Tension determination for suspenders of arch bridge based on multiple vibration measurements concentrated at one end

Considering the specific arrangement of boundary constraints for the suspenders of arch bridge, this research extends a recently developed method to carry out the determination of suspender tension simply with multiple measurements concentrated at one end. The virtual hinged boundary of the equivalent cable is first decided by the optimal shifting parameter solved from best fitting the identified mode shape ratios with an unsymmetrical formulation. The effective vibration length for the suspender with a hinged connection at the higher end is taken as the distance between the virtual and actual hinged boundaries to directly estimate its tension. On the other hand, an iteration algorithm using a finite element model is developed to find the convergent tension for the suspender with a fixed constraint at the arch end. The feasibility and accuracy of the proposed method are extensively verified with demonstrative numerical examples, laboratory experiments, and practical applications in real bridges.