## 3 Results and Discussion
### Relationship between Load and Instrumental Signal
In Table 3, it is observed that all the regression coefficients (slopes) of the linear model rejected the null hypothesis. Furthermore, significant differences in the magnitude of the slope of the linear model were identified between sensors, which implies that the regression coefficient was individual for each one. The mean values for the slope of the linear model were lower for the sensors G1, G3, and G5, which had an embedment ratio of 0.30-0.45 from the axis of the sensing area of the strain gauge. The confidence intervals for these sensors were narrower than those of G2, G4, and G6. On the other hand, the intercept values for G2, G4, G5, and G6 were significantly different from zero. This is attributed to a shift in the initial voltage of the instrumental signal, which was different from the initial value of the instrumental signal at the beginning of the test only for sensor G1 (see  
Figure 7: Estimation error of the dimensionless load, \(\mathrm{P/P_{max}}\). Tables 2 and 3). Although the difference between the values of the instrumental signal, V\({}_{\rm so}\), was greater than 18% for sensors G2 and G4, it was not considered significant because of the broad confidence interval of the intercept due to the absence of a perfect embedment. Thus, the V\({}_{\rm so}\) value was an important source of uncertainty for the linear model that only influenced the intercept of the model. This is due to the settling of the sensor before taking the load and determining the moment when the loading nose touched the surface of the sensor. Nevertheless, the uncertainties regarding the coupling time between the load and the instrumental signal were reduced by using 1-s time-weighted average intervals. On the other hand, Figure 7 shows the approximation error concerning the maximum load of the linear model between load and instrumental signal, according to the dimensionless load (P/P\({}_{\rm max}\)). In Figure 7, it can be noticed that the greatest relative errors of approximation of the linear model were presented for the strain gauges embedded on the edge or in the center of the sensing area (G2, G4, and G6), which implied an error in the specification of the regression model used. On the other hand, for the embedment ratios close to 0.30-0.45 from the central axis of the sensing area (G1, G2, and G4), the linear model adequately approached the data obtained between the values 0.2 and 0.8 of the dimensionless load and showed a relative error inferior to 5%. This can lead to the conclusion that the location of the embedment relative to the strain gauge was the main factor affecting the regression model. Provided that this embedment was located within 30% to 45% of the sensing area, a linear response between the load and the instrumental signal was obtained. Alternatively, Figure 8 shows an inverse relationship between the slope of the load-instrumental signal curve and the location of the embedment concerning the central axis of the sensing area (embedment ratio). Figure 8 also shows an inverse relationship between the maximum load on each sensor and the embedment ratio. The foregoing is because both the maximum load and the slope of the load-instrumental signal curve were inversely related to the distance of application of the loading nose. This is because the location of the embedment (k) on the sensor was a fraction of the distance of application of the loading nose (x\({}_{\rm o}\)). Thus, both P\({}_{\rm max}\) and x\({}_{\rm o}\) influenced the values of the parameters of the linear regression model, intercept, and slope; however, they did not affect the specification of the model, which depended solely on the location of the embedment within the sensing area. Figure 8: Slope and maximum load versus embedment ratio.