The vertical component of ground motions can affect the seismic performance of reinforced concrete (RC) piers as significant as its horizontal counterpart. However, real-time testing for RC piers subjected to both horizontal and vertical ground motions has been scarcely conducted due to the difficulty in multi-axial control of actuators. In this study, the seismic response of a bridge RC pier was investigated by conducting real-time hybrid simulation (RTHS), where the RC pier was physically tested in the laboratory and the bridge superstructure was numerically modeled. The test setup that can synchronously apply both horizontal and vertical ground motions was constructed by using three dynamic actuators and a flexible loading beam (FLB). The lateral response of the RC pier was investigated by varying the intensities for vertical ground motions, while the same intensity for horizontal ground motion is used. It was found that the axial force from the dead load of superstructure can significantly affect the initial stiffness, strength, and post-yield response of the RC pier. For the selected earthquake ground motions, however, the intensity of vertical ground motion did not make a substantial difference in the lateral response, although there was a notable difference in the fracture pattern.
In a building subjected to seismic loading, large compressive force may develop in reinforced concrete (RC) coupling beams because of axial restraint imposed by the neighboring shear walls against the elongation of the coupling beams during the failure process. The axially compressive force can increase the shear stiffness and strength of the coupling beam and may change its failure mode. In this paper, a novel coupling beam testing procedure adopting hybrid simulation method is proposed in which the axial restraint is determined through hybrid simulation and the calculated axial restraint is imposed on a specimen during the test. RC coupling beams were tested by adopting both the proposed test procedure and the conventional testing approach in which the effect of the axial restraint is not accounted for. Test results depict a clear difference in the response of the coupling beam, such as shear capacity and failure mode, depending on the consideration of the axial restraint during the test. The test outcome demonstrates the usefulness and applicability of the proposed test procedure.
Several actuators need to be controlled to impose a multi-degree of freedom displacement boundary conditions on a specimen in multi-axial hybrid simulations or conventional multi-axial displacement-controlled tests. As the displacement boundary conditions are typically defined in the Cartesian coordinate system, kinematic transformation is required to transform the boundary conditions into actuator strokes. In previous studies, the kinematic transformation was carried out assuming no elastic deformation of the reaction system where the actuators and specimens are mounted. Accordingly, the kinematic transformation becomes inaccurate if the elastic deformation are not negligible, thereby impacting the accuracy of the experiments. There are methods to compensate for these errors by instrumenting specimens, but the existing methods often require many iterations or do not monotonically approach the target displacements. This study proposes a new method for kinematic transformation from the Cartesian system to the actuators' local coordinate systems. The method adopts a model identification technique by which the influence of the elastic deformation can be effectively considered in calculating the actuator strokes. Numerical verification and experimental validation with the proposed transformation method are carried out. The results show that the proposed transformation method can decrease the number of iterations to achieve the target displacement boundary conditions and thus avoiding overshooting the displacement boundary conditions and reducing the interaction between actuators. It is expected that the proposed method can reduce the overall time to run a multi-axial hybrid simulation or multi-DOF displacement-controlled experiments.
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