3 Analysis of Variation Rate of Displacement to Temperature of Service Stage. . . 23 −15 −10 −5 0 80 GPS(p2-L) GPS(PY1-L) GPS(p2-L) GPS(PY1-L) (a) (b) (c) (d) 70 60 50 y = −2.323x + 35.64 R2 = 0.923 y = −2.323x + 35.64 R2 = 0.923 y = −1.831x + 41.07 R2 = 0.848 y = −1.831x + 41.07 R2 = 0.848 40 30 20 10 −10 −20 −30 0 60 40 20 −20 −40 −60 −80 0 0 5 10 Temperature (°C) Displacement (mm) 80 60 40 20 −20 −40 −60 −80 Displacement (mm) Displacement (mm) 70 60 50 40 30 20 10 −10 −20 −30 0 Displacement (mm) 15 20 25 30 35 40 −15 −10 −5 0 5 10 Temperature (°C) 15 20 25 30 35 40 −15 −10 −5 0 5 10 Temperature (°C) 15 20 25 30 35 40 −15 −10 −5 0 5 10 Temperature (°C) 15 20 25 30 35 40 Fig. 3.2 Relationship between air temperatures and displacement. (a) Relationship between air temperatures and P2. (b) Relationship between air temperatures and PY1. (c) Relationship between air temperatures and PY2. (d) Relationship between air temperatures and A2 Sxy DXxiyi Xxi Xyi =n (3.5) Sxx DXx 2 i Xxi 2 =n (3.6) 3.3 The Analysis Through the analysis of measured data, we confirmed a high correlation between two variables as shown in Fig. 3.2 by setting the effective temperature considering expansion directions of bridges and the expansion measured at each location of the bridge as two variables and displayed their distribution [5–8]. We found our coefficient of linear expansion as 0.00001 after calculating the slope of the linear regression equation as displayed in Fig. 3.3. We estimated the theoretical expansion amount per unit temperature as shown in Table 3.1 after applying the coefficient of linear expansion analyzed through our measurement, put it into the formula (3.4), and compared the expansion amounts per unit temperature of temperature and displacement data as presented in Table 3.2.
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