# Seismic Retrofit of Steel Truss Bridge Using Buckling Restrained Damper
## 2 Analysis Model  
### Model of the Existing Bridge  
The existing truss bridge is a single-span simply supported bridge with a span length of 74.40 m. It has a reinforced concrete upper deck with a width of 10.60 m and a thickness of 200 mm. The schematic of the bridge is given in Figure 2, and the member details, including the steel grades, are shown in Table 1. Steel grades, employed for the truss bridge, are SM490Y (yield stress, \(\sigma_{y}=355\) N/mm\({}^{2}\)) and SM400 (yield stress, \(\sigma_{y}=235\) N/mm\({}^{2}\)). The mass density, Young's modulus, and Poison's ratio of each steel are taken to be \(\rho=7.851\times 10^{-9}\) /mm\({}^{3}\), E \(=2.0\times 10^{5}\) N/mm\({}^{2}\), and \(\
u=0.3\), respectively. Figure 1: Buckling restrained damper (BRD) with a non-yielding part. Moreover, beyond the yield stress, the material stiffness is assumed to be E/100, and the elastic-plastic behavior of von Mises type with kinematic hardening rule is assumed. For the concrete deck, the mass density, Young's modulus, and Poison's ratio are taken to be \(\rho=2.35\times 10^{-9}\) t/mm\({}^{3}\), E = \(2.1\times 10^{4}\) N/mm\({}^{2}\), and \(\
u=0.2\), respectively. The damage in the concrete deck slab is not taken into account in this study; therefore, the simplified elastic model is employed to consider its spatial stiffness and inertia in the dynamic analysis. ABAQUS [12] is used for all the analyses in the present study. A three-dimensional beam-element of type B33 is employed. Ten finite elements are used in the modeling of each member of all the lateral bracings (27-30, 2-3, 1-28, 5-32, etc. in Figure 2), and five finite elements are used for other members of the truss. The joints of each truss member are modeled to be the fully rigid connections since the difference in any types of joints has little effect on the dynamic response of the stress [13]. The concrete \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Name Description** & **Location between the Nodes** & **Cross** & **Web (mm)** & **Flange (mm)** & **Steel Grade** \\
**of Members** & **Numbered in Figure 2** & **Section** & & & \\ \hline Lower chord & 1–5, 21–25, 2–6, 22–26 & & 430 \(\times\) 9 & 450 \(\times\) 10 & SM400 \\  & 5–9, 17–21, 6–10, 18–22 & & 412 \(\times\) 22 & 450 \(\times\) 19 & SM490Y \\  & 9–17, 10–18 & & 400 \(\times\) 25 & 450 \(\times\) 25 & SM490Y \\ Upper chord & 27–33, 45–51, 28–34, 46–52 & & 518 \(\times\) 14 & 450 \(\times\) 16 & SM490Y \\  & 33–37, 41–45, 34–38, 42–46 & & 506 \(\times\) 19 & 450 \(\times\) 22 & SM490Y \\  & 37–41, 38–42 & & 502 \(\times\) 21 & 450 \(\times\) 24 & SM490Y \\ \hline Inclined post & 1–29, 49–25, 2–30, 50–26 & & 412 \(\times\) 28 & 400 \(\times\) 19 & SM490Y \\  & 5–33, 45–21, 6–34, 46–22 & & 418 \(\times\) 22 & 400 \(\times\) 16 & SM400 \\  & 9–37, 41–17, 10–38, 42–18 & & 430 \(\times\) 13 & 400 \(\times\) 10 & SM400 \\ End vertical & 1–27, 2–28, 25–51, 26–52 & & 430 \(\times\) 13 & 400 \(\times\) 10 & SM400 \\ \hline Inclined post & 29–5, 21–49, 30–6, 22–50 & & 422 \(\times\) 14 & 350 \(\times\) 14 & SM490Y \\  & 37–13, 13–41, 38–14, 14–42 & & 430 \(\times\) 11 & 350 \(\times\) 10 & SM400 \\  & 33–9, 17–45, 34–10, 18–46 & & 422 \(\times\) 12 & 350 \(\times\) 14 & SM400 \\ Inner vertical & 5–31, 6–32, and etc. & & 422 \(\times\) 12 & 350 \(\times\) 14 & SM400 \\ Outer vertical brace & 25–52, 26–51, 1–28, 2–27 & & 318 \(\times\) 16 & 350 \(\times\) 16 & SM400 \\ \hline Upper lateral bracing & 27–30, 28–29, and etc. & & 138 \(\times\) 10 & 350 \(\times\) 14 & SM400 \\ \hline Lower lateral bracing & 1–4, 2–3, and etc. & & 180 \(\times\) 10 & 200 \(\times\) 10 & SM400 \\ Floor beam & 27–28, 39–30, and etc. & & 1068 \(\times\) 10 & 350 \(\times\) 16 & SM400 \\ Outer strut & 1–2, 25–26 & & 424 \(\times\) 10 & 400 \(\times\) 13 & SM400 \\ Inner strut & 3–4, 5–6, and etc. & & 230 \(\times\) 10 & 250 \(\times\) 10 & SM400 \\ \hline Inner vertical brace & 5–31, 6–32, 22–48, and etc. & & 140 \(\times\) 16 & 250 \(\times\) 10 & SM400 \\ \hline \hline \end{tabular}
\end{table}