Numerical Modelling and Analysis of Post-Tensioned Precast Prestressed Slab-Beam-Column Composite Joint

In order to study the seismic performance of post-tensioned precast prestressed slab-beam-column composite joint under low cycle loads, ABAQUS was used to simulate the quasi-static behavior of the composite joint. On the premise of verifying the accuracy of the FEM for post-tensioned precast prestressed concrete joints, a comparative analysis was conducted on the hysteresis performance, bearing capacity, energy consumption performance, and deformation capacity differences between concrete joint and composite joints. The seismic performance of the post-tensioned prestressed composite joint has been obtained, providing assistance for the design of the joint.


Introduction
Precast concrete structure has good component quality and high construction efficiency.With the popularization of large-scale mechanical equipment and the increase in labor costs, precast concrete structure has been increasingly widely used.In the 1990s, the US-Japan joint research project Precast Seismic Structural Systems (PRESSS), investigated various post-tensioned precast concrete structural systems [1][2][3][4].
There are two application methods for post tensioned steel strands: bonded or unbonded [5].The bonded post-tensioned precast prestressed joints mainly used in Japan are equipped with steel strands in the upper and lower parts of the joints.This type of joints have good self-centering capability, but their energy dissipation (ED) is poor [6].The unbonded post-tensioned precast prestressed joints are studied and applied more widely.Hybrid frame system, studied by Stanton et al [7], is suitable for high-intensity earthquake areas.Previous studies [8] have proved that this system has good initial stiffness, self-centering performance, ductility and low damage performance.Some scholars have further developed the Hybrid frame system.The main improvement is to remove the lower ED rebars or improve the energy dissipator of the joints.
Hybrid frame joint has complex configuration to achieve excellent self-resetting performance, which is not necessary for the structure.However, this approach has increased construction difficulty and cost.To solve the above problem, Guo et al. [9] proposed a new Precast Prestressed Efficiently Fabricated Frame (PPEFF) system that simplifies the construction of slab-beam-column joints.This system makes it easy to compose two-way moment-resisting frames without reinforcement congestion in the joint, and avoids complex construction techniques such as hidden grouting or welding.Guo et al. conducted comprehensive research and engineering practice on the PPEFF system [10][11].Research and engineering applications have shown that the PPEFF system has high construction efficiency and low steel consumption.Furthermore, a PPEFF joint with steel tube concrete column suitable for high-rise and super high-rise buildings is proposed.Unlike the hybrid system, the performance analysis of the PPEFF system must consider the role of the slab.This paper establishes a FEM that considers the joint action of the slab.The rationality of the FEM is verified through comparison with experimental results of PPEFF concrete joint.The hysteresis performance, bearing capacity, energy dissipation performance, and deformation capacity differences between concrete joint and composite joint are compared and analyzed.The seismic performance of the PPEFF composite joint is obtained, providing assistance for the design of the joint.

Specimen design
The prototype structure information, component dimensions, and reinforcement information of the joint can be found in reference [10].The forms of PPEFF concrete joint and PPEFF composite joint are shown in figure 1 and figure 2. The beams and slabs are all made of C40 concrete, while the columns are made of C50 concrete.HRB400 grade steel bars are used for the longitudinal bars and stirrups.Seven wire prestressed steel strands with a yield strength of 1860 MPa are used as prestressed reinforcement.
The size and reinforcement of the composite node beam and slab are the same as those of the concrete node.The column adopts a square steel tube concrete column with a steel pipe thickness of 8mm, and the concrete beam is placed inside a U-shaped steel bracket with a thickness of 6mm.The thickness of the inner partition is 6mm.The beam and slab dimensions and reinforcement of the composite joint are the same as those of the concrete joint.The column adopts a square steel tube concrete column with a steel pipe thickness of 8mm.The concrete beam is placed on a 6mm thick U-shaped steel corbel, and the thickness of the partition inside the column is 6mm.The number of specimens for PPEFF concrete joint is MJ-1, and the number of specimens for PPEFF composite joint is MJ-2.

