# Seismic Response Analysis of Prestressed Concrete
## 1 Introduction  
The rocking structure concept was first proposed by [PERSON], based on the surveys of earthquake damage [1, 2]. With continuous research of resilient structures, the rocking structure has received increasing attention from researchers [3, 4, 5, 6, 7]. A rocking structure generally has minor damage after an earthquake and its main components can even be undamaged [8]. Frames are a very common form in concrete structures. The energy dissipation of a traditional frame during an earthquake mainly depends on its structural ductility. Such an earthquake damaged frame usually requires a long repair time with great cost. To deal with this problem, a type of rocking frame is presented based on the conceptual fusion of the rocking structure and frame. [PERSON] et al. [9] analyzed the rocking response and stability of the rocking frame. It was found that the stability of the rocking frame is strengthened with an increase in cap beam mass. The seismic response of a plane rocking frame with geometric asymmetry was studied by [PERSON] et al. [10]. Although the rocking mechanism of a symmetrical rocking frame is very different from that of an asymmetric one, the influence of structural asymmetry on the stability of the rocking frame is minute. [PERSON] et al. [11] suggested a new finite element modeling method for a deformable rocking frame based on zero length fiber cross-section elements and Hilber-Hughes-Taylor energy consumption algorithm. Prestressed tendons are often arranged in the column or beam of a rocking structure in actual projects to enhance the self-centering ability of the structure, to increase the structural stability and to reduce the residual deformation. Based on this measure, different forms of prestressed concrete rocking frame (PCRF) were presented by researchers. [PERSON] et al. [12] proposed a concrete rocking frame derived from a precast unbonded prestressed concrete frame. Beams can be connected to columns through tendons, and thedisengagement of the beam from the interface for the beam-column joint can be allowed. A cyclic loading test of beam-column joints for precast PCRF was carried out by [PERSON] et al. [13] and the test results demonstrated that the joints had great ductility. [PERSON] et al. [14] completed an experimental study on the seismic behavior of joints of an unbonded PCRF. The failure of joints did not occur in the experiment and the damage of tested joints was minor, which can be quickly repaired after an earthquake. Nonlinear static pushover analysis and dynamic time history analysis of an unbonded post-tensioned PCRF were conducted by [PERSON] et al. [15]. The fiber model and spring model used for such structural analysis were also presented. The analysis results showed that the strength, ductility and self-centering ability of an unbonded post-tensioned PCRF can meet the requirements for resisting rare earthquake. The rocking response and stability of a prestressed rocking frame was studied theoretically by [PERSON] et al. [16]. It was found that the effects of prestress on rocking columns with different sizes are basically the same as that of a single independent prestressed rigid rocking column. The seismic response of a prestressed rocking frame with buckling restrained braces which has flag-shaped hysteretic behavior was analyzed by [PERSON] et al. [17]. They revealed that prestress is not always beneficial to the seismic performance of the prestressed rocking frame, but this also depends on the size of the frame columns. [PERSON] et al. [18] proposed a kind of controlled rocking concrete frame. A reversed cyclic loading test and shaking table test were accomplished and the corresponding finite element model was built in the study. The research results proved that the frame has excellent seismic performance. A self-centering prestressed concrete frame with web friction devices was devised by [PERSON] et al. [19; 20].