## 3 Bridge Case Study  
### FE Modeling  
A top-stiffened steel truss bridge comprising nine main trusses with a span arrangement of 124 m + 132 m + 132 m + 168 m + 300 m + 168 m + 132 m + 132 m + 124 m was selected as a case study, as shown in Figure 2. The bridge had two layers; the upper layer was a six-lane road, and the lower layer was a four-lane road and two-track railway. Sidewalks on both sides were also cantilevered on the lower layer. Two upper stiffening rods were arranged in the middle three spans.  
The horizontal chords were box-shaped cross-sectionally, the web members were h-shaped cross-sectionally, the bridge slabs were orthotropic, the upper stiffening rods were rectangle-shaped cross-sectionally, and the booms consisted of parallel steel wires. The substructure included two abutments and eight piers. W1 and W10 were joint piers, which combined an upper road pier and a lower rail pier. The others were hollow piers with 6 \(\times\) 8-m rectangular sections. The upper stiffening rods were made of Q420q steel, the booms were made of Q370q steel, and the truss members were made of Q500q steel. The elastic modulus of all steel materials was 206 GPa, and the mass density was 7850 kg/m\({}^{3}\). The concrete strength of the substructure was 45 MPa and the mass density was 2500 kg/m\({}^{3}\). Moreover, PETE elastomeric bearings were installed at the top of each bridge pier. The cross-section arrangement of the pier cap beam and the standard main beam are shown in Figure 3.  
ABAQUS software was applied to develop the nonlinear FE model of this bridge, which is presented in Figure 4. The pier top and mid-span were selected as the most important parts of the structure with the minimum remaining life. Based on the consideration of the safety of the entire structure, the remaining life of this part determines the remaining life of the whole bridge. The refined models of the small-scale segments were built by S4R shell elements, while the large-scale models of the other main beam segments were built by B31 truss elements. The shell and truss elements were assembled by the \"coupling\" command.  
Figure 2: The front elevation of the truss bridge (unit: m).  
Figure 3: The main beam section layout (unit: mm). (**a**) The layout of the main section on the pier, top. (**b**) The layout of the standard main section.  
To avoid the influence of the Saint Venant effect, the modeling length of the beam element in the non-test area was appropriately lengthened so that the distance between the test section and the coupling surface was more than three times the chord section size. In practice, sliding supports are used at all piers, so only vertical displacement constraints were used for simulation, and the mesh size of the whole bridge was about 500 mm.  
During bridge operation, the vehicle load will produce an uneven surface load on the bridge slab. Considering the refined analysis requirement, bridge slabs were also built by S4R shell elements. The global mesh size of the slabs was about 300 mm, and that near the upper chord was reduced to 100 mm. There were at least four layers of the elements along the thickness direction of the bridge slab.  
To accurately simulate the actual force state of the longitudinal and transverse stiffened beams interacting with the bridge slab, different connection strategies were developed. Near the pier top and mid-span, S4R shell elements were used to establish longitudinal and transverse stiffener beams, while the slab and top chord were connected by Boolean operations. In the other main beam areas, B31 truss elements were used to establish longitudinal and transverse stiffener beams, while the connection between the slab and top chord was assumed to be strong enough and the \"MPC\" (multipoint constraint) command was applied on the interface between them.