THE HYPERCONE METHOD FOR STRUCTURAL RELIABILITY-ANALYSIS - ITS THEORETICAL PRINCIPLES

The hypercome method is a new geometrical technique which aims to evaluate the probability of failure, Pf, by consdering the whole geomeometry of the failure domain Df. Since this latter is generally irregular and very distorted, lower-and upper-bound values of Pf are calculated (instead of a unique value of Pf). The theoretical aspects of the method are presented in the first part of this paper. Practical applications, dealing with an isostatic reinforced beam while the applied loads and the material strengths are considered as random variables, are reported in the second part. The hypercome method is compared with Monte Carlo simulations, levels-2 method and other operational procedures. Through the results obtained, it can be noticed that: 1. (1) the two bounds calculated by the hypercone method are in very small relative ratios, ranging from 4 (for under-reinforced structures) to 10 (for over-reinforced structures) approximately; 2. (2) the operational values of Pf deduced from the Lind-Hasofer index β (assuming that the limit state surface is linear), and Pf values evaluated by Monte Carlo simulations are in accordance with the hypercone method; 3. (3) rmPf, calculated under the hypothesis that the state random variable E (E = resistance-action) might follow a gaussian distribution, are slightly inaccurate. © 1990.