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 general class of post-tensioned frames. The proposed nonlinear single degree of freedom system isderived from energy considerations. It is demonstrated that the equation of motion for the entire, general, 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. Catchment basins of both Poincaré phase and system parameter spaces are explored. Failure boundaries and system integrity surfaces indicate robust bounds on safe forcing amplitudes.