1 Department of Structural Engineering and Materials, Technical University of Denmark
Report based on Ph.D.-thesis (supervisor: Ove Ditlevsen)
The response of the white noise excited multi-degree-of-freedom (MDOF) oscillator has been analyzed in order to describe the plastic displacements of the relative response. Three different types of structural systems have been considered. The first type is a shear-wall frame having elastic-ideal plastic stiffness properties of the columns connecting the two top-most floors. The second type is a shear-wall frame having elastic-ideal plastic stiffness properties of all columns, while the third type is a single-degree-of-freedom (SDOF) oscillator excited by horizontal and vertical white noise ground acceleration. The basic tool in the analysis is the use of the Slepian model process to obtain the plastic displacements. The results have been presented in terms of density functions for the plastic displacements and the results obtained by use of the Slepian model process have been compared to the results obtained from a direct simulation of the response. The comparative analysis has been made for varying values of the system parameters and has shown good agreements. The Slepian model has been used in two different ways, depending on the expression of the plastic displacement. By using an approximate expression of the plastic displacement neglecting a term related to energy considerations, the use of the Slepian model process is leading to closed form solutions to the density functions for plastic displacements. When the energy related term is taken into consideration a simulation procedure based on the Slepian model process is used to obtain outcomes of the plastic displacements, from which a density function can be estimated. The single plastic displacements is considered separately leading to different expressions of the density functions, depending on whether the first plastic displacement in a clump of plastic displacements or one of the following plastic displacements in a clump is considered. There is a good agreement between the obtained density functions determined on the basis of the Slepian model process and the estimated density functions based on the outcomes of the direct simulation.Certain features, such as inter-clump durations and the time distance between any two consecutive crests in a clump, are not available from the Slepian model process and are estimated solely from the direct simulation of the response. Comparisons of the estimates of these parameters are done by considering the envelope process of the displacement process and determining approximate analytical expressions of the inter-clump duration on the basis of the envelope process. The results show good agreements. Experiments have been made for a MDOF-oscillator of the same type as considered in the numerical analysis. Comparison with results obtained from the numerical analysis show good agreements. The influence of the vertical ground acceleration on the horizontal displace ment process is examined for a SDOF-elasto-plastic oscillator. The parametric excitation coming from the vertical ground acceleration is included in the direct simulation of the response, and the results show that the influence on the displacement is almost vanishing for the considered load cases.