Abstract
Abstract In this paper, uncertainties and failure criteria of structure are mathematically expressed by random variables and a limit state equation. A limit state equation is approximated by Fleishman's 3rd order polynomials and the theoretical moments of an approximated limit state equation are calculated. Fleishman introduced a 3rd order polynomial in terms of only standard normal distiribution random variables. But, in this paper, Fleishman's polynomial is extended to various random variables including beta, gamma, uniform distributions. Cumulants and a normalized limit state equation are used to calculate a theoretical moments of a limit state equation. A cumulative distribution function of a normalized limit state equation is approximated by a Pearson system. Keywords :reliability analysis, pearson system, moments, cumulants † Corresponding author: Tel: +82-42-860-2282; E-mail: lsg@kari.re.krReceived January 21 2013; Revised June 11 2013;Accepted June 12 2013Ⓒ2013 by Computational Structural Engineering Institute of KoreaThis is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License(http://creativecommons. org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
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