Abstract
The main aim of this work was to investigate a numerical error in determining limit state functions, which describe the extreme magnitudes of steel structures with respect to random variables. It was assisted here by the global version of the response function method (RFM). Various approximations of trial points generated on the basis of several hundred selected reference composite functions based on polynomials were analyzed. The final goal was to find some criterion—between approximation and input data—for the selection of the response function leading to relative a posteriori errors less than 1%. Unlike the classical problem of curve fitting, the accuracy of the final values of probabilistic moments was verified here as they can be used in further reliability calculations. The use of the criterion and the associated way of selecting the response function was demonstrated on the example of steel diagrid grillages. It resulted in quite high correctness in comparison with extended FEM tests.
Highlights
Diagrid structural systems have come out as some of the most efficient, most adaptable and most innovative approaches to structural buildings of this century [1,2]
A solution of the structural problem including randomness can be accompanied by a verification of the reliability indices calculated, for example, according to Cornell [3]—or using more sophisticated indicators [4,5,6,7,8]—by using a simple limit state function g defined as the difference between structural responses f a (b) and their given thresholds f max (Figure 1)
The diathe results was related to the error, so the analysis of the results focused on the range grams in this part of the experiment were partially analyzed visually and the most im−4 to 100 —two orders of magnitude difference
Summary
Diagrid structural systems have come out as some of the most efficient, most adaptable and most innovative approaches to structural buildings of this century [1,2]. Of the method choice, the determination of structural responses—with respect to some input parameter subjected to uncertain fluctuations—is required. In practical cases, it is one of the crucial issues in the reliability assessment of structures, and the main aim of this work since the exact dependence is usually unavailable. It is one of the crucial issues in the reliability assessment of structures, and the main aim of this work since the exact dependence is usually unavailable It can only have discrete results with some error, obtaining which takes additional time. Thesome choice is obtaining a compromise between unavailable It can only have discrete results with error, which takes ad- accuracy and computational efficiency.
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