Exploring the dynamics of a class of post-tensioned, moment resisting frames

In this paper, we present an equivalent low-order nonlinear system that describes the dynamics of a generic class of post-tensioned frames. The proposed nonlinear single degree of freedom system is derived from energy considerations. We demonstrate that the equation of motion for the entire, planar, post-tensioned frame is equivalent to the dynamics of a single tied rocking block on an elastic foundation. As validation for this analytical model we present physical tests (1/4 scale) undertaken at Bristol. Quasi-static push-pull-over tests and dynamic frequency sine sweep shake table tests are conducted on the physical model. Comparison of results indicate that the analytical model predicts both quasi-static nonlinear push-over and nonlinear dynamic resonant behaviour very well. Further numerical simulations on the analytical model identify the nonlinear resonant frequency backbone curves for a range of system parameters. We explore catchment basins of both Poincaré phase and system parameter spaces. In addition we describe failure boundaries and system integrity surfaces giving an indication as to likely bounds on forcing amplitudes.