## 2 Experimental Program
### PDT and QST Programs  
PDT method has been widely used to predict the seismic resistant capacity of structures subjected to earthquake waves. During the online PDT procedure, the Newmark-\(\beta\) method was adopted to calculate the input force provided by electro-hydraulic actuators. The dynamic equation can be expressed as follows:  
\[M\ddot{X}+C\dot{X}+\widehat{R}=-Ma_{g} \tag{1}\]  
where \(a_{g}\) is the input earthquake acceleration, \(M\) is the mass matrix, \(C\) is the damping matrix, \(\ddot{X}\) and \(\dot{X}\) are respectively the acceleration response and velocity response, \(\widehat{R}\) is the restoring force obtained from the hydraulic actuators. The effect of damping on the seismic response can be ignored since the input velocity of PDT is very small. Therefore, the base shear force method is utilized to calculate the restoring force of the primary actuator as follows:  
\[\widehat{R}_{i}=\left(\frac{\sum F_{i}u_{i}}{\sum F_{i}}\right)\cdot V_{B} \tag{2}\]  
where \(V_{B}\) is the base shear force, \(F_{i}\) is the exterior force applied at \(i\)-th floor, \(u_{i}\) is the modal displacement at \(i\)-th floor. Figure 6 shows the schematic configuration on the framework employed in the PDTs.  
The initial 8 s of El-Centro (NS) record was selected as the input ground motion for its ample spectral components and adaptability to the sites. The scaled duration and time interval of the ground motion were respectively 2.8 s and 0.0035 s, which were obtained by a time scaling factor of \(1/\sqrt{8}\) for the original record. The specimen was subjected to a sequence of seven PGAs of 0.05, 0.10, 0.20, 0.30, 0.40, 0.60 and 0.80 g to simulate different seismic intensities. Besides, in order to investigate the changing rules of dynamic characteristics with the increase of PGA, free vibration with duration of 1.75 s was added for each loading case. Finally, each PGA level was loaded by 1300 steps (2.8 s) and subsequent 500 steps (1.75 s).  
The loading capacities of the two actuators at top of A-shaped bracket and middle part of steel truss are both 1000 kN. The mass matrix of specimen at each position of the load actuator was derived as follows:  
\[M=\left(\begin{array}{cc}m_{1}&\\ &m_{2}\end{array}\right)=\left(\begin{array}{cc}12470&\\ &16800\end{array}\right)\text{kg}. \tag{3}\]  
Dynamic characteristics tests were carried out through free vibrations before connecting the hydraulic actuators to the specimen. And the obtained first mode of natural vibration was used as the basic displacement mode as follows:  
\[\phi_{1}=\left\{\begin{array}{cc}1&0.955\end{array}\right\}^{T} \tag{4}\]  
Figure 6: Schematic of pseudo-dynamic tests (PDT) procedure.  
The lower actuator located in the middle part of steel truss was set as the main control point, since the stiffness is larger than other positions. The loading ratio between the two actuators was set based on the first fundamental mode of specimen. It was derived by the first mode vibration and mass matrix as follows:  
\[F=\{F_{1}:F_{2}\}=M\times\phi=\{1:1.28\} \tag{5}\]  
After the final PDT case with PGA of 0.8 g, cyclic QST was conducted by controlling the amplitude of the roof displacements in cooperation with China specification for seismic test of building [18]. The loading ratio between the two actuators was same with PDTs. Figure 7 shows the cyclic loading protocol. First, each displacement level has one cycle at amplitude of 10, 20, 30, 40, 50, 60, 70 mm. Then, each displacement cycle was repeated three times at amplitude of 80, 90, 110, 130, 150, 170, 190 mm. The test is terminated when the lateral force decreased below 85% of the maximum load.