# Dynamic Deflection Measurement on Stiff Bridges with High Piers by Preloaded Spring Method
## 1 Introduction
DLAs require discerning the difference between dynamic and static deflections rather than the absolute deflection itself, as \(\Delta y\) Figure 1. DLAs will also be exponentially amplified even if the deflection error is minor, so they are the most sensitive \"indicator\" in deflection measurements. To summarize, dynamic deflection measurements of stiff bridges with high piers are challenged by (1) the continuous acquisition of structural deflections at a high sampling frequency from a distance of tens of meters, (2) requiring a sub-millimeter accuracy, (3) not being affected by light, temperature, atmosphere, wind, and long-signal transmission, and (4) the need for a low cost and multi-point measurement. It has been found that most stiff  
Figure 1: Static and dynamic deflection of a bridge due to vehicles. Note: \(\Delta y\) represents the difference between dynamic deflection and static deflection. bridges with high piers have deflection measurements with DLA errors above 20%, which may eventually lead to unsafe bridge design and evaluation. Presently, it is indisputable that conventional contact methods are more reliable because of the higher contact force transfer between rigid bodies compared to the advanced non-contact methods. When the piers of a stiff bridge are shorter, the combination of scaffoldings and a string potentiometer device is typically used for dynamic deflection measurements and is denoted as the scaffold method (SFM) [49]. Although the SFM can capture the real dynamic deflection of a stiff bridge, the application of scaffoldings is time-consuming and laborious work when pier heights are higher. In view of this, a wire-connection device (steel wire and heavy hammer) has been utilized in dynamic deflection measurements of stiff bridges with high piers to avoid scaffoldings and is referred to as the suspension hammer method (SHM) or suspension hammer system [6]. As an indirect-contact type method, the SHM seems to be the uniquely reliable-so-far solution for dynamic deflection measurement on stiff bridges with high piers when the SFM is unavailable. However, a too-long signal transmission path will reduce the measurement accuracy of the SHM. Additionally, the eccentricity of the suspension hammer mass and environmental wind will also adversely affect the SHM. [PERSON] [50] has demonstrated that the dynamic deflection of a bridge based on the SHM is affected by the hammer mass, load duration, excitation frequency, and wire length. [PERSON] [51] developed a weighted stretched-wire system and demonstrated its effectiveness for measuring static and dynamic responses. In any case, a stationary platform under the bridge as a fixed reference point is necessary for the SFM and the SHM. Motivated by (1) the unavailability of non-contact methods and (2) the loss of accuracy of the SHM in dynamic deflection measurements of stiff bridges with high piers, a preloaded spring method (PSM) and related stretched-wire-spring system (SWSS) are proposed in this study. The PSM is achieved by improving the SHM, overcoming some of its shortcomings. The PSM is characterized as follows: (1) the PSM is proposed by combining the spring-mass vibration characteristics, which can capture high-accuracy deflections even on stiff bridges with high piers; (2) limited lateral constraints are provided by implementing an initial preload within the SWSS, which can resist the effects of wind or mass eccentricity in the dynamic deflection measurements; (3) the optimized system allows for the measurement error of peak dynamic deflections to remain within 10%. The application of the PSM can significantly improve the accuracy of the indirect-contact method in dynamic deflection measurement by controlling the properties of the SWSS, while solving the challenge of attaining accurate DLA evaluation for stiff bridges with higher piers. The remainder of this paper is organized as follows. The principles of static and dynamic deflection measurement of the PSM are illustrated in Section 2.