modern glued-laminated timber (glulam) footbridges, characterized by their slenderness, often feature low stiffness, damping, and modal mass, rendering them susceptible to human-induced vibrations. When primary vibration serviceability requirements are unmet, mitigation measures such as tuned mass dampers (TMDs) are necessary. This paper evaluates the vibration serviceability of a glulam model bridge under realistic pedestrian traffic and presents the optimal design of multiple tuned mass dampers (MTMDs). The model is an approximately 13 m long three-hinged deck arch bridge with two circular arch ribs of 8.7 m radius. The fundamental vertical frequency of the footbridge fell within the critical range specified by recent European guidelines EN 1990 and BS 5400, necessitating further analysis against maximum acceleration thresholds. Beyond peak dynamic responses from pedestrian interaction tests, peak accelerations were calculated per the Chinese guideline JTG D60 and compared with comfort limits. Experimental and analytical results indicate that peak vertical and lateral accelerations of the model bridge must be verified under both single- and crowd-induced loading for the serviceability limit state (SLS). Replacing a moving pedestrian load with fixed-position stepping to excite the footbridge simplifies the solution procedure and yields slightly more conservative results. A genetic algorithm-based optimization method is employed to address the multi-objective optimization problem in MTMD design for reducing human-induced vibrations