Abstract
A feasibility study was conducted to develop a novel method to determine the temporal changes of tensile forces in bridge suspender cables using time‐frequency analysis of ambient vibration measurements. An analytical model of the suspender cables was developed to evaluate the power spectral density (PSD) function of a cable with consideration of cable flexural stiffness. Discrete‐time, short‐time Fourier transform (STFT) was utilized to analyze the recorded acceleration histories in both time and frequency domains. A mathematical convolution of the analytical PSD function and time‐frequency data was completed to evaluate changes in cable tension force over time. The method was implemented using acceleration measurements collected from an in‐service steel arch bridge with a suspended deck to calculate the temporal variation in cable forces from the vibration measurements. The observations served as proof of concept that the proposed method may be used for cable fatigue life calculations and bridge weigh‐in‐motion studies.
Highlights
Background andMethodology e authors have developed a methodology which demonstrates the ability to relate temporal changes of the cable frequency to variations in axial tension force of the cable.e results show that the amplitude of the oscillatory tension force and corresponding fatigue stress in a suspender cable may be determined by relating vehicle traffic passing over the bridge to the vibration response of the cable
If the suspender cable forces are known under typical service conditions, variation of the forces due to different environmental loads such as wind and thermal forces may be accounted for under extreme conditions. is allows the tensile force history in one or more cables to be directly related to the vibration frequency of the cable caused by the passing vehicles. is approach may be used to determine the remaining fatigue life of the member based on the long-term variation and cyclical loading of the cable tension forces
E tension force time history was determined by evaluating the temporal changes of frequency content of a cable because the frequency response of a dynamic cable system varies with respect to the tension force in the cable. e time resolution of the power spectral density (PSD) function from (18) had to be fine enough to track the temporal changes of the tensile force. us, the recorded acceleration history was split into multiple window segments
Summary
Infinite life region Mean stress, σm Figure 1: Example of a Haigh diagram for fatigue life estimation. E frequency response of the cable may be captured by attaching accelerometers to individual cables to measure the vibration under loading This method may only be used to calculate mean tension force in the cables. Us, a vibration-based method is needed to accurately determine the tension load history and remaining fatigue life of a cable. Is paper presents the development and validation of this feasibility study and the formation of a new method to determine the fluctuation of tension forces in suspender cables over time with both adequate time and frequency resolution through acceleration measurements of the cable vibration. E results show that the amplitude of the oscillatory tension force and corresponding fatigue stress in a suspender cable may be determined by relating vehicle traffic passing over the bridge to the vibration response of the cable. Modal frequencies may be derived from the PDE of motion using modal coordinates. e modal mass and modal stiffness of the system for the rth mode may be found by (3) and (4), respectively: ρAL
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