# Progressive Collapse Performance of Prefabricated Step-Terrace Frame Structures in Mountain Cities
## 3 Finite Element Model and Experiments Verification
### Experiment Analysis
#### 3.4.2 Joint Model Establishment  
According to the joint connection forms and force mechanisms of assembled members, a simplified treatment is carried out from the angle steel plate connection at the upper bolt of the beam end, the connection between the lower part of the beam end and the corbel dowel bar, and the joint surface of the beam-column, as shown in Figure 10. Among them, the zero-length element is used to simulate the angle steel, dowel bar, and other related connecting parts, and corresponding material model characteristics are given to simulate the mechanical behavior of the actual components. Taking the assembled edge joint model as an example, the model building method is briefly explained in the following part. The joints of the model were numbered successively, and the displacement beam-column element, which means the displacement-based nonlinear beam-column element, was applied to connect joints 1, 2, 3, and 4 to form a prefabricated column, and to connect joints 12, 7, and 13 to form a prefabricated beam. Elastic beam-column elements were used to connect joints 14, 10, and 15 to simulate the corbels, which were perfectly connected to the prefabricated columns. The zero-length element was used to simulate the action of bolt-angle steel for joints 5 and 6. The zero-length element was used in joints 8 and 9 to simulate the interaction between the dowel bar, the corbel, and the prefabricated beam; the post-cast mortar was used between the prefabricated beam and the column of the joint, only the compression load was considered, and the tension load was not considered. The two-node link element was used to connect joints 11 and 12, and it was also endowed with the concrete intrinsic model Concrete01 without considering tension. A rigid link was used to couple the degree of freedom from the slave joint of the beam with the master joint. For the connection of the bolt-angle steel plate, the uniaxial hysteretic constitutive relation was used in OpenSees to simulate the simplified analysis model of the bolt-connected angle steel plate, as shown in Figure 11, and the uniaxial elastic multilinear relation was used to construct a bilinear intrinsic model to simulate the bolt shear analysis model, as shown in Figure 12. Considering the mechanical characteristics of the bolts and angle steel plate comprehensively, the hysteretic and elastic multilinear material intrinsic models were combined by a series of material commands. The connection performance of the dowel bar, beam, and column was simulated by the zero-length element, and the shear transfer between them was simulated by equipping its uniaxial hysteretic material. In consideration of the development process from elasticity to elastic plasticity, the elastic beam-column unit was used to simulate the corbel, and the rigid connection between the corbel and the column was adopted. The beam edge and column were connected by post-cast mortar, considering only the compression of the beam edge, regardless of its tensile strength. The two-node link element was set and a Concrete01 intrinsic segment  
Figure 10: Models of prefabricated joints. was engrafted, regardless of the tensile strength of concrete. The skeleton curve is shown in Figure 13.  
In Figure 11, $s1p and $e1p are the stress and strain or force and deformation at the first point on the forward curve, $s1n and $e1n are the stress and strain or force and deformation at the first point on the negative curve, and the meanings of the parameters such as $s2p, $e2p, $s3p, $s3p, $s2n, $e2n, $s3n, and $e3n are as follows. In addition to the parameters shown in the preceding figure, the following parameters are required in OpenSees to call command: Figure 12.0pinchY is the pinch factor of stress or force during reloading; Figure 12.1damage2 is the energy damage factor; $beta is the power of the ductility based unloading stiffness degradation function, which defaults to 0. There are two methods to determine the curve of hysteretic materials.