## 1 Introduction
### Structure Characterization of a Simply Supported Composite Beam Bridge  
This study focuses on a simply supported steel-concrete composite beam bridge located on Shanghai Metro Line 3, where on-site strain monitoring of the composite section was conducted. Built in 1997, the bridge features a structure comprising bottom I-shaped steel beams and an upper concrete slab. The standard span of the bridge is 45.0 m, with a calculated span of 44.0 m. The bottom I-beams are constructed from Q345 steel, while the upper concrete slab is composed of C40 concrete. The lower part of the composite section consists of four horizontally arranged I-beams totaling 2376 mm in height. Each I-beam web measures 2316 mm in height with a 14 mm thickness. The upper flange plate of the I-beam is 500 mm wide and 30 mm thick, while the lower flange plate is 600 mm wide and 30 mm thick. Additionally, within a 30 m range at the mid-span of the bridge, the lower flange of the composite section's I-beams features localized thickening, with a plate width of 480 mm and a thickness of 24 mm. The upside concrete slab varies in thickness from 180 to 300 mm and spans a width of 8900 mm. Diaphragms, 2200 mm high and 12 mm thick, are installed longitudinally every 4 m between the bottom I-beams to enhance lateral connection and girder structure stability. Vertical stiffening plates, 2200 mm high, 220 mmwide, and 12 mm thick, are placed every 2 m. Figure 1 depicts the layout and cross-section diagram of the simply supported steel-concrete composite beam bridge.  
Shanghai Metro Line 3 operates AC03-type trains manufactured by ALSTOM, each measuring 140 m in total length. The AC03 train configuration consists of a 6-carriage formation comprising two end locomotives (Tc) and four middle carriages (Mp). The locomotive weighs 32 t and spans 24.4 m, while each middle carriage weighs 35.65 t and measures 22.8 m in length. The train adheres to a standard lateral gauge of 1435 mm, with each carriage having a lateral width of 3.0 m. Every carriage is equipped with four axles, with each pair sharing a bogie. The long wheelbase within a single carriage is 15.7 m, and the short wheelbase is 2.5 m. The adjacent wheelbase between the two carriages is 4.6 m. Seating capacity includes 54 seats in the locomotive and 58 seats per carriage, accommodating up to 270 passengers (at 6 people/m\({}^{2}\)) when fully loaded. The composition of the AC03 train is depicted in Figure 2. To simplify the train load, the weight of each carriage is evenly distributed across its four axles. Due to the negligible difference in wheelbase between adjacent axles within the same bogie, they are merged in the train axle load model as a single calculated axle positioned at the midpoint between the two short wheels, carrying half of the carriage's weight [24]. Consequently, the AC03 train is modeled with 12 calculated axles labeled \(p_{1}\) to \(p_{12}\) from front to back. The model assumes an even distribution of crowd load within each carriage, transmitted equally to two calculated axles per carriage. The simplified train axle load model of the AC03-type train is illustrated in Figure 2.  
Figure 1: Structural and field measurement details of the simply supported steel-concrete composite beam bridge on Shanghai Metro Line 3.  
Figure 2: Simplified train axle load model of AC03 type train on Shanghai Metro Line 3 (unit: m).