## 3 Quasi-Static Component of Deflection Response and Its Extraction
Figure 2: Superstructure of simply supported T-beam bridge with 30-m span (unit: mm). The performance of various materials is shown as follows: (1) C50 (high-performance concrete) is used for precast main girders and diaphragm girders, wet joints, sealing and anchoring ends, and cast-in-place continuous sections on top of pixels; (2) C50 (high-performance concrete) is used for cast-in-place concrete of the bridge decks; (3) asphalt concrete is used for bridge deck paving; (4) Reinforcing steel mainly adopts HPB300 and HRB400; (5) A seven-wire twisted standard-type low relaxation high-strength strand is adopted, with a nominal diameter of 15.20 mm, a nominal area of 140 mm\({}^{2}\), a tensile standard strength of \(\text{f}_{\text{pk}}=1860\) MPa, a modulus of elasticity of \(\text{E}_{\text{P}}=1.95\ \times\ 10^{5}\) MPa, and a maximum relaxation rate of 3.5%. For the finite element simulation, ANSYS was used to establish the finite element model of the bridge, and a BEAM4 element was used to simulate the main beam, a MASS21 element was used to simulate the mass, as well a COMBIN14 spring element. The finite element model of the bridge with a 30-m span simply supported T-beam is shown in Figure 6.  
Figure 4: Schematic diagram of fulcrum section of a 30-m span simply supported T-beam bridge (unit: mm). (**a**) A-A cross-section diagram. (**b**) A-A section steel bundle layout diagram. Figure 5: Schematic diagram of a midspan section of a 30-m span simply supported T-beam bridge (unit: mm). (**a**) B-B cross-section diagram. (**b**) B-B section steel bundle layout diagram. Figure 6: Finite element model of 30-m T-beam. In this paper, the bridge structure adopts a BEAM4 unit, which is a common type of unit for main beam modeling. It is a 3D elastic beam unit with 6 degrees of freedom directions (UX, UY, UZ, ROTX, ROTY, ROTZ), which can withstand axial tension, pressure, bending moment, and torsion, and does not have the function of plasticity and eccentric force. Here, the mid-span section of a 30-m span simply supported T-beam is taken as an example. The section size and structure are shown in Figures 2-5, using the International System of Units, and the specific values are shown in Table 1.  
The moving mass block adopts the MASS21 unit, and each node has 6 degrees of freedom in each direction (UX, UY, UZ, ROTX, ROTY, ROTZ), and each coordinate direction has a different mass and moment of inertia. This type of unit can define the moment of inertia effect and the choice of 2D or 3D functions via KEYOPT(3). Table 2 shows the relevant characteristics of a midspan cross-section and a fulcrum cross-section corresponding to the simple supported T-beam bridge with different spans, including the principal moment of inertia of the main beam, the secondary moment of inertia, and the torsional moment of inertia. Based on the analysis of the ANSYS modal calculation results, the first three natural vibration frequencies of simply-supported beam bridges with different spans under the bridge state were extracted and are drawn in \[u_{st}=\frac{2F}{\rho AL}\sum_{i=1}^{n}\frac{1}{\omega_{i}}sin\frac{i\pi\overline {x}}{L}sin\frac{i\pi x}{L} \tag{2}\]0  
For the finite element simulation, the specific operation steps for obtaining the midspan deflection time-history curve are as follows:  
Step 1: Set the mass of the moving load, and keep driving on the bridge deck at low speed and at a uniform speed to obtain the midspan deflection time-history curve caused by the moving load;  
Step 2: Because the moving speed is small, the amplitude of the time-history curve is small, so the GUASS curve fitting method is used to fit the static time-history curve; the fitting result is shown in \[u_{st}=\frac{2F}{\rho AL}\sum_{i=1}^{n}\frac{1}{\omega_{i}}sin\frac{i\pi\overline {x}}{L}sin\frac{i\pi x}{L} \tag{2}\]1