NEWMARK IMPLICIT TIME INTEGRAL FOR APPLICATION IN PSEUDO-DYNAMIC TESTING - MATHEMATICAL VERIFICATION

Conventional experimental techniques like, quasi-static, effective force and shake-table techniques are generally being adopted to evaluate the seismic response of a civil engineering structure under earthquake loading. Among these techniques, shake-table technique has a merit over the other techniques due the fact that it realistically simulates all the three basic dynamic force parameters namely inertial, damping and elastic forces in the test structure. However this technique needs a sophisticated shake-table driven by servo hydraulic actuators with excellent control electronics. In the absence of such an expensive shake-table, it is possible to simulate the three dynamic force parameters using a static actuator through application of an equivalent pseudo-dynamic force system by computation of inertial forces in the back-ground. Such a hybrid Pseudo-dynamic (PsD) technique needs a specialized algorithm based on an appropriate mathematical model for the off-line time integration and computation of inertial forces such that the dynamic displacements/forces are applied statically through static actuators. Restoring forces offered by the structure are experimentally measured on-line at each time step and reflects the actual in-elastic and energy dissipation characteristics of the tested structure. The paper presents the mathematical formulation of a ‘predictor-corrector’ method using Newmark implicit relations and its implementation in PsD technique for seismic response evaluation of structures. In the proposed method displacement iterations are made in the corrector phase in achieving the implicit displacement which is an improvement over the conventional method where displacement iterations are made to achieve the explicit displacement resulting in lesser accuracy. To experimentally verify this improved PsD technique, the seismic response quantities including base shear, roof displacement and energy dissipation of a model steel frame structure subjected to a simulated earthquake predicted using PsD technique were calibrated with seismic responses evaluated using standard shake-table technique. The paper also presents the causes for the deviation in the predicted seismic responses using PsD technique and highlights its merits and demerits over shake-table technique.