# Load Testing and Analysis of a Large Span Through Simply-Supported Steel Box Arch Bridge
## 4 Static Load Test
### Static Load Test Conditions  
The static load test was conducted in accordance with the relevant provisions of the _Technical Code for the Inspection and Evaluation of Urban Bridges_[31]. The number of loading vehicles and the arrangement of wheel positions for each test condition were determined based on the most unfavorable effect value generated by the live load in a specific condition, as calculated according to the following formula:  
\[0.85\leq\eta=S_{stat}/S_{(1+\mu)}\leq 1.05 \tag{1}\]  
where: \(\eta\)--Static load test efficiency;  
\(S_{stat}\)--Effect value under test load for a specific condition;  
\(S\)--Most unfavorable calculated effect value for the test condition, based on the design standard live load without considering impact effects;  
\((1+\mu)\)--Dynamic coefficient used in the design calculation.  
Figure 3: Arch bridge design live load moment envelope diagram (kN-m).  
Figure 2: Arch bridge model diagram.  
A total of 16 loading vehicles were used in the test, with each loading vehicle weighing 350 kN. The vehicle loading method is relatively simple and convenient to operate, and it is closer to actual working conditions, making it highly applicable. However, the load size may vary due to factors such as vehicle type, weight, and tire size, which could result in uneven load distribution and make it difficult to achieve precise load control. Additionally, differences between the field experimental conditions and theoretical assumptions may cause discrepancies between the test loading scheme and the loading schemes specified in the standards. The static load test is shown in Figure 4.  
The test parameters of the static load test are analyzed.  
(1) The Structural Calibration Factor is defined as the ratio of Measured Elastic Strain to Calculated Strain or Measured Elastic Displacement to Calculated Displacement. This metric serves as a comparison between the actual and theoretical states of the structure. Specifically, a Structural Calibration Factor of less than 1 signifies that the bridge's actual condition surpasses its theoretical condition. Conversely, a factor greater than 1 implies that the bridge's actual condition is inferior to its theoretical state, indicating a potential insufficiency in structural load-bearing capacity, as per the _Specifications for Load Capacity Testing and Evaluation of Highway Bridges_[32].  
(2) Relative Residual Strain or Relative Residual Displacement:  
\[S^{\prime}_{p}=\frac{S_{p}}{S_{t}}\times 100\% \tag{2}\]  
where: \(S^{\prime}_{p}\) represents the relative residual strain, \(S_{p}\) represents the residual strain, and \(S_{t}\) represents the total strain.  
A smaller value of \(S^{\prime}_{p}\) indicates that the structure is closer to an elastic working state. When the relative residual strain or relative residual displacement exceeds 20%, it indicates that the actual condition of the structure is unsafe compared to the ideal condition. In such cases, the load-bearing capacity should be directly judged as inadequate based on the test results, in accordance with the _Specifications for Load Capacity Testing and Evaluation of Highway Bridges_[32].  
(3) Upward displacement is considered negative, and downward displacement is considered positive.  
(4) Tension is considered positive, and compression is considered negative. Stress is measured in MPa, and strain is measured in \(\mu\varepsilon\). When calculating the measured stress, the elastic modulus of the steel structure is taken as \(E=2.06\times 10^{5}\) MPa.  
(5) The influence of pier settlement has been deducted from the displacement measurements.  
Figure 4: Static load test.