## 5 Results
### Analysis of Accuracy and Reproducibility
Current guidelines [30,31] recommended that for stress measurement in masonry elements, the gage length \(l\) should be composed between 0.3 and 0.6 times the flat-jack primary dimension \(L\) defined in Figure 3. However, no specific guidance exists for concrete elements. In this study, gage lengths of 14 cm and 20 cm were chosen as practical options for in situ testing of post-tensioned concrete beams. The 14 cm gage length corresponded to an \(l/L\) ratio of 0.56 with the 25 cm flat jack and 0.42 with the 33 cm flat jack. With the 20 cm gage length, these ratios were 0.80 and 0.61. As shown in Figure 11, the deformation pattern on the measurement area of the concrete slab under the incremental application of the axial load was more consistent when the smaller (14 cm) gage length was considered. This observation suggested that the stress redistribution was more uniform or predictable over this shorter distance. The inference was confirmed by the data in Tables 3 and 4, which clearly demonstrated that the 14 cm gage length provided better accuracy (lower average error \(E\)) across both flat jacks. Conversely, no clear trend was observed regarding repetitiveness. Inconsistent stress redistribution due to the cutting process could lead to either overestimation or underestimation depending on how strains were measured and recovered. Interestingly, with the 20 cm gage length, the accuracy tended to improve at higher stress levels, while the 14 cm gage length exhibited the opposite trend. However, these specific patterns were not further explored in this preliminary study. A second influential factor, also exhibiting characteristics of a systematic error due to its direct relation to the testing setup, concerned the dimensions of the flat jack. As shown in Tables 3 and 4, the 33 cm flat jack generally provided more accurate estimates when combined with the 14 cm gage length. With the 20 cm gage length, the accuracy was similar to the 25 cm device but at 2 MPa. The _CoV_ was similar at 2 and 3 MPa, but it halved for the 33 cm instrument at 4 MPa, indicating improved consistency at higher stress levels with the larger jack. However, since only two tests were conducted with the larger flat jack, no definitive conclusions should be drawn from this observation alone. The observed variability, including both overestimation and underestimation of stress, was likely a consequence of the flat-jack test's interaction with the inherent heterogeneity of concrete, the localized nature of the measurement, and the specific geometric parameters of the test setup (gauge length and flat-jack size). It is worth mentioning that random sign of the error (either positive or negative) is typical of the flat-jack test on masonry as well: the American standard [3] indeed reports that \"laboratory studies have shown that the in situ stress test exhibits no inherent bias in predicting the state of compressive stress present in the masonry, that is, the method may over or under estimate the actual compressive stress\". A plausible explanation for the improved performance of the larger flat jack was its size, and specifically its height as shown in Figure 5c, relative to the maximum aggregate size of the concrete. The 25 cm flat jack penetrated to a depth of 5 cm in the slab, whereas the 33 cm flat jack penetrated to 12 cm. The larger surface of the 33 cm flat jack likely allowed it to interact with a sufficiently large volume of concrete such that the material could be effectively considered a more homogeneous medium, thereby reducing the influence of individual aggregate particles on the stress measurement. On the other hand, with the 25 cm flat jack, the heterogeneity of the concrete across the smaller surface of the device may not be negligible, contributing to higher variability. The statistical scatter (e.g., 43% for the 25 cm flat jack at 2 MPa with a 14 cm gauge length) directly reflected this localized interaction with the material's heterogeneity.