# Effects of Freeze-Thaw and Wet-Dry Cycles on Tension Stiffening Behavior of Reinforced RAC Elements
## 3 Results and Discussion
### Effects of Freeze-Thaw and Wet-Dry Aging on Main Properties of Reinforced RAC Elements
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Mixtures**} & \multirow{2}{*}{**ID**} & \multicolumn{4}{c}{**Pre-Cracking Phase**} & \multicolumn{4}{c}{**Post-Cracking Phase**} & \multicolumn{2}{c}{**Isolated Matrix**} \\ \cline{3-10}  & & **E\({}_{\text{pre}}\)** & **f\({}_{\text{1 st}}\)** & \(\epsilon_{\text{1 st}}\) & \(\epsilon_{\text{final}}\) & **E\({}_{\text{post}}\)** & **f\({}_{\text{m,1 st}}\)** & **f\({}_{\text{m,final}}\)** \\  & & **(GPa)** & **(MPa)** & **(\(\upmu\)c)** & **(\(\upmu\)c)** & **(GPa)** & **(MPa)** & **(MPa)** & **(MPa)** \\ \hline \multirow{4}{*}{C35-NAT} & REF(WD25) & 25.8 (2.0) & 2.54 (1.6) & 89 (1.0) & 486 (11.0) & 2.71 (1.6) & 2.34 (1.8) & 1.40 (1.7) \\  & WD25 & 25.0 (1.4) & 2.49 (1.3) & 90 (2.6) & 466 (6.8) & 2.59 (2.9) & 2.28 (1.2) & 1.31 (3.2) \\  & REF(WD50) & 26.3 (1.0) & 2.70 (1.7) & 93 (2.3) & 467 (6.2) & 2.67 (1.8) & 2.48 (1.7) & 1.40 (4.2) \\  & WD50 & 23.5 (2.5) & 2.44 (2.7) & 94 (0.6) & 479 (7.7) & 2.69 (5.2) & 2.22 (2.9) & 1.23 (3.9) \\ \hline \multirow{4}{*}{C35-L-C1} & REF(WD25) & 26.1 (0.3) & 2.88 (0.9) & 99 (1.1) & 469 (12.3) & 2.48 (4.2) & 2.65 (0.9) & 1.57 (6.4) \\  & WD25 & 24.7 (0.7) & 2.74 (0.6) & 100 (1.2) & 507 (8.0) & 2.76 (3.7) & 2.51 (0.6) & 1.37 (7.6) \\ \cline{1-1}  & REF(WD50) & 26.7 (2.4) & 2.98 (0.4) & 101 (2.9) & 517 (6.1) & 2.67 (1.8) & 2.76 (0.4) & 1.59 (2.4) \\ \cline{1-1}  & WD50 & 22.3 (2.6) & 2.54 (3.9) & 103 (6.0) & 481 (4.1) & 2.62 (8.1) & 2.30 (4.3) & 1.19 (2.5) \\ \hline \multirow{4}{*}{C35-D-C1} & REF(WD25) & 25.5 (2.7) & 2.71 (2.2) & 96 (0.7) & 480 (4.7) & 2.49 (4.0) & 2.49 (2.4) & 1.54 (2.0) \\ \cline{1-1}  & WD25 & 24.4 (1.8) & 2.62 (2.7) & 97 (4.5) & 494 (5.2) & 2.67 (2.5) & 2.40 (2.6) & 1.37 (7.5) \\ \cline{1-1}  & REF(WD50) & 26.5 (4.0) & 2.80 (0.7) & 95 (3.5) & 507 (11.7) & 2.63 (5.6) & 2.58 (1.0) & 1.61 (6.9) \\ \cline{1-1}  & WD50 & 23.1 (0.5) & 2.48 (1.7) & 97 (2.2) & 454 (3.4) & 2.83 (3.1) & 2.25 (1.6) & 1.26 (2.8) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Main representative parameters for tested reinforced elements subjected to wet-dry cycles. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Mixtures**} & \multirow{2}{*}{**ID**} & \multicolumn{4}{c}{**Pre-Cracking Phase**} & \multicolumn{4}{c}{**Post-Cracking Phase**} & \multicolumn{2}{c}{**Isolated Matrix**} \\ \cline{3-10}  & & **E\({}_{\text{pre}}\)** & **f\({}_{\text{1 st}}\)** & \(\epsilon_{\text{1 st}}\)** & **\(\epsilon_{\text{final}}\)** & **E\({}_{\text{post}}\)** & **f\({}_{\text{m,1 st}}\)** & **f\({}_{\text{m,final}}\)** \\  & & **(GPa)** & **(MPa)** & **(\(\upmu\)c)** & **(\(\upmu\)c)** & **(GPa)** & **(MPa)** & **(MPa)** \\ \hline \multirow{4}{*}{C35-NAT} & REF(FT150) & 25.8 (2.0) & 2.54 (1.6) & 89 (1.0) & 486 (11.0) & 2.71 (1.6) & 2.34 (1.8) & 1.40 (1.7) \\  & FT150 & 24.2 (1.1) & 2.41 (0.6) & 90 (0.6) & 432 (4.5) & 2.65 (4.1) & 2.20 (0.8) & 1.24 (2.0) \\  & REF(FT300) & 26.3 (1.0) & 2.70 (1.7) & 93 (2.3) & 467 (6.2) & 2.67 (1.8) & 2.48 (1.7) & 1.40 (4.2) \\  & FT30  
non-aged and aged specimens (Tables 3 and 4). No relationship was identified between the types of aggregates and the deformation length of the cracking process phase. As expected, the post-cracking elastic modulus of the composite (\(\mathrm{E_{post}}\)) approaches the elastic modulus of the steel rebar. The tension stiffening effect was evaluated by isolating the contribution of the concrete matrix from the composite force-strain diagram. The matrix stress-strain curve is defined by the opening of the first crack, marking the matrix strength to the first crack, \(\mathrm{f_{m,lst}}\). In non-degraded mixes, the highest matrix strength was obtained for C35-L-C1, followed by C35-D-C1. As this property of the composite is directly related to the tensile strength of the matrix, these results are in agreement with the values shown in Table 2, since C35-L-C1 also presented the highest value of \(\mathrm{f_{t,28}}\).