# Estimation of Live Load Distribution Factor for a PSC I Grider Bridge in an Ambient Vibration Test
## 2 Estimation of Live Load Distribution Factor Using Empirical Mode Decomposition
### Estimation of Live Load Distribution Factor  
Composite girder bridges under live loads exhibit the complex behavioral characteristics of main girders, cross beams, and slabs. The load distribution indicates a process in which a load directly applied to a girder is transferred to nearby girders. A load acting on a bridge is distributed to each girder due to the flexural and torsional stiffness of girders and cross beams. LLDF simply represents the magnitude of the horizontally distributed load as a proportion and can be expressed as Equation (6). Here, LLDF\({}_{i}\) is the value of the LLDF if the \(i\)-th girder, \(R_{max,i}\) is the maximum response measured at the \(i\)-th girder, and \(n\) is the number of girders.  
\[\text{LLDF}_{i}=\frac{R_{max,i}}{\sum_{i}^{n}R_{max,i}} \tag{6}\]  
Figure 2 shows the process of decomposing the displacement response measured from each girder (G1 to G4) using EDTM and extracting the displacement response of the static component from the decomposed displacement response. The extracted displacement response of the static component represents the weight of vehicles, while that of the dynamic component indicates the response caused by the interaction between the vehicles and the bridge. The maximum value of the displacement response of the static component can be used to estimate LLDF.  
When IMFs that include the frequency of the first mode are superimposed, the result is identical to the displacement response of the static component in Figure 2. When mode decomposition is performed using EMD, each mode is inaccurately decomposed and one frequency component is included in several IMFs. Thus, several IMFs are required for one mode. In the process of superimposing IMFs, the response of the dynamic component is slightly included in the response of the static component as shown in Figure 2.  
Figure 2 shows the process of decomposing the displacement response measured from each girder (G1 to G4) using EDTM and extracting the displacement response of the static component from the decomposed displacement response. The extracted displacement  
Figure 2: Procedure for extracting the static displacement component from the measured displacement response.  
response of the static component is the response caused by the weight of the vehicles, while the extracted displacement response of the dynamic component represents the response induced by the interaction between the vehicles and the bridge. Here, the maximum displacement response of the static component can be used to estimate LLDF.  
The superposition of IMFs with a frequency smaller than the first mode becomes equal to the displacement response of the static component shown in Figure 2. If mode decomposition is performed using EMD, accurate decomposition for each mode is not achieved and one frequency component is included in several IMFs. Thus, several IMFs are required for one mode. In this instance, we can see that in the process of superimposing IMFs, some of the response of the dynamic component is included in the response of the static component in the frequency domain that used fast Fourier transform (FFT) in Figure 2.