## 3 Results and Discussion  
Figure 8 shows the curvature diagram according to the load for each case. Based on these diagrams, the deflections under the following applied moments were calculated using Equation (1): \(M_{cr}\), which is the moment immediately prior to the application of the cracked moment; \(M_{cr}^{{}^{\prime}}\), which is the moment immediately following the application of the cracked moment; \(1.5M_{cr}\); \(2M_{cr}\); and \(2.5M_{cr}\).  
Table 4 gives the results and Figures 9 and 10 display the load-deflection curves. All calculated cases exhibited an increase in the difference in deflection as the load increased. However, after \(1.5M_{cr}\), the difference decreased as the slope of the deflection of the modular specimen decreased. For Case 1, the deflection was accurately predicted to be a ratio of 0.74 compared to the experimental result before the application of the cracking moment. The deflection was overestimated after the application  
Figure 8: Proposed curvature diagrams for the modular specimen: (**a**) Case 1; (**b**) Case 2; (**c**) Case 3; (**d**) Case 4.  
of the cracking moment as it dramatically increased to a ratio of 1.38. For Case 2, which reflects the attached transmission length, the deflection was overestimated for all loads with a ratio ranging from 1.21 to 1.7. For Case 3, the deflection ratio before the application of the cracking load was 0.32, which is the most underestimated ratio of all cases. However, after the cracking moment was applied, the deflection was most accurately predicted for ratios ranging from 0.96 to 1.17. Case 4 somewhat accurately predicted the deflections for both before and after the application of the cracking load. The former had a value of 0.78, whereas the latter ranged from 1.02 to 1.28. The error rates were calculated to be 36.5%, 46.6%, 22.8%, and 19.5% for the four cases, respectively.  
Reflecting the attached transmission length to the left and right sides of the initial cracked surface below the cracking moment and considering that cracking occurs on the UHSC when the failure load is reached were effective to calculate the deflection of the precast modular slab with a joint. Because the steel reinforcements connected in the lapped splice shared the tensile forces on the left and right  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Load**} & \multirow{2}{*}{**Modular**} & \multicolumn{2}{c}{**Case 1**} & \multicolumn{2}{c}{**Case 2**} & \multicolumn{2}{c}{**Case 3**} & \multicolumn{2}{c}{**Case 4**} \\ \cline{3-10}  & & **mm** & **Ratio** & **mm** & **Ratio** & **mm** & **Ratio** & **mm** & **Ratio** \\ \hline \(M_{cr}\) & 3.47 & 2.57 & 0.74 & 4.21 & 1.21 & 1.12 & 0.32 & 2.7 & 0.78 \\ \(M_{cr}^{\prime}\) & 3.56 & 4.92 & 1.38 & 6.04 & 1.7 & 3.40 & 0.96 & 4.47 & 1.26 \\ \(1.5M_{cr}\) & 6.32 & 9.79 & 1.55 & 10.45 & 1.65 & 7.41 & 1.17 & 8.06 & 1.28 \\ \(2M_{cr}\) & 10.86 & 13.83 & 1.27 & 14.27 & 1.31 & 10.64 & 0.98 & 11.07 & 1.02 \\ \(2.5M_{cr}\) & - & 17.63 & - & 17.95 & - & 13.64 & - & 13.95 & - \\ \hline Avg. error & - & 0.365 & & 0.4675 & & 0.2275 & & 0.195 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Deflection results.  
Figure 10: Load and deflection curves of Cases 3 and 4.  
Figure 9: Load and deflection curves of Cases 1 and 2.  
sides of the cracked surface, tensile stress in UHSC minimized when the separation of the joint occurred and UHSC is assumed non-cracking section until fail the specimen.