Adaptive time stepping in pseudo-dynamic testing of earthquake driven structures

The problem of assessing errors in implementing time-marching algorithms in the context of pseudo-dynamic seismic testing of structures is considered. These errors occur in implementing the numerical and experimental steps of the test procedure. The study investigates how a linearized variational equation can be augmented with the governing equation of motion to track the effect of the errors, and, accordingly, adjust the step size of integration adaptively to keep a global error norm within specified limits. The governing augmented equations are integrated using an explicit operator splitting scheme. Additional efforts, in terms of evaluation of the tangent stiffness matrix, are shown to become necessary while modelling the errors. Illustrative examples include numerical studies on a set of nonlinear systems and an experimental study on a geometrically nonlinear two-storied building frame. The experimental results from pseudo-dynamic test are shown to compare reasonably well with pertinent results from an effective force test.