# Effect of Temperature on the Modal Variability in Short-Span Concrete Bridges
## 1 Introduction  
The dynamic characteristics of a structure can be obtained through modal identification in the presence of dynamic data measurements such as acceleration responses. Modal identification methods can be classified into EMA (experimental modal analysis) and OMA (operational modal analysis) according to the type of input. Unlike EMA that requires known force input, OMA relies on a random process without the need of any test setting, which makes it easily applicable and adapted for long-term monitoring of bridges in operation. Among the OMA methods, there are the frequency domain decomposition [1], the Bayesian spectral density approach [2], the eigensystem realization algorithm [3], the subspace identification method [4], and the Bayesian time-domain approach [5].  
The dynamic characteristics such as natural frequency, damping ratio, and mode shape obtained from such modal identification methods can be utilized for evaluating the health of the structure. The occurrence of damage in a structure can be assessed when the dynamic characteristics deviate from a definite range or exceed a specific threshold. These dynamic characteristics are known to be affected not only by damages but also by environmental factors such as temperature. Accordingly, the changes in the dynamic characteristics caused by environmental factors shall be considered when setting the thresholds for the assessment of the conditions of the structure. Specifically, temperature must imperatively be accounted for because it has the greatest effect on the variability of the long-term dynamic characteristics of the structure.  
Numerous studies have been dedicated to the analysis of the effects of environmental factors as well as their extent on the dynamic characteristics. [PERSON], et al. [6] analyzed the temperature and wind effects on cable-stayed bridges and reported their significantinfluence on the natural frequencies and damping ratio. [PERSON], et al. [7] revealed that temperature together with traffic loading were important external factors affecting the natural frequencies of suspension bridges. Relations between temperature and the natural frequencies were proposed by [PERSON] and [PERSON] [8] for curved bridges with box sections and by [PERSON], et al. [9] for steel girder bridges supporting concrete decks.  
However, the lack of research on short-span bridges shorter than 15 m is noteworthy since these previous studies focused on medium-span bridges or special bridges such as long-span bridges. This study intends to evaluate the extent of the effect of environmental factors such as temperature on the dynamic behavior of short-span bridges, especially the natural frequency. To that goal, one RC slab bridge and one RC rahmen (rigid-frame) bridge are selected to examine the difference in their behaviors according to the bridge type. Modal identification is performed on the data measured in the operating bridges to obtain their natural frequencies with respect to temperature. Regression analysis and PCA (principal component analysis) are carried out to assess the changing patterns of the natural frequencies according to temperature changes, and to investigate the main factors influencing the temperature dependency of the bridges. In addition, the distribution pattern of the natural frequencies excluding the effect of temperature is analyzed to provide basic data for assessing the eventual occurrence of damages in the bridges.