# Decision Support Model for Allocating Maintenance Budgets for Bridges
## 5 Example Project  
A hypothetical network of four bridges is used as an example project to illustrate the methodology and the features of the proposed model. Tables 6-8 summarize the data for the example project. Table 6 depicts the information provided by the bridge engineer, which is the input data to the BMS based on their evaluation of the bridges. These data include condition assessment, bridge age in years, bridge location, the last previous maintenance in years, scheduled maintenance in years, and traffic volume. This information is to be used to determine the score of each posterization criteria. Table 7 depicts the details of the bridge's structural elements, namely bridge deck and parquet, bearing pads, expansion joint, abutment walls, pier columns, and foundations. In addition, the table depicts the quantity take-off for each structural element. Table 8 depicts the maintenance cost for bridge structural elements which can be carried out by the bridge engineer or through the quotation of the maintenance contractor. The bridges are of the same type, i.e., conventional reinforced concrete bridges. Equation (4) below is a sample calculation to demonstrate the use of the utility curves to determine the equivalent utility values, and then the overall bridge rank. For example, the overall condition assessment of bridge 1 can be calculated as follows:  
Overall score of condition assessment of bridge = 0.0061(X)\({}^{2}\) - 0.2217(X) + 1.2281 \begin{table}
\begin{tabular}{c c c c c} \hline  & **Bridge 1 (B1)** & **Bridge 2 (B2)** & **Bridge 3 (B3)** & **Bridge 4 (B4)** \\ \hline Condition assessment & 4 & 6 & 3 & 5 \\ Age (years) & 15 & 9 & 23 & 26 \\ Location & Industrial & Industrial & Commercial & Political \\ Previous maintenance (years) & 10 year. ago & 0 & 15 & 5 \\ Scheduled maintenance (years) & 5 year. later & 6 & 0 & 10 \\ Traffic volume (ADT) & 78,563 & 89,487 & 54,127 & 104,369 \\ \hline \end{tabular}
\end{table} 
Table 6: Bridge information. \begin{table}
\begin{tabular}{c c c c c c} \hline  & & \multicolumn{4}{c}{**Condition Assessment**} \\  & & **Bridge 1 (B1)** & **Bridge 2 (B2)** & **Bridge 3 (B3)** & **Bridge 4 (B4)** \\ \hline Bridge Deck and Parapet & M\({}^{2}\) & 4 & 6 & 3 & 5 \\ Bearing Pads & EA & 3 & 5 & 4 & 5 \\ Expansion Joint & LM & 5 & 4 & 3 & 4 \\ Abutment Walls & M\({}^{3}\) & 4 & 6.5 & 2 & 3 \\ Pier Columns & M\({}^{3}\) & 4 & 6.5 & 2 & 6 \\ Foundations & M\({}^{3}\) & 4 & 7 & 4 & 6 \\ \hline  & & \multicolumn{4}{c}{**Quantity**} \\  & & **Bridge 1 (B1)** & **Bridge 2 (B2)** & **Bridge 3 (B3)** & **Bridge 4 (B4)** \\ \hline Bridge Deck and Parapet & M\({}^{2}\) & 1314 & 2044 & 876 & 1752 \\ Bearing Pads & EA & 44 & 60 & 24 & 60 \\ Expansion Joint & LM & 53.8 & 68.4 & 39.2 & 68.4 \\ Abutment Walls & M\({}^{3}\) & 860 & 950 & 685 & 890 \\ Pier Columns & M\({}^{3}\) & 350 & 490 & 280 & 420 \\ Foundations & M\({}^{3}\) & 900 & 1125 & 675 & 810 \\ \hline \end{tabular}
\end{table} 
Table 7: Details of bridge structural elements. \begin{table}
\begin{tabular}{c c c c c c} \hline  & **Bridge 1 (B1)** & **Bridge 2 (B2)** & **Bridge 3 (B3)** & **Bridge 4 (B4)** \\ \hline Bridge Deck and Parapet & SAR & 394,200.00 & 613,200.00 & 262,800.00 & 525,600.00 \\ Bearing Pads & SAR & 660,000.00 & 900,000.00 & 360,000.00 & 900,000.00 \\ Expansion Joint & SAR & 134,500.00 & 171,000.00 & 98,000.00 & 171,000.00 \\ Abutment Walls & SAR & 645,000.00 & 712,500.00 & 513,750.00 & 667,500.00 \\ Pier Columns & SAR & 262,500.00 & 367,500.00 & 210,000.00 & 315,000.00 \\ Foundations & SAR & 675,000.00 & 843,750.00 & 506,250.00 & 607,500.00 \\ \hline Total & SAR & 2,771,200.00 & 3,607,950.00 & 1,950,800.00 & 3,186,600.00 \\ \hline \end{tabular}
\end{table} 
Table 8: Maintenance cost for bridge structural elements.