## 4 Finite Element Study of Novel SCPC Joint  
To evaluate the seismic behaviors of the novel SCPC frame, a 5-story prototype building is modelled as a 2D plane numerical model using the OpenSees software and the nonlinear time-history analysis was performed [35]. When the gap-opening occurred under the load, the sections do not fit the plane section assumption; the mechanical behavior of the novel connection is complex. The connection analysis model is based on the following basic assumptions--(1) the joint only considers the load in the plane and has the deformation in the plane without torsion; (2) shear failure of beam and column can be avoided through the reasonable stirrup arrangement; (3) the hysteretic dampers, beam and column do not slip in the whole loading process. Figure 11 displays the accurate finite element model of the novel SCPC joint, which mainly consists of nonlinear beam column elements, zero length elements and truss elements. Two different types of constitutive relationships were used for concrete materials of the connection--(1) unconfined concrete in protective cover (without stirrup restraint); (2) concrete in core area (stirrup restraint). They are simulated by Concrete 01 material model consisting of three parts--nonlinear ascending section, linear descent section and horizontal section [36]. Concrete 01 material model do not consider the tensile strength of concrete and the concrete crushing, residual strength is accounted for. Considering the amplification effect of stirrup on confined concrete, there are various confined concrete model to calculate the confined concrete strength enhancement for both normal-strength and high-strength concrete [37; 38; 39; 40]. The amplification factor of compressive strength and strain is 0.2 according to the parameters such as stirrup ratio and stirrup spacing. The steel fiber including steel bars and PT tendons are assigned to the Steel 02 material model, which are based on Giuffre-Menegotto-Pinto model [41]. Steel 02 material model has an initial stress, the Bauschinger effect and isotropic reinforcement effect can be reflected in the cyclic loading. As shown in Figure 12, all the beams and columns are modelled by  
Figure 10: Acceleration response spectrum of near-fault earthquake waves. Nonlinear Beam Column element, which consider the spread of plasticity along the element through a number of integration points. Each element is divided by many fiber cross sections by integration points and each fiber was given a uniaxial stress-strain relationship. The hysteretic dampers arranged at the upper and lower at the beam-column interface are simulated by zero length spring elements between node 14, 15 and 16, 17 [42]. The gap opening and closing behavior is also modelled by two pairs of zero length elements. The element is assigned to Elastic PP Gap material model with compression-only material properties. Although the gap is opened, the hysteretic dampers and beam-column interface do not slip. When the gap is opened, the sum of horizontal relative displacements of the upper and lower rotation points is \(\Delta_{gap}\), the vertical distance of the two points is \(h\), so the relative connection rotation is \(\theta_{r}=\Delta_{gap}/h\). Three degrees of freedom of node 15 and node 17 are coupled with node 9, three degrees of freedom of node 14 and node 16 are coupled with node 4 and node 3. The rigid link elements (which is used to construct a single multipoint constraint) are selected to reflect the coupling characteristics between the above nodes. In the modelling of the beam-column interface, the effect of critical region length was considered. The critical region length is the distance between node 9 and node 10, where the most severe damage will take place [43; 44]. The constitutive relationships of the concrete and steel materials model in the critical region are assigned to compression only material properties in the critical region. Truss element model between node 7 and node 12 are used to simulate the unbonded tendons at the beam center.