# An Investigation of the Temperature-Drift Effect on Strain Measurement of Concrete Beams
## 2 The Temperature-Resistance Effect of the Strain Gauge  
This section examines the effects of temperature changes on the data measured by the strain gauge attached to the object to be tested. When the test object was not given any constraints, temperature changes would cause the object to generate free thermal expansion and contraction strains (\(\varepsilon_{f}\)) that would be detected by the strain gauge. However, the electrical resistance in the gauge would also change due to temperature changes, and this change would generate unwanted strain (\(\varepsilon_{u}\)) in the measurement. Therefore, when an object without constraints is subjected to temperature changes, the measured temperature strain (\(\varepsilon_{T}\)) can be expressed using the following equation:  
\[\varepsilon_{T}=\varepsilon_{f}+\varepsilon_{u}=\alpha\Delta T+\beta\Delta T=( \alpha+\beta)\Delta T=\gamma\Delta T \tag{1}\]  
where \(\alpha\) is the thermal expansion coefficient of the object; \(\beta\) is the temperature-resistance effect of the strain gauge; and \(\gamma\) is the combined temperature effect coefficient (\(\gamma=\alpha+\beta\)). Mechanical strain monitoring for steel beams and concrete beams was the study subject of this paper. There was a need to perform separate tests to obtain the combined temperature effect coefficients (\(\gamma\)) for the strain gauge attached to steel and the strain gauge attached to concrete. First, a strain gauge (model number: FLA-10, Tokyo Sokki Kenkyujo Co., Ltd. (TML), Tokyo, Japan, length: 10 mm) was affixed on the steel beam, and the steel beam was placed in a temperature-controlled box as illustrated in Figure 2a. During the experiment, a sample was obtained per minute and the temperature underwent changes from 20 to 52 \({}^{\circ}\)C. Figure 2b shows the relationship of the strain changes and temperature changes within the temperature-controlled box in the experiment; through linear regression, the slope of the regression equation was obtained to be approximately 5.45, meaning that, under unit temperature changes, the combined temperature effect coefficient (\(\gamma\)) of the FLA-10 mm strain gauge affixed to the steel beam was 5.45 \(\mu\)c/\({}^{\circ}\)C.  
Next, this study measured the combined temperature effect coefficient (\(\gamma\)) of the strain gauge (PFL-20) attached to the concrete beam. Because the size of the concrete specimen was relatively large, the temperature change test was conducted outdoors as illustrated in Figure 3a. During the test, a box was used to shield the specimen from direct sunlight. Figure 3b depicts the relationship of the strain changes and temperature changes. Through linear regression analysis, the slope of the regression equation was obtained as approximately 20.17, meaning that, under unit temperature change, the combined temperature effect coefficient (\(\gamma\)) of the strain gauge (PFL-20 mm) attached to the concrete specimen was 20.17 \(\mu\)  
Figure 2: The combined temperature effect coefficient \(\gamma\) value test of a strain gauge (FLA-10) attached to the steel beam: (**a**) temperature-controlled box test; (**b**) strain change and temperature change relationship. To verify the test results of the combined temperature effect coefficient (\(\gamma\)) of the aforementioned resistance strain gauge, the study used a glass ceramic plate manufactured by Zerodur, Germany with an extremely small thermal expansion coefficient of \(2\times 10^{-8}\)/\({}^{\circ}\)C as the base material for the test; the size of the glass ceramic was \(150\times 150\times 5\) mm. For the test, a variety of resistance strain gauge models were affixed on the glass ceramic as shown in Figure 4 and the glass ceramic was placed in a temperature-controlled box. The temperature-resistance effect coefficient (\(\beta\)) of the strain gauge was obtained under the conditions that the base material exhibited no thermal expansion or contraction.