## 3 Quasi-Static Component of Deflection Response and Its Extraction  
The concept of a quasi-static response is introduced so that the feasibility of the evaluation method for reasonable acquisition frequency can be investigated further [27]. The quasi-static response of a vehicle-bridge coupled vibration system [28; 29; 30; 31; 32; 33] pertains to the response of the bridge structure as the vehicle's velocity perpetually approaches zero. Therefore, the quasi-static response of the bridge is not affected by the moving speed of the load; on the contrary, the moving speed of the load will not cause a change in quasi-static components. It is assumed that there is no displacement and speed at the beginning of beam vibration, and the midspan deflection response of a simply supported beam bridge under moving load is divided into moving the load frequency component \(u_{m}\) and the bridge natural vibration frequency component \(u_{n}\). Accordingly, it can be deduced that the component controlled by the natural vibration frequency \(\omega_{i}\) of the bridge is zero, and the frequency component of the moving load is mainly controlled by the excitation frequency \(i\pi\
u/L\) of the external load, which can be expressed as shown in (1):  
\[u_{m}=\frac{2F}{\rho AL}\sum_{i=1}^{n}\frac{1}{\omega_{i}\big{(}1-S_{i}^{2} \big{)}}sin\frac{i\pi\
u t}{L}sin\frac{i\pi x}{L} \tag{1}\]  
where \(S_{i}\) is a dimensionless speed parameter, and it is the ratio of the \(i-\)order moving load frequency to the \(i-\)order bridge natural vibration frequency, which can be expressed as \(i\pi\
u/L\omega_{i}\). In practical engineering, when the speed parameter is equal to 1, the bridge structure will resonate with the vehicle load, which will easily cause structural damage. [PERSON] et al. [34], according to the statistics of natural frequencies of highway bridges, determined that the reasonable range for dimensionless speed parameters \(S_{i}\) is between 0 and 0.15. For the deflection response, when the moving speed of the vehicle is infinitely close to zero, the moving load can be approximately regarded as a quasi-static load, and the dimensionless speed parameter \(S_{i}=0\) can be further derived, and the quasi-static component \(u_{st}\) of the bridge response can be expressed as shown in (2):  
\[u_{st}=\frac{2F}{\rho AL}\sum_{i=1}^{n}\frac{1}{\omega_{i}}sin\frac{i\pi\overline {x}}{L}sin\frac{i\pi x}{L} \tag{2}\]  
where, \(\overline{x}=vt\) represents the position where the quasi-static load acts, and \(u_{st}\) represents the deflection response at measuring point \(x\) when the static load acts on \(\overline{x}\). The quasi-static response is mainly concentrated in the low-frequency section of the overall dynamic response [35]. It is assumed that the discrete signal \(x(t)\) obtained after continuous signal \(x(n)\) acquisition can be in the form of a series of harmonic superposition, and the expression is shown in (3):  
\[x(n)=\sum a_{i}cos(\omega_{i}\cdot n\cdot\Delta t+\varphi_{i}) \tag{3}\]  
where, \(a_{i}\), \(\omega_{i}\), and \(\varphi_{i}\) represent the amplitude, frequency, and initial phase of the \(i\) th harmonic, respectively; where \(\Delta t=1/f_{s}\) is the acquisition interval. The dynamic response of a bridge caused by a moving load includes not only quasi-static components, but also signal components caused by natural bridge vibration, vehicle speed, noise, and other factors. It is difficult to directly and clearly observe the quasi-static components. Therefore, it is necessary to use a method to extract quasi-static components from the dynamic response of the bridge structure. In this case, the data obtained from the side span of a simply supported T-beam bridge with a 30-m span are analyzed as an example, while the vehicle travels through the side beam. The superstructure and section dimensions are illustrated in Figures 2-5. Figure 3: Layout of prestressed reinforcement of simply supported T-beam bridge with 30-m span (unit: mm).