# Studying the Cable Loss Effect on the Seismic Behavior of Cable-Stayed Bridge
## 2 Three-Dimensional FE Model of the Cable-Stayed Bridge
### Material Properties and Cable Pre-Tension of FE Model  
The pylons (PY1, PY2), main girder, stringer, floor beam, and concrete slab were modeled using the elastic material model *MAT_ELASTIC offered in LS-DYNA, and the cables were modeled using the *MAT_CABLE_DISCRETE_BEAM material model which allows for direct input of cable pre-tension. The properties applied to the material model are shown in Table 1, and the pre-tension forces introduced into the cables are shown in Table 2.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Element** & **Strand** & **Fracture** & **Yield** & **Pre-tension** & **Element** & **Strand** & **Fracture** & **Yield** & **Pre-tension** \\
**No** & **(EA)** & **(K)** & **(K)** & **(K)** & **No** & **(EA)** & **(K)** & **(K)** & **(K)** \\ \hline B6101 & 91 & 24,103 & 21,425 & 4963 & B6137 & 91 & 24,103 & 21,425 & 5252 \\ B6102 & 91 & 24,103 & 21,425 & 5117 & B6138 & 91 & 24,103 & 21,425 & 5630 \\ B6103 & 91 & 24,103 & 21,425 & 5466 & B6139 & 75 & 19,865 & 17,658 & 6652 \\ B6104 & 91 & 24,103 & 21,425 & 6917 & B6140 & 75 & 19,865 & 17,658 & 6080 \\ B6105 & 73 & 19,336 & 17,187 & 6013 & B6141 & 71 & 18,806 & 16,716 & 5673 \\ B6106 & 67 & 17,746 & 15,774 & 5853 & B6142 & 66 & 17,481 & 15,539 & 5083 \\ B6107 & 64 & 16,952 & 15,068 & 4999 & B6143 & 64 & 16,952 & 15,068 & 4571 \\ B6108 & 61 & 16,157 & 14,362 & 5153 & B6144 & 61 & 16,157 & 14,362 & 4301 \\ B6109 & 61 & 16,157 & 14,362 & 5164 & 6145 & 61 & 16,157 & 14,362 & 3379 \\ B6110 & 55 & 14,568 & 12,949 & 3931 & B6146 & 55 & 14,568 & 12,949 & 3786 \\ B6111 & 55 & 14,568 & 12,949 & 3366 & B6147 & 55 & 14,568 & 12,949 & 3134 \\ B6112 & 48 & 12,714 & 11,301 & 2895 & B6148 & 48 & 12,714 & 11,301 & 3045 \\ B6113 & 48 & 12,714 & 11,301 & 3549 & B6149 & 48 & 12,714 & 11,301 & 2934 \\ B6114 & 48 & 12,714 & 11,301 & 3395 & B6150 & 44 & 11,654 & 10,359 & 2754 \\ B6115 & 44 & 11,654 & 10,359 & 2469 & B6151 & 44 & 11,654 & 10,359 & 3472 \\ B6116 & 44 & 11,654 & 10,359 & 2365 & B6152 & 44 & 11,654 & 10,359 & 3535 \\ B6117 & 37 & 9800 & 8711 & 2460 & B6153 & 37 & 9800 & 8711 & 2794 \\ B6118 & 55 & 14,568 & 12,949 & 3433 & B6155 & 55 & 14,568 & 12,949 & 4390 \\ B6120 & 37 & 9800 & 8711 & 2807 & B6156 & 37 & 9800 & 8711 & 2884 \\ B6121 & 44 & 11,654 & 10,359 & 3438 & B6157 & 44 & 11,654 & 10,359 & 2148 \\ B6122 & 44 & 11,654 & 10,359 & 3265 & B6158 & 44 & 11,654 & 10,359 & 2392 \\ B6123 & 44 & 11,654 & 10,359 & 2650 & B6159 & 48 & 12,714 & 11,301 & 3047 \\ B6124 & 48 & 12,714 & 11,301 & 2702 & B6160 & 48 & 12,714 & 11,301 & 3549 \\ B6125 & 48 & 12,714 & 11,301 & 3413 & B6161 & 48 & 12,714 & 11,301 & 3697 \\ B6126 & 55 & 14,568 & 12,949 & 3515 & B6162 & 55 & 14,568 & 12,949 & 3895 \\ B6127 & 55 & 14,568 & 12,949 & 4238 & B6163 & 55 & 14,568 & 12,949 & 3939 \\ B6128 & 61 & 16,157 & 14,362 & 3803 & B6164 & 61 & 16,157 & 14,362 & 4197 \\ B6129 & 61 & 16,157 & 14,362 & 4300 & B6165 & 61 & 16,157 & 14,362 & 4816 \\ B6130 & 64 & 16,952 & 15,068 & 4394 & B6166 & 64 & 16,952 & 15,068 & 5344 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Seohae Bridge cable list.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Part** & **Classical** & **Yield** & **Density** & **Poisson’s Ratio** \\  & **Modulus** & **Stress** & **(ton/m3)** & **Poisson’s Ratio** \\  & **(MPa)** & **(MPa)** & **(MPa)** & **(ton/m3)** & **Poisson’s Ratio** \\ \hline Pylon & 33.76 & - & 2.50 & 0.167 \\ Main Girder & 210 & - & 7.85 & 0.300 \\ Stringer & 210 & - & 7.85 & 0.300 \\ Floor Beam & 210 & - & 7.85 & 0.300 \\ Deck Slab & 33.76 & - & 2.5 & 0.167 \\ Cable & 200 & 1569.6 & 7.87 & 0.300 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Material properties of FE model.  
The cables applied to the target bridge are composed of multi-strand cables with a bundle of 15.7 mm strands. Each 15.7 mm strand has a cross-sectional area of 150 mm\({}^{2}\), with an ultimate stress of 1760 MPa and a yield stress of 1570 MPa. Material property and cable strand data were applied to the FE model by referencing the design report [16].