## 4 Blast Analysis Results
### Deck  
Table 7 summarizes the damage types and maximum stresses of the steel girder in each scenario, for a blast load applied between and above the crossbeams of the superstructure. The slab's displacement and response to rebar stress were not examined, because the analysis results included the occurrence of perforation. In blast analysis between the superstructure crossbeams, the damage range of the slab was found to increase with the blast load; however, the main damage occurred only between the crossbeams. In the damage assessments for each scenario, scabbing of the slab was observed in Scenario A, and slab perforations were observed in Scenarios B-D. When the effective stress and degree of damage of the steel girder were examined, the effective stress was found to increase with the blast load. Furthermore, the maximum stresses in Scenarios A-D were 434, 452, 479, and 509 MPa, respectively, and deformation occurred in the upper flange of the crossbeam. The ultimate strength (f\({}_{\text{u}}\)) of the steel girder was 520 MPa; hence, it was concluded that the steel girder plastically deforms but does not fracture when a blast load is applied between the crossbeams of the superstructure. In the analysis of a blast above the superstructure crossbeam, the damage range of the slab was found to increase with the blast load and was wider than that seen for the blast between the crossbeams. The damage types of each scenario were identical to those of the previous case. When the effective stress of the steel girder was examined, a stress of 602 MPa (exceeding the ultimate strength (f\({}_{\text{u}}\)) of the steel girder (520 MPa)) occurred momentarily in the upper flange and web of the crossbeam in Scenario A; however, it appears that no damage occurred owing to the strain rate effect of the material. In Scenarios B-D, the crossbeam was damaged, and the damage range increased with the blast load. This suggests that in the case of the superstructure, a blast load applied to the crossbeam causes greater damage (and has a larger effect on the structural behavior of the cable-stayed bridge) than the blast load applied between the crossbeams. Figures 9-12 show the damage and effective stress contours generated by the blast load. The fringe range of the effective stress contour was set to 0-520 MPa, considering the ultimate strength of the steel girder; the resulting output time was 0.05 s, at which point the analysis was terminated. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{**Number of Elements**} & **Time Step Size** & **CPU Time** \\  & & **(10\({}^{-6}\) s)** & **(s)** \\ \hline Deck & 198,550 & 4.826–4.943 & 49,670–50,568 \\ Cable no. 37 & 77,868 & 0.861–0.868 & 54,115–56,275 \\ Cable no. 53 & 35,316 & 0.545–0.554 & 37,015–40,345 \\ Cable no. 68 & 65,232 & 0.735–0.745 & 52,948–54,090 \\ Pylon & 917,438 & 7.257–11.092 & 87,009–95,547 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Summary of utilized time step size and CPU time. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Blast Scenario**} & \multirow{2}{*}{**Blast Position**} & **Damage Type of** & \multicolumn{2}{c}{**Steel Girder**} \\  & & **Slab** & **Maximum Stress** & **Damage Type** \\ \hline Scenario A & & Scabbing & 434 MPa & \\ \hline Scenario B & 2 nd lane/ & & 452 MPa & \\ \hline Scenario C & & & 479 MPa & \\ \hline Scenario D & & & 509 MPa & \\ \hline Scenario A & & Scabbing & 602 MPa & Plastic deformation \\ \hline Scenario B & 2 nd lane/ & & - & \\ \hline Scenario C & & & - & Ruptured \\ \hline Scenario D & & & - & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Summary of blast analysis results of the deck. Figure 10: Effective stress contours of the steel girder (between the crossbeams): (**a**) Scenario A, (**b**) Scenario B, (**c**) Scenario C, and (**d**) Scenario D (fringe level unit: MPa).