Equivalent linearization for random vibrations of a building with yielding girders

The stochastic response of a yielding 2DF system subjected to a stationary Gaussian white noise excitation is investigated. The particular model considered represents a structure with yielding girders, so is more realistic than the common rigid floor model. The responses considered are the stationary root mean square (RMS) distortions of columns and rotations of girders. Simulation results are presented, as well as an equivalent linearization to approximate the response levels. A numerical integration scheme is presented to obtain simulation data on the stationary RMS distortions and rotations. The stationary RMS response is obtained by averaging a long sample time history (assuming ergodocity) of the response after the response has reached stationarity. The equivalent linearization approach is based on a substitute structure concept. Values of linear parameters are determined from simulation data for the SDF system and are functions of ductility. The Lyapunov equation is then written to calculate the stationary RMS response of the linearized system. (Abstract shortened with permission of author.