Stochastic response of multistorey yielding frames

A model for the random vibration of hysteretic and degrading plane frames to Gaussian shot noise or filtered shot noise is presented. The model, which combines the discrete hinge concept previously used in deterministic frame analysis with Bouc's smooth system hysteresis, results in a non-linear set of differential equations which can be linearized in closed form without recourse to the Krylov-Bogoliubov assumptions. Solution is iterative in the stationary case and by numerical integration with stepwise updates in the non-stationary case. Numerical studies are presented of strong girder and strong column two storey, one bay frames. These studies indicate that the model can locate the sites of yielding and provide reasonable values of structural response as compared with simulation data. Moreover, the model can provide a joint by joint breakdown of the structure energy dissipation rate.