## 3 Inertial Systems for Shake Table Tests
### Inertial Mass Supported by an External System  
Another configuration for including the additional mass in shake table testing is to locate it outside the table. In this configuration, the additional mass is positioned on an articulated supporting frame adjacent to the shaking platform, and it is attached to the test specimen through a pinned-end connection that allows free rotation and, therefore,  
Figure 3: Representation of an inertial mass with safety structure outside the shake table.  
Figure 2: Representation of an inertial mass without auxiliary-supporting structure.  
transmits axial force only. Relevant advantages are associated with this configuration [8]. Taking the additional mass off from the platform reduces the risk of damaging the test equipment and laboratory personnel if lateral instability of the specimen occurs during testing. Another benefit of this approach is the decrease in the time taken to assemble and disassemble a test setup. This is because the simple connection between the mass-rig and the specimen needs to be disconnected from the model only. Therefore, if the experimental program includes many tests, the research time decreases considerably. Additionally, another benefit of this configuration is that it allows the use of the full capabilities of the shake table since the performance of the shaking platform depends on the weight acting on the simulator.  
In the literature, three types of mass-rig system placed outside the shake table can be distinguished: a linear sliding, a rotational, and a pendulum system. Among these systems, the rotational mass-rig has been used in experiments involving RC columns as the specimen, as proposed by [PERSON] et al. [15]. This mass-rig system is presented in Figure 4 and consists of an articulated frame to provide the inertial loading during the testing program. The axial force applied to the column is accomplished by means of a steel spreader beam connected to the top of the specimen's head and two center-hole jacks. To restrict the translation of the inertial mass, constraint cables must be included. In the case of column failure, the mass-rig translates until reaching the maximum displacement preset by the restraining cables. Thus, safety concerns are eliminated if the specimen fails. Furthermore, the mass-rig restrains the out-of-plane movement of the specimen and, therefore, additional elements for this purpose are not necessary. Another benefit of this mass-rig configuration, as indicated above, is that it also enables quick installation and removal of specimens.  
Although this system eliminates various problems related to the testing of cantilever columns using shake tables, it still has some concerns associated with the proper representation of P-\(\Delta\) effects. From their experimental findings, [PERSON] et al. [15] concluded that the experimental shear forces were lower than those estimated from the numerical analysis including P-\(\Delta\) effects.  
Conclusions from these two types of test indicate that (1) placing a large mass on top of a column leads to higher mode effects that are not typically observed in an actual bridge  
Figure 4: Adapted representation of a rotational system for supporting additional inertial mass.  
configuration and that (2) placing the additional mass on an external mass-rig system does not properly represent the P-A effects that cantilever columns undergo during earthquake ground motions. In an effort to overcome these two issues, a new inertial mass system (IMS) is introduced. In this configuration, the extra inertial mass is supported by the shake table by employing a stiff-pinned column attached to the platform. The features of this system are described in detail, and the equations of motion of the internal system and the shake table are developed. It is worth mentioning that the proposed system was successfully used in the dynamic testing of six RC bridge column specimens, whose results and discussion can be found in the literature [9].