22 H.-J. Kim Fig. 3.1 Installation place of GNSS and thermometer 3.2.2 Data Collection Method We collected our data using the sensors utilized to measure the expansion of Cheong-Poong Dae-Kyo in the 2 receivers in the central girder and the rest 4 GNSSes except for 2 reference stations among the 8 previously installed GNSS receivers as shown in Fig. 3.1 and also the member thermometer installed at the ¼ location of the stiffner. The duration of our data collection was a year, from January 1st, 2014 to December 31st, 2014, and we performed a correlation analysis of GNSS displacements along the direction of the bridge using the 10-min average data of GNSS. The GNSS data consists of three components, dN, dE, and dH, and we defined directions as “perpendicular” and “corresponding” to the bridge line by turning the azimuth 22ı counterclockwise when our Y-axis is due north (N) and X-axis due east (E). 3.2.3 The Analysis of Expansion per Unit Temperature The amount of expansion due to the temperature change of a structure is calculated as shown in the formula (3.1). Here, L implies the temperature change, L the expansion length, and ’ the coefficient of linear expansion of a material. In the formula (3.1), ’andLbecome the values for the boundary conditions depending on the used material and the member length, respectively. We can see that this is a linear relationship between the expansion amount and temperature and define it as the formula (3.2) shown below. ST is defined as the expansion per unit temperature (mm/ıC) [1] LT D’ T L (3.1) LT= TD’ LDST (3.2) The calculation of expansion per unit temperature using measured data is to estimate the linear regression (3.3) from the measured values, ˇ0, ˇ1 of two variables using the least square method (3.4) and its formula is presented below. y Dˇ0 Cˇ1x (3.3) b ˇ1 DP xi x yi y P xi x 2 D Sxy Sxx (3.4)
RkJQdWJsaXNoZXIy MTMzNzEzMQ==