Real-time hybrid simulation is an attractive method to evaluate the response of structures under earthquake loads. The method is a variation of the pseudodynamic testing technique in which the experiment is executed in real time, thus allowing investigation of structural systems with rate-dependent components. Real-time hybrid simulation is challenging because it requires performance of all calculations, application of displacements, and acquisition of measured forces, within a very small increment of time. Furthermore, unless appropriate compensation for actuator dynamics is implemented, stability problems are likely to occur during the experiment. This paper presents an approach for real-time hybrid simulation in which compensation for actuator dynamics is implemented using a model-based feedforward compensator. The method is used to evaluate the response of a semi-active control of a structure employing an MR damper. Experimental results show good agreement with the predicted responses, demonstrating the effectiveness of the method for structural control performance assessment.

Real-time hybrid testing is an attractive method to evaluate the response of structures under earthquake loads. The method is a variation of the pseudodynamic testing technique in which the simulation is executed in real time, thus allowing investigation of structural systems with timedependent components. Real-time hybrid testing is challenging because it requires performance of all the calculations, application of the displacements, and acquisition of the measured forces, within a very small time frame (i.e., a single time step). Furthermore, unless appropriate compensation for time delays and actuator time lag is implemented, stability problems are likely to occur during the experiment (especially during testing of structures with high natural frequencies, e.g., stiff structures or multi-degree-of-freedom systems). This paper presents an approach for real-time hybrid testing in which time delay/lag compensation is implemented using model-based response prediction. The efficacy of the proposed strategy is verified by conducting substructure real-time hybrid testing of a steel frame under earthquake loads. Experimental results agree well with the analytical solution and show that the approach is capable of achieving a time-scale expansion factor of one (i.e., real time). Additionally, the proposed method allows testing structures with larger frequencies than when using the conventional polynomial extrapolation method, thus extending the capabilities of the real-time hybrid testing technique.

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This paper unites two major legacies of James Clerk Maxwell's ground-breaking paper, "On Reciprocal Figures, Frames, and Diagrams of Forces" (Maxwell, Philos Mag 26:250-261, 1864; Edinb Roy Soc Proc 7:160-208, 1870): (i) the fundamental theorem used by Michell (Philos Mag 8(47): [589][590][591][592][593][594][595][596][597] 1904) to derive trusses of least weight and (ii) reciprocal frames. This paper presents some remarkable relationships between discrete Michell frames and their corresponding reciprocal force polygons using Graphic Statics. Several examples are given to illustrate the notions of duality and self-reciprocity in these diagrams, with particular emphasis placed on discrete optimal benchmark structures. For a given connectivity of nodes, Graphic Statics provides all of the information needed to determine the total load path of the structure in the form and force diagrams. Because the form and force diagrams are reciprocal, in the course of finding one minimum load path structure, a second minimum load path structure is also found. These observations between the corresponding form and force diagrams are generalized for discrete cantilever Michell frames, and several comments on the extensions of this work are included.

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