## 2 Numerical Model and Experimental Verification
### Numerical Model and Parameter Setting  
In order to verify the accuracy of the LS-DYNA program, a test on the progressive collapse of reinforced concrete frame structures in Document 17 was numerically simulated [17]. The test device and instrument layout are shown in Figures 2 and 3. The column was discretized into 10 beam elements along the axial direction; the length of each element was less than the length of the plastic hinge of the column foot; the beam was divided into three sections of reinforcement along the axial direction (the middle span, the left support bearing, and the right support bearing); each section of the beam was discretely divided into 4 elements; the length of each element was 0.5 m. The columns and beams were separated into 100 concrete fibers along the cross section; the steel bars were separated into 4 or 8 fibers. The schematic diagram of the cross-section of the beam and column is shown in Figure 4 (the marked part is reinforced fiber). This paper uses LS-DYNA as the solver to solve the finite element model; the finite element model uses MAT-174 material to simulate reinforced concrete. The material model can simulate plain concrete and steel reinforcement materials by setting the reinforcement ratio (FRACR = 0, representing plain concrete; FRACR = 1, representing steel reinforcement). The reinforcement adopts a uniaxial elastoplastic flow strengthening constitutive model,  
Figure 4: Discrete of RC column. (a) Column section fiber element (b) Beam section fiber element. (Red and blue represent steel fiber, with different colors to distinguish the role of different steel). Figure 3: Collapse limit state of model frame. Figure 2: Test equipment and instrument layout. 1. Hydraulic actuator; 2. Two jacks connected in series; 3. Force sensor; 4. Motion detector 4-1–4-4; 5. Dial indicator; 6. Concrete strain gauge 6-1–6-8. and the yield stress and elastic modulus were measured using actual values. The Ramberg-Osgood equation [18] is used to simulate the stiffness degradation of the material under repeated loading [19]. In the monotonic compression stage, the [PERSON] and [PERSON] methods described by [PERSON] and [PERSON] were used [20]; the material follows a parabolic stress-strain curve. In the stretching stage, the stress increased linearly with the strain until the stretching limit was reached. Thereafter, the stiffness and strength decayed as the strain increased. When the frame model was established, stirrups were not set, but the effect of stirrups was realized by considering the reinforcement of confined concrete. Core concrete adopted the Kent-Park constitutive model [21]. The axial compressive strength and elastic modulus of concrete were measured as standard values. Considering the restraint effect of stirrups on concrete, the constitutive relationship formula of concrete in the core area is as follows:  
\[f_{c}=\left\{ \begin{array}{c}Kf_{c}^{\prime}[\frac{2\varepsilon_{c}}{K \varepsilon_{0}}-\left(\frac{\varepsilon_{c}}{K\varepsilon_{0}}\right)^{2}], \varepsilon_{c}\leq K\varepsilon_{0}\\ Kf_{c}^{\prime}[1-Z_{m}(\varepsilon_{c}-K\varepsilon_{0})],\varepsilon_{c}>K \varepsilon_{0}\end{array} \right. \tag{1}\]  
when \(\varepsilon_{c}>K\varepsilon_{0}\), \(f_{c}>0.2 Kf_{c}^{\prime}\).