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Keywords: reliability, imperfection, material, structural, probability, fuzzy.

Summary

The paper deals with the stochastic and fuzzy analyses of uncertainty of the behaviour of steel strut with imperfections. The dispersions that can be obtained in the statistic analysis in the event that the random variables, which are not or cannot be obtained experimentally, are assigned as subjective statistical characteristics of input random variables according to expert knowledge is illustrated.

A strut of non-dimensional slenderness lambda^-=1.0 defined according to EC3 [1] was solved. The load-carrying capacity of a strut with is very sensitive to the variability of the imperfection e₀ [2]. According to results of experimental research [3], the dominant shape of initial curvature is given as one half-wave of the sine function.

Information on the statistical characteristics of the amplitude e₀ is dissonant due to varying conditions under which the measurements were performed. In the event that the amplitude e₀ is measured for a higher number of struts, the positive and negative realizations should occur with the same frequency. However, the statistical evaluation is frequently performed only for the positive values. Expert opinion on the statistical characteristics and type of density functions may however vary.

In view of the fact that imperfection e0 is the dominant variable, we are interested in how the uncertainty of variants of different subjectively selected distribution types and statistical characteristics will manifest on the statistical characteristics (histograms) of the random load-carrying capacity. The seventh random variable of e₀, is considered in several variants. Variants were chosen subjectively because experts' opinion on what frequency of realization will be found within the tolerance limits (which are also chosen subjectively) may differ.

The statistical analysis of the load-carrying capacity was evaluated by means of the Monte Carlo method. The load-carrying capacity was computed with the elastic Timoshenko solution [4]. The variants of the statistic solution demonstrate the vague uncertainty of the random load-carrying capacity due to the vague uncertainty of the input statistical characteristics of the amplitude e₀ of the initial strut curvature. The theory of fuzzy sets can be employed for the analysis of this problem. Kurtosis, which is the input parameter of the Hermite density function, was considered as a fuzzy number. The fuzzy analysis output is the fuzzy set of the density functions of the load-carrying capacity.

References

1: EN 1993-1-1:2005 (E): Eurocode 3: Design of Steel Structures - Part 1-1: General Rules and Rules for Buildings, CEN, 2005.
2: Kala Z., "Sensitivity Analysis of the Stability Problems of Thin-walled Structures", Journal of Constructional Steel Research, 61, pp. 415-422, 2005. doi:10.1016/j.jcsr.2004.08.005
3: Fukumoto Y., Kajina N., Aoki T., "Evaluation of Column Curves Based on Probabilistic Concept", In Proc. of Int. Conference on Stability, Prelim. Rep., publ. by Gakujutsu Bunken Fukyu - Kai, Tokyo, pp. 1-37, 1976.
4: Timoshenko S., Gere J., Theory of Elastic Stability, McGraw-Hill, New York, 1961.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 88 PROCEEDINGS OF THE NINTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping and M. Papadrakakis Paper 54 Fuzzy Probabilistic Models in Structural Reliability A. Omishore, Z. Kala and L. Puklický Department of Structure Mechanics, Faculty of Civil Engineering, Brno University of Technology, Czech Republic doi:10.4203/ccp.88.54 purchase the full-text of this paper Full Bibliographic Reference for this paper , "Fuzzy Probabilistic Models in Structural Reliability", in B.H.V. Topping, M. Papadrakakis, (Editors), "Proceedings of the Ninth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 54, 2008. doi:10.4203/ccp.88.54 Keywords: reliability, