## 3 Force Analysis of Steel Bracket  
The cases of the most unfavorable trainload acting on each of the three lines of this bridge are considered and classified as follows (Figure 7): Case 1: trainload applied on line I; Case 2: trainload applied on line II; Case 3: trainload applied on line IV. The maximum stress of each component in the support system under the three cases is obtained through finite element calculation and analysis, as shown  
From Table 4:  
1. The middle-span steel columns directly bear the trainload transferred by the supporting longitudinal beam and cross-beam when the trainload operates on line I and line II, whereas the trainload acting on line IV has no direct effect on the middle-span steel columns, which only bear the self-weight generated by the superstructure, so the maximum stress of the middle-span steel columns under case 3 is 35% of that under case 1 and 2;
2. The diagonal braces are subjected to the greatest stress among the components in the three cases, whose maximum stress is less than the yield strength of Q235 steel [31], indicating that the entire steel bracket system is in an elastic stage under the trainload, which means that the bracket design can meet the safety requirements. The stress condition of the steel pipe piles can reflect the force law of the bridge and steel support system structure under the trainload for the train, and the superstructure load is mostly passed from the steel pipe piles to the foundation. Figure 8 illustrates the analysis of the stress and displacement cloud diagram of the steel pipe piles in each case. The maximum stress of the steel pipe pile is \(\sigma_{\text{max}}=6.65\text{ MPa }<\text{ f}_{\text{d}}=215\text{ MPa}\), which meets the design requirements. Under these cases, the steel pipe piles located directly below the line of the trainload are subjected to the greatest force. The maximum stress appears at the bottom of the pile, while the maximum displacement appears at the top of the pile, and the magnitude of stress and displacement of the steel pipe piles decreases from the area affected by the trainload to both sides. The steel structure is permitted to deflect up to 1/400 of its span length under the effect of constant load and live load [31]. The allowable deflection of the supporting longitudinal beam in the temporary support is \(2800/400=7\text{ mm}\), and the allowable deflection of the supporting cross beam is \(5000/400=12.5\text{ mm}\). The maximum deflections of the longitudinal beams and cross beams, respectively, are \(2.13\text{ mm}\) and \(2.05\text{ mm}\), which are less than the allowable deflection and satisfy the requirements from Table 5.  
The comparison of case 1 and case 2 demonstrates that the maximum deflection of the longitudinal beams in line IV is 2.07 times and 1.82 times that in line I and line II, respectively, due to a greater distance between the two intersection points of the longitudinal beams and the supporting crossbeams below. At the same time, there are 60 cm diameter middle-span steel columns in the steel brackets under lines I and II to share the force of the side-span steel columns and diagonal braces, which enhances the stiffness of the brackets. As a result, the maximum deflection of the cross beam is 47% of what it is in case 3. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Components**} & \multicolumn{3}{c}{**Maximum Stress (MPa)**} \\ \cline{2-4}  & **Case 1** & **Case 2** & **Case 3** \\ \hline Supporting longitudinal beam & 73.62 & 73.82 & 68.69 \\ Supporting cross beam & 29.09 & 18.71 & 29.79 \\ Diagonal brace & 81.97 & 89.35 & 88.01 \\ Cross linkage & 78.92 & 80.33 & 85.60 \\ Longitudinal linkage & 30.01 & 35.53 & 30.38 \\ Side-span steel column & 23.48 & 20.34 & 15.33 \\ Middle-span steel column & 8.99 & 9.05 & 3.18 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Maximum stress of each component in steel support system.