# Performance Evaluation of a Long-Span Cable-Slayed Bridge Using Non-Destructive Field Loading Tests
## 2 Non-Destructive Field Loading Test for Pingnan Xiangszhou Bridge
### Structural Theoretical Calculation for Pingnan Xiangszhou Bridge
#### 2.4.2 Establishment of a Finite Element Model for Pingnan Xiangszhou Bridge  
The finite element model of Pingnan Xiangszhou Bridge could be established by using the general spatial finite element analysis software MIDAS/Civil, with the functions of linear analysis and nonlinear analysis [32]. Based on the \"single-beam model\", the structural internal force of the bridge structure under the control load could be extracted, and the static load test condition was also designed. Based on the \"plate element model\", the calculated deflection, strain, and cable force of the test section of the bridge structure under the test load were extracted for comparison with the measured results. The finite element models are shown in Figure 4. In the finite element model, ordinary reinforcement and steel strands are not considered in sections, which may cause the stiffness of the finite element model to be less than that of the actual bridge. However, this stiffness difference would be considered in the performance evaluation, and should not affect the accuracy of the bridge safety performance evaluation results. The single-beam model consists of 1064 nodes and 875 elements, of which the truss element is used for the stay cable, while the beam element is used for other components. The plate element model consists of 19,129 nodes and 20,946 elements, of which the steel-concrete composite girder uses the plate element, the stay cable uses the truss element, and other components use the beam element. The bottom of the pier has rigid nodes, which constrain all of the degrees of freedom. An elastic connection is adopted between the main beam and the bridge pier, and the corresponding stiffness and constraints are set according to the parameters and specifications of the beam in the design drawing. The following assumptions are adopted in modeling:  
* Concrete and steel are ideal elastic materials, and the elastic moduli of the concrete and steel of the new bridge are constant, being essentially consistent with the design values;
* The section deformation of the beam element conforms to the plane section assumption;
* Deformation coordination between the bridge's concrete deck and the main beam's steel plate, and there is no relative slip between the deck and the main beam.  
According to the Chinese standard \"General specifications for design of highway bridges and culverts\" (JTG D60-2015), lane load (Highway Class I) and vehicle load should be considered in the test control load. When calculating the load distribution for 1-6 lanes, the lane transverse reduction coefficients are 1.20, 1.00, 0.78, 0.67, 0.60, and 0.55, respectively. Since the maximum span of the bridge is 450 m, which is greater than 150 m, the longitudinal reduction coefficient is 0.96. The impact coefficient of the local load of vehicle load is 0.3; the impact coefficient (\(\mu\)) is calculated according to the following equation:  
\[\left\{\begin{array}{c}\mu~{}=~{}0.05,\quad f<1.5\mathrm{Hz}\\ \mu~{}=~{}0.1767\ln f-0.0157,\quad 1.5\mathrm{Hz}\leq f\leq 14\mathrm{Hz} \\ \mu~{}=~{}0.45,\quad f>14\mathrm{Hz}\end{array}\right., \tag{6}\]  
where \(f\) is the structural fundamental frequency (Hz).