Staggered coordination in substructure online hybrid test on a RC frame retrofitted by BRBs

Proposed in this paper is an online hybrid test framework using a static and dynamic separated model scheme, where the equations of motion are solved by the operator-splitting (OS) algorithm, while the restoring force is obtained from a static analysis or quasi-static test of substructures. One of the keys of a successful substructure online hybrid test is the boundary coordination between the numerical and physical substructures. This is easily determined for the dynamic boundary whose displacement target is determined by the displacement predictor of the OS algorithm. However, the coordination is not straightforward for boundaries associated with static forces. This paper proposes an approximate method to determine the compatibility of the boundaries of static degrees of freedom, where the numerical substructure is analyzed first with the static boundary at the displacement of the previous step. The reaction force is then acquired from the analysis results as the target force of the corresponding degree of freedom of the physical substructure. The measured displacement is used as the target for the numerical substructure in the next step. In this procedure, the numerical substructure and the physical substructure alternatively move forward. Therefore, it is call staggered coordination. This is not a rigorous method to analyze boundary compatibility and equilibrium. However, it does make the substructure online hybrid test much easier and more feasible. Here, the staggered coordination scheme is examined by a six-story RC frame equipped with BRBs through both numerical simulation and physical testing. An energy-based index shows that the error introduced by this method can be ignored and that the proposed framework of online hybrid test works precisely without any malfunction.