# Experimental Study of a New Precast Prestressed Concrete Joint
## 6 Ductility and Energy Dissipation  
Ductility refers to the ability of a structure to withstand inelastic deformation without significant reduction in its bearing capacity after the structure enters plasticity. Ductility is related to the energy dissipation capacity of the structure. The ductility of a joint can be expressed by the displacement ductility coefficient of the beam at the loading end. This coefficient is calculated as follows:  
\[\mu=\frac{\Delta_{u}}{\Delta_{y}}, \tag{3}\]  
Figure 21: Bearing capacity degradation coefficient for right beam of joint. Figure 20: Bearing capacity degradation coefficient for left beam of joint. where \(\mu\) is the ductility coefficient of the joint; \(\Delta_{u}\) is the ultimate displacement of the joint when it is broken, generally taken as the corresponding displacement when the bearing capacity of the joint drops to 85% of the peak load; \(\Delta_{y}\) is the yield displacement of the joint. The ductility coefficients of the three joints are shown in the two rightmost columns of Table 3. The ductility coefficients of the three joints were similar, and it can be considered that the three joints had considerable ductility. The different strength of concrete in the keyway area had little influence on the ductility as seen by comparing the precast prestressed concrete joints. The ductility coefficient for each joint was between 5.3 and 6.3, and these values are greater than the ductility coefficient of 3-4 as required for seismic structure design. Thus, the joints tested have good ductility and meet the structural seismic requirements. Energy dissipation is an important indicator of the seismic performance of a structure. The equivalent viscosity damping coefficient is used to describe the energy dissipation capacity of a test joint under different loading displacements. A larger equivalent viscosity damping coefficient correlates with greater energy dissipation. The calculated values of the equivalent viscous damping coefficients of the three joints are listed in Table 4 and are calculated according to  
\[h_{e}=\frac{1}{2\pi}\cdot\frac{A_{1}}{A_{2}+A_{3}}, \tag{4}\]  
where \(h_{e}\) is the equivalent viscous damping coefficient; \(A_{1}\) is the area of the hysteresis loop BFDE in Figure 22; \(A_{2}\) is the area of the triangle OAB in Figure 22; \(A_{3}\) is the area of the triangle OCD in Figure 22. There average is taken when there are multiple cycles of the same level of loading displacement. At the start of yielding, the equivalent viscous damping coefficient of each joint increased with the loading displacement. As yielding began, the plasticity of the beam developed rapidly, and the energy dissipation increased. The equivalent viscous damping coefficient had only slight fluctuations in the displacement from 20 mm to the peak displacement. The local damage of concrete lowered the energy dissipation beyond 20 mm of displacement. However, the plasticity of the joint had room for development. The plasticity development and concrete damage were in a dynamic equilibrium that caused this stable portion of the coefficient. The coefficient tended to decrease slowly after the peak load was reached. After the peak load, part of the concrete was destroyed, and the energy dissipation of the joint was reduced. The average value of the equivalent viscous damping coefficient for the cast-in-place joint at peak load was 0.2413. The average viscous damping coefficients at peak load of the precast prestressed concrete joints PPCJ1 and PPCJ2 were 0.2340 and 0.2470, respectively. The equivalent viscous damping coefficient was close for all joints. This similarity indicates that the energy dissipation capacity of the precast prestressed concrete joint was similar to that of the cast-in-place joint. Thus, the precast prestressed concrete joint had the same energy dissipation as the equivalent monolithic system. Figure 22: Schematic diagram of calculation for the equivalent viscosity damping coefficient.