Material Constitutive
The constitutive model of concrete adopts the built-in CDP model of Abaqus, as shown in figure 3. The stress-strain constitutive relationship of concrete under uniaxial tension and compression, as provided in Appendix C of the Code for design of concrete structures, is adopted.In order to consider the restraining effect of stirrups on the three-dimensional compression of concrete in the core area of the section, this paper adopts a Mander constrained concrete constitutive model for concrete constrained by stirrups.

Figure 3. Concrete damage plastic model
The steel in the FEM involves column steel pipe, steel corbel, stiffener, HRB400 grade steel bars, and 1860 grade steel strands.The steel bars and steel strands adopt the constitutive model USteel02 developed by UMAT, with E0 being the elastic modulus.According to the recommendations of China's Steel strand for prestressed concrete and Code for design of concrete structures, the elastic modulus of steel bars and steel strands is taken as 2.0×10 5 MPa and 1.95×10 5 MPa respectively.Poisson's ratio is 0.3.E0 is the elastic modulus of the strengthened section after yielding, taken as 0.0001.The yield strength of steel is based on experimental data [10].Considering the strengthening and failure stages of the steel, the column steel pipe, steel corbel, and transverse stiffener in the model are all made of low-carbon mild steel Q345B.The constitutive relationship is based on the trilinear model, and the yield strength is based on the standard strength.

Interaction
Surface to surface contact is used to simulate the mechanical behavior of the contact interface between the concrete main beam and column, between the concrete secondary beam and the concrete floor, and between the column steel pipe and the internal concrete.The normal action adopts "hard contact".The tangential action adopts "penalty" friction, where the friction coefficient between concrete beams and concrete columns is taken as 0.8, and the friction coefficient between column steel pipes and internal concrete is taken as 0.45.The remaining interfaces adopt tie constraints.These interfaces include: slab and main beam, load block and slab, secondary beam and column, column steel pipe and transverse stiffener.The steel skeleton adopts embedded constraints and is embedded into the corresponding concrete beams, columns, and slabs.The internal nodes of the steel strand are coupled with the two degrees of freedom U1 and U3 of the adjacent concrete nodes, achieving longitudinal free relative sliding between the steel strand and the concrete.

Boundary conditions and loading
The upper and lower ends of the precast column are fixed hinge supports.Two reference points are set at the top and bottom centers of the column, and the reference points are coupled with six degrees of freedom on the two surfaces of the top and bottom of the column through coupling constraints.All degrees of freedom at the bottom reference point are constrained except for UR1, and all degrees of freedom at the top reference point except for U3 and UR1 are constrained.
The initial prestress of the first step is applied through the equivalent cooling method.The second step is to apply gravity load and column top axial force.The third step is to apply an anti-symmetric reciprocating load on the beam end, and the loading displacement drift is defined as the ratio of the vertical displacement of the beam end to the horizontal distance from the loading point to the center of the joint.When the loading displacement drifts are 1/2000, 1/1000, 1/800, 1/550, 1/400, 1/300, 1/200, 1/100, 1/67, 1/50, 1/40, and 1/33.

Mesh
Concrete beams, concrete columns, concrete slabs, column steel pipes, transverse stiffeners, and steel corbels use a linear reduced integral element C3D8R, while steel bars and steel strands use a two node linear three-dimensional truss element T3D2.The mesh of joints is shown in figure 4.

Result analysis
In Reference [10], a comparative analysis has been conducted between the experimental results of PPEFF concrete joints and the FEA results.The comparative results show that the FEM used in this paper can better simulate the seismic performance of the PPEFF joints under low cycle loads.Comparative analysis was conducted on PPEFF concrete joint and PPEFF composite joint from the perspectives of hysteresis curve, skeleton curve, energy dissipation performance, deformation recovery ability, and joint plastic strain.

Hysteretic curve
Figure 5 shows the moment-drift hysteresis curves of two specimens.It can be seen that the hysteresis curves of the two specimens are symmetrically centered.The hysteresis curve of concrete joint MJ-1 is more plump than that of composite joint MJ-2.The hysteresis curve of composite joint MJ-2 shows obvious pinching phenomenon, with smaller residual deformation and better self-centering performance.The bearing capacity of composite joint is higher than that of concrete joint.

