Abstract
This study is an attempt to assess the effect of node location imperfections on the reliability dome. The analysis concerns a single-layer steel lattice dome that is very sensitive to node snap-through. The load-displacement path of the structure was determined using the program, Finite Element Method-Krata. To determine the failure probability, reliability index, and elasticity index, the first-order reliability method approximation method was employed. The reliability analysis was conducted with Numpress Explore software, developed at the Institute of Fundamental Technological Research of the Polish Academy of Sciences, Warsaw. In this paper, it is shown how large differences in the assessment of the safety of a structure can appear when we incorrectly estimate the standard deviation of the random variable responsible for the imperfections of node locations.
Highlights
The reliability theory is a well-established research area
It must be remembered that, in reality, every physical quantity is a random variable; for computational purposes, a part of them are assumed as deterministic parameters
Identification of variables determines the solution of the problem in a significant way; it is essential to investigate the elasticity index
Summary
The reliability theory is a well-established research area. The most well-known textbooks and monographs are: Madsen, Krenk, and Lind [1], Melchers [2], Ditlevsen and Madsen [3], Thoft–Christensen and Baker [4], and Augusti, Baratta, and Casciati [5]. Special attention should be paid to publications by Harr [6] and Nowak and Collins [7]. These publications present the basic concepts of reliability theory with a particular reference to their uses in civil engineering. Hasofer and Lind developed the concept of localization of the so-called ‘design point’, i.e., such realization of random variables from the failure surface, which corresponds to the greatest value of the probability density function. With the linearization of the limit state function at the design point, it is possible to obtain a measure of reliability that is invariant, due to the equivalent formulations of the boundary condition, i.e., the so-called Hasofer–Lind reliability index.
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