## 4 Application to the RG8 Test
### Results
#### 4.2.1 From 0 to 120 h: Maturation and Cracking Period  
_Relative forces developed in the central section_--Within a given cross-section, three main structural elements were considered: concrete, rebar, and struts. From the strain gauges located on the rebar, and assuming that they remain elastic, it is straightforward to deduce the stress acting at a given time on each element, from which the force \(F_{rb}\) absorbed by the set of reinforcements within a given section can be deduced. Strain gauges were also placed on the struts. With knowledge of the strut surface area, the force \(F_{st}\) being exerted on them can also be deduced. At a given time, each cross-section is in equilibrium. From this balance, the force \(F_{c}\) supporting the concrete section can be deduced as:  
\[F_{c}(t)=-[F_{rb}(t)+F_{st}(t)]=-[\Sigma(E_{s}\varepsilon_{i}(t)A_{i})+2E_{s} \varepsilon_{st}(t)A_{st}] \tag{17}\]  
in which \(E_{s}\) is the Young's modulus for steel, \(A_{i}\) and \(\varepsilon_{i}\) are, respectively, the area and strain on rebar i \(I\), and \(A_{st}\) and \(\varepsilon_{st}\) are, respectively, the cross-sectional area of each strut and corresponding strain. The evolution in these three global forces is compared in Figure 4b. It should be emphasized that the comparison between calculation (solid line) and experiment (dashed line) is in good agreement. After a period during which the struts are in tension and both the concrete and rebar in compression, the sign of the forces changes at around 50 h, with an initial crack appearing on the concrete (hour 71 measured and hour 76 calculated). Due to bending caused by the gravity load, the crack is located in the central beam section. This phenomenon leads to a concrete force peak followed by a sudden decrease of this force, with a concurrent increase in the rebar-related force. At 103 h, the calculation forecasts a second series of cracking, which, due to the diffuse description of the damage, appears to be an extension on both sides of the previous cracking area (Figure 4c). This second cracking process was observed experimentally at approx. 167 h.  
_Local stress evolution in the rebar_. During this restrained shrinkage process, the rebar remained elastic. Figure 5b provides the stress evolution over time that corresponds to both the upper rebar (blue line) and lower rebar (red line) in the central section for the first 100 h. The jump caused by rebar loading due to the initial cracking is clearly visible. For the lower rebar, this jump has been  
Figure 4: Evolution during the 0–120 h time frame: (**a**) the 3 section elements: struts (red), rebar (blue), concrete (green); (**b**) global forces supported by the 3 systems in the central beam section (dashed line: experiment—solid line: calculation); and (**c**) damage contour at 76 h (time of initial cracking) and 103 h (time of extended cracking). correctly predicted, and the difference obtained for the upper rebar is the counterpart due to use of the Timoshenko beam approach (a plane section remains plane, which is not the case in practice). Figure 5a shows the same stress evolution but outside the cracking zone (this section lies roughly 1 m from the central section). For both the pre-cracking experiment and calculation (at about 70 h), the evolution in this section is the same as in the central section. After this time threshold, the stress only evolves slightly and, due to concrete shrinkage, stress in the rebar remains negative. _Cracking and crack opening_. The experimenters placed three optic fibers in the beam, as shown in Figure 6. The active zone of the fibers lies at 2.50 m. On the same beam portion, changes in displacement have been compared (experiment vs. calculation). The offset between the two series of curves (dashed line: experiment--solid line: calculation) is due to the difficulty encountered in setting the reference zero on the optic fibers, but in both cases a spike clearly appears during cracking.