## 3 Estimation of Reinforcement Strain
### Estimation Results
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Type**} & \multicolumn{5}{c}{**Estimated Strain (\(\chi 10^{-6}\) mm/mm)**} \\ \cline{2-5}  & & **At Yield Load (\(\epsilon_{y\#}^{*}\))** & **Ratio (\(\epsilon_{y\#}^{*}\)/\(\varepsilon_{y}\))** & **At Ultimate Load (\(\epsilon_{\text{aM}}^{*}\))** & **Ratio (\(\epsilon_{\text{aM}}^{*}\)/\(\epsilon_{y\#}^{*}\))** \\ \hline \multirow{3}{*}{\
\begin{tabular}{c} First-order \\ formula \\ \end{tabular} } & E1-1 & 1676.33 & 0.838 & 1974.72 & 1.178 \\  & E2-1 & 1699.55 & 0.850 & 2009.07 & 1.182 \\  & EH-1 & 1426.84 & 0.713 & 1799.2 & 1.261 \\  & Average & 1600.91 & 0.800 & 1927.66 & 1.204 \\ \hline \multirow{3}{*}{
\begin{tabular}{c} Second-order \\ formula \\ \end{tabular} } & E1-2 & 621.90 & 0.311 & 920.2 & 1.480 \\  & E2-2 & 645.10 & 0.323 & 954.54 & 1.480 \\ \cline{1-1}  & EH-2 & 775.95 & 0.388 & 1148.25 & 1.480 \\ \cline{1-1}  & Average & 680.98 & 0.340 & 1007.66 & 1.480 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Estimated strains of the integral specimen at the yield and ultimate loads. Figure 7: Estimated steel reinforcement strain: (**a**) integral specimen; (**b**) modular specimen. Regarding the estimated strain at the yield load (Table 5), the average strains estimated using the first- and second-order formulas were 80% and 34%, respectively, of the yield strain (\(2000\times 10^{-6}\) mm/mm). The strains of the ultimate load, estimated using the first- and second-order formulas, were 20.4% and 48% higher, respectively, than the estimated strains of the yield load. At the yield-load stage, the strain estimated using the first-order formula reflected the behavior of the integral specimen, and the second-order formula underestimated the strain compared with the first-order formula. Regarding the estimated strain at the yield load (Table 6), the average strains, estimated using the first- and second-order formulas, were 137.2% and 91.2%, respectively, of the yield strain (\(2000\times 10^{-6}\) mm/mm). The strains at the ultimate load, estimated using the first- and second-order formulas, were 53.6% and 80.6% higher, respectively, than the estimated strains at the yield load. The average increment of the estimated strain from the yield load to the ultimate load was 450% that of the integral specimen. At the yield load stage, the strain estimated using the second-order formula reflected the behavior of the modular specimen, and the second-order formula underestimated the strain compared with the first-order formula. The estimated strains for the integral and modular specimens are compared in Table 7. All the estimated strains of the modular specimen were greater than those of the integral specimen. At the yield loads, the estimates based on the first- and second-order formulas were 71.4% and 167.9% larger, respectively, than those for the integral specimen. At the ultimate loads, the estimates based on the first- and second-order formulas were 118.7% and 227.0% larger, respectively, than those for the integral specimen. These results are attributed to the fact that for the modular specimen, the steel reinforcement of the discontinuity bore a greater load compared with the integral specimen owing to the larger crack width. Therefore, if the same load is applied, the steel reinforcement yield at a discontinuity in the modular specimen would occur earlier than that in the integral specimen. Table 8 presents the estimated strains at the service, yield, and ultimate loads for comparing the estimated strain changes of the integral and modular specimens. The estimated strains were obtained using the first-order formula for the integral specimen and the second-order formula for the modular specimen, so that the steel reinforcement yielded when the yield load was reached. The service load was applied as 60% of the yield load, which is generally considered to be the serviceability limit state. The average estimated strain of the modular specimen at the service load was 12.9% lower than that of the integral specimen.