## 1 Introduction  
Recently, structural health monitoring (SHM) has become a necessary tool to evaluate the condition of important structures, such as bridges, buildings, tunnels, and so forth. The SHM systems are categorized into short and long-term monitoring systems. Long-term systems are used for a continuous monitoring of the structures that need real-time performance analysis, on the other hand, short-term monitoring systems are mostly low-cost monitoring systems used to evaluate the performance of existing structures for a short period of time. Many researchers developed low-cost monitoring techniques in order to decrease the costs of the long- and short-term assessment of structures. For example, a system was developed by [PERSON] et al. [1] using smartphone application for structures monitoring; however, the accuracy of the developed system is limited. [PERSON] et al. [2] employed a deep learning algorithm to decrease the cost of SHM by estimating the strain responses from acceleration responses. Furthermore, image processing has been used to reduce the monitoring cost [3] where the displacement can be estimated from real time image monitoring systems [4]. [PERSON] et al. [5] presented a low-cost monitoring technique using global positioning system (GPS) sensors by using four low-cost sensors for estimating the dynamic behavior of structures; the results of this study showed low accuracy, 20-30 cm. In addition, compared to accelerometers and strain sensors, GPS sensors are expensive and their sampling frequency is low,10-100 Hz [6; 7]. Therefore, to accurately estimate the performance of structures, accelerometers, displacement or strain sensors are usually used [8; 9; 10]. These sensors are used to estimate the accurate dynamic and static behavior of structures, as well as the fatigue can be extracted using strain measurements [11]. The present study introduces a low-cost monitoring system to extract the full behavior of a monitoring point, including the accurate dynamic performance, of highway steel bridges using only strain measurements. Strain sensors have proven to be effective tools to measure the fatigue of structures, particularly bridges [11; 12; 13; 14]. Moreover, strain sensors have been widely used to estimate the behavior of bridges under environmental effects [14; 15] and traffic loads [13], as well as to assess traffic volume over bridges [16]. However, the possibilities to estimate bridges' deflection and acceleration from strain measurement remain limited, as it is very sensitive for the measurement noises [17]. [PERSON] and [PERSON] [18] calculated natural frequencies of the first 10 mode shapes of a bridge, and their results showed that the computed first mode shape was 5.32 Hz compared to that extracted from strain measurements, 4.92 Hz. Furthermore, [PERSON] and [PERSON] [19] used experimental models and the frequency response function to estimate the strain performance of beams using acceleration measurements. Their study used two accelerometers sensors and the frequency response functions between them were estimated based on different positions of these sensors to a fixed one. They found that the correlation between the acceleration measurements and strain prediction was high. In addition, [PERSON] [17] proposed a method to estimate the strain from acceleration and displacement sensors; however, the proposed method depends on the transformation matrices and the methods of analysis used. [PERSON] et al. [20] utilized mode shapes changes to estimate displacement from strain. [PERSON] et al. [21] used the cross-correlation matrix of a modal coordinates to estimate the mode shapes of the beam element though strain measurements. [PERSON] and [PERSON] [22] used a hybrid modal analysis to transfer displacements to strains and assess the dynamic behavior of steel structures. Additionally, when the frequency response function was used to convert the acceleration to strain for an experimental steel bar, the accuracy observed was less than 10% [23].