Substructure Modeling and Loading-Control Techniques for the Test of a Full-Scale Spatial RC Frame with Buckling-Restrained Braces Subjected to Bidirectional Loading

To investigate the performance of reinforced-concrete frames with buckling restrained braces (RCF-BRB) subjected to bidirectional earthquakes, a full-scale two-story RCF-BRB was tested using substructured pseudodynamic (PsD), quasistatic, and pushover techniques. This paper focuses on the structural modeling for the substructured PsD tests, and the control and measurement issues of the bidirectional loading system. To make a credible reproduction of the structural response using substructured PsD technique, an overlap modeling technique together with tuning the mass of the lamped-mass model and stiffness of the numerical substructure was employed to reduce errors caused by the incomplete boundary condition. The outer-loop control method based on Newton’s iteration method was introduced for the loading system, with the data from external displacement sensors as the feedback to avoid errors caused by possible gaps in the connection parts of the loading system. The redundancy issue, caused by the actuators outnumbering the degrees of freedom of the floor to be controlled, is addressed with a force-displacement mixed control technique. The three of four actuators were controlled in displacement mode, whereas the redundant one was in force mode. The force command to the redundant actuator was determined with the optimization criteria to minimize the loads relative to the capacities of the actuators. The working range of the displacement sensors is investigated using numerical and geometric approaches. Failure examples from numerical simulation and experiment were shown to emphasize the importance of proper arrangement of displacement sensors. A rearrangement of the displacement sensors was proposed for the pushover test to enlarge the working range. Time-history results of the prototype structure using the calibrated finite-element model show that the PsD substructure test results could represent seismic responses of the prototype structure. The measured mass-center displacements accurately tracked the target displacements throughout the test, indicating the effectiveness of the loading control and measuring system.