# Dynamic Deflection Measurement on Stiff Bridges with High Piers by Preloaded Spring Method
## 6 Conclusions  
To solve the problems of the dynamic deflection measurement and accurate assessment of DLAs for stiff bridges with high piers, the PSM was proposed. The parameters of the SWSS were optimized by VBI analysis, and its feasibility and accuracy in measuring the dynamic deflection of bridges were verified by indoor experiments and field tests. The effects of wind on the suspension hammer system and SWSS were further compared. The conclusions drawn are as follows:  
1. The SWSS associated with the PSM consists of a stretched wire, a pull bar, a compression spring, a dial gauge, a bracket, some heavy objects, and a data-acquisition system. The SWSS achieves synchronized vibration of the bridge and material points by applying compression springs and a preload force;
2. In a windless environment, the errors of the deflections and DLAs obtained by the PSM increase with the spring stiffness and stretched-wire length and decrease with stretched-wire section stiffness and material point mass, while being independent of the initial preload force;
3. Applying the comprehensive stiffness and comprehensive index, the errors of deflection of the DLAs are controlled within 10% by the optimized design of the SWSS. Verified by a 4 \(\times\) 30 m bridge engineering case, the average error of the deflection DLA measured by the PSM is 4.67%, which results in a smaller error of 2.01% in deflections;
4. When the wind speed is less than or equal to 8 m/s and the pier height is less than or equal to 30 m, the measured deflection errors of the PSM and SHM range from \(-0.41\%\) to \(-2.53\%\) and from \(-15.87\%\) to \(7.31\%\), respectively. The measurement accuracy of the PSM is not susceptible to external factors such as the eccentricity of the hammer mass and wind. In a windy environment, a larger preload force is recommended to reduce the influence of transverse wind. The proposed PSM is a major advance in the dynamic deflection measurement of stiff bridges with higher piers;
5. For deflection measurements of only a few minutes, the environmental temperature is practically invariable and has almost no effect on the SWSS or the measurement results. For deflection measurements over days or months, large variations in the environmental temperature and wire relaxation do have some effect on the stiffness of the steel wire and compression spring, which can lead to greater measurement errors. Therefore, the proposed PSM is only used for short-term deflection measurements, such as in bridge dynamic load tests;Although the numerically simulated wind loads may not always accurately reflect the real situation, there is no doubt that the preload effect greatly reduces the effects of wind disturbances. It is worth noting that the measurement errors of the PSM can be further reduced by replacing the steel wire with a new material with a higher strength and lower relaxation. The SWSS shows great potential in dynamic deflection measurement due to its low cost, easy maintenance, and high accuracy, especially on stiff bridges with higher piers. Conceptualization, Y.W., X.J. and Y.Z. ([PERSON]); Software, Y.W. ; Validation, Y.W. ; Formal analysis, Y.Z. ([PERSON]); Methodology, Y.W. ; Investigation, Y.W. and Y.Z. ([PERSON]); Resources, Y.W., X.J., Y.Z. ([PERSON]) and H.Z. ; Data curation, Y.W., Y.Z. ([PERSON]), X.J. and H.Z. ; Writing--original draft, Y.W. and H.Z. ; Writing--review & editing, Y.Z. ([PERSON]), X.J. and H.Z. ; Visualization, Y.W. ; Supervision, Y.Z. ([PERSON]) and Y.Z. ([PERSON]); Project administration, Y.Z. ([PERSON]); Funding acquisition, Y.Z. ([PERSON]). All authors have read and agreed to the published version of the manuscript. Not applicable. The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author. Author [PERSON] was employed by the company Shandong Hi-Speed Construction Management Group Co., Ltd.