Skeleton curve
Figure 6 shows the skeleton curves of two specimens, and it can be seen that the skeleton curves of both specimens are similar in shape, both presenting an inverted "Z" shape.The positive and negative yield loads of composite joint MJ-2 are 560.24kN•m and 571.02 kN•m, respectively, while the positive and negative yield loads of concrete joint MJ-1 are 543.30kN•m and 536.84 kN•m.Compared with MJ-1, the yield load of MJ-2 increases by 3.12% in the positive direction and 6.37% in the negative direction.The positive and negative peak loads of composite joint MJ-2 are 634.24kN•m and 636.67 kN•m, respectively.The positive and negative peak loads of concrete joint MJ-1 are 599.63kN•m and 596.01 kN•m, respectively.Compared with MJ-1, the peak loads of MJ-2 increase by 5.77% in the positive direction and 6.82% in the reverse direction.It can be seen that composite joint have better bearing capacity than concrete joint.

Energy dissipation
Figure 7 shows the cumulative energy dissipation comparison curves of the two specimens.It can be seen that both the concrete joint and the composite joint specimens begin to experience energy dissipation at a drift of 0.5%.The cumulative energy dissipation curves of the two basically coincide, indicating that the energy consumption capacity of the composite joint MJ-2 and the concrete joint MJ-1 is not significantly different.Observing the hysteresis curves of the two, it was found that although the hysteresis curve of the concrete joint MJ-1 was fuller, its bearing capacity was smaller than that of the composite joint MJ-2.Therefore, the areas surrounded by two hysteresis loops were basically the same, and the difference in energy dissipation capacity was relatively insignificant.

Residual deformation
Figure 8 shows the residual deformation comparison curves of two specimens.It can be seen that as the drift increases, the residual deformation of both specimens gradually increases, and the concrete damage continues to increase.When the drift is 3%, the residual deformation of composite joint MJ-2 in the positive and negative directions is 0.80% and 0.74%, respectively.The residual deformation of concrete joint MJ-1 in the positive and negative directions is 1.39% and 1.47%, respectively.The residual deformation of MJ-2 in the positive and negative directions is reduced by 42.45% and 49.66% compared to MJ-1, respectively.The residual deformation of composite joint at various drifts is smaller than that of concrete joint, indicating that under low cycle loads, composite joint have better self-centering performance than concrete joint and better repairable performance after quake.

Plastic Strain
Figure 9 shows the plastic strain diagram of the concrete parts of the joints.The plastic strain of concrete exceeding 0.0033 is shown in gray, indicating that the equivalent plastic strain of the two joints is mainly concentrated at the beam end, manifested as the beam hinge failure mechanism.When the drift reaches 3%, the plastic concrete area of MJ-2 is smaller than that of MJ-1.The concrete column of MJ-1 enters plasticity in the joint area, while the concrete inside the steel tube concrete column of MJ-2 does not enter plasticity in the joint area.The steel pipe and steel corbel of the composite joint MJ-2 did not enter plasticity when the drift reached 3%, while the inner diaphragm entered plasticity when the drift was 2%.

Conclusion
A comparative analysis was conducted on the hysteresis performance, load-bearing capacity, energy dissipation performance, and deformation capacity differences between PPEFF concrete joint and PPEFF composite joint.The seismic performance of the composite joint was obtained, providing support for joint design.The following conclusions can be drawn.
 The bearing capacity of composite joint has increased to a certain extent compared to concrete joint, and composite joint have better bearing performance.


The difference in energy dissipation capacity between composite joint and concrete joint is not significant.Under low cycle loads, composite joint have better self-centering performance than concrete joint, and their repairable performance after quake is better.
 Both the steel pipe and steel corbel of the composite joint did not enter plasticity when the drift reached 3%.The concrete area of the composite joint entered plasticity was smaller than that of the concrete joint.

Figure 4 .
The mesh of joints

Figure 9 .
The plastic strain diagram of the concrete parts of the joints