The Non-probabilistic Reliability Of Structures Based-on Capacity Spectrum Method

The basic ideas of performance-based seismic design, a trend of earthquake engineering, will be used as a design criterion and be applied to the present projects. The performace-based earthquake engineering is on the basis of probabilistic reliability theory. However, when the data is insufficient to support a probabilistic assumption, the probabilistic approach is not effective in dealing with the uncertainty in earthquake engineering. In this study, the convex model is applied in describing the uncertainty of the earthquake action. Based on capacity spectrum method, the thoery of non-probabilistic reliability is applied to anlyse the reliability of the structrual system under the action of high-level earthquake. The main contents of this research are as follows:Firstly, the basic concepts of probabilistic theory and the limitation of probabilistic model are discussed. The key concepts and characters of the convex model are briefly introduced. By using a norm measure in the standard space, the quantified definitions of non-probabilistic reliability indexes based on interval model and ellipsoid convex model are proposed. Accordingly,the defination of the non-probabilistic reliability degreee is proposed. Three methods are proposed to calculate the structural reliability under hybrid probability and convex set model representing the coexistence of stochastic variables and non-probabilistic variables in practical engineering. The application of convex set model in earthquake engineering is systematically introduced, and the necessarity of using convex set theory in dealing with uncertainty in earthquake engineering is pointed out.Secondly, the basic concept of response spectrum is introduced. The uncertainties of the two key variables of the response spectrum, the earthquake influence coefficient maximum and the predominant peried,are systematically analysed. Their uncertainties are represented by the interval model. Based on the statistical analysis of a large number of earthquake acceleration records collected from the western America and other regions, the interval ranges of the earthquake influence coefficient maximum and the predominant peried are given respectively. And the interval response spectrum are presented by the method of convex problem.Finally, based on capacity spectrum method,double capacity curves are used to consider the uncertainty of the resistence capacity of the structure caused by the lateral loading modes. Under determinate loading mode,the influence of the variability of the concrete to the resistence capacity of the structure is considered by using probabilistic method. The uncertainties of the earthquake are considered by appling interval response spetrum, and the interval of the earthquake response is obtaind by using capacity spectrum method. The non-probabilistic reliability of the system resisting high-level earthquake is further calculated by the computational method of the non-probabilistic reliability proposed. Through the case of two RC building structures of seven stories and ten stories, designed in accordance with Chinese code for seismic design of buildings,the reasonability of the method proposed in this paper can be proved.