RESPONSE OF YIELDING MDF STRUCTURES TO STOCHASTIC EXCITATION

The random response of bilinear hysteretic yielding systems subjected to a stationary Gaussian white noise excitation is studied. The responses considered are the root mean square (rms) interfloor displacements of yielding multi-degree-of-freedom (MDF) shear beam type building structures. Simulation results are presented as well as analytical methods to approximate the response levels. Both stationary response levels and the transient build-up of response for systems which are initially at rest are investigated. Nearly elastoplastic 2DF, 4DF and 10DF systems are studied with different stiffness distribution over the height (uniform or tapered) and with different damping ratios. In the simulation studies, the stationary rms interfloor displacement of the yielding MDF bilinear hysteretic system are taken as the time averages of responses to a particular time history (assuming ergodocity). Determining the transient rms interfloor displacements, though, involves computing averages across an ensemble of response time histories. Each response time history is obtained by numerical integration of the equations of motion for a particular time history of excitation. The analytical method presented for predicting the response levels of the yielding MDF system is based on a substitute structure concept. The parameters of the substitute structure are determined from an equivalent third-order system model for single-degree-of-freedom (SDF) structures. That is, each yielding story in the MDF system is replaced by springs and dashpots corresponding to a third-order model for a SDF system. The values of these linear parameters depend on the expected ductility ratio and are determined empirically from simulation data for SDF systems. The Liapunov covariance matrix equation of this higher order linear system is then established to compute the stationary rms interfloor displacements. The stationary results obtained by this method compare very well with those from simulation. The transient rms interfloor displacements of this higher order linear system are also investigated. The Liapunov covariance differential equation is integrated to obtain the transient mean squared responses numerically. The computed results are in good agreement with those from simulation for stories with very high or very low stationary expected ductility factors. . . . (Author's abstract exceeds stipulated maximum length. Discontinued here with permission of school.) UM