In quasi-static and hybrid tests, accurate reproduction of structural responses often requires multi-degree-of-freedom (multi-DOF) loading methods. A successful loading method should not only be used on specific specimens for research purposes, but also be applicable to all possible types of specimen and testing setups for engineering purposes. However, for different specimens, the concerned nodes and DOFs differ in size, leading to non-uniform kinematic transformation between the Cartesian system and the actuators/transducers coordinate systems. While for different testing setups, the type of loading targets on each DOF varies, they can be displacement or force. These diversities together make it difficult to achieve versatility in applying loading methods. To address this challenge, a control nodes based loading method was proposed. This method was constructed based on the viewpoint that any specimen can be treated as a combination of several control nodes, and the loading loop should be constructed on each control node. In this method, at first, the loading targets, actuators and external transducers were assigned to each control node accordingly. Then, the loading loops were constructed based on each control node instead of the entire specimen DOFs, which is capable of achieving uniform kinematic transformation and also convenient to apply redundant controlling. Finally, all the control nodes were assembled in one closed loop to support mixed force-displacement loading considering the coupling of multiple DOFs. Hybrid tests and quasi-static tests of a full-scale steel frame were carried out to demonstrate the accuracy and feasibility of the proposed loading method.

Hybrid simulation is a powerful testing method that combines numerical analysis and physical experiments through on-line interaction. The substructuring technology enables hybrid simulation to evaluate the structural performance with large-scale specimens. However, this technology also increases the complexity of specimen boundary conditions. Due to limited equipment resources of structural laboratories, not all the degrees of freedom of the boundary conditions can be realized during tests, which will induce error to the experimental restoring forces and decrease of accuracy of hybrid simulation. In this case, the hybrid simulation method based on restoring force correction was proposed to reduce this error. In this method, the error in experimental restoring forces were corrected using an auxiliary numerical model of the experimental substructure. The effectiveness of the proposed method was verified through both theoretical analysis and numerical examples. This method was then adopted to evaluate the seismic performance of a spatial reinforced concrete frame with buckling-restrained braces numerically. Results showed that the proposed method can enhance the accuracy of tests compared to conventional hybrid simulation, and keep computational efficiency in the meanwhile.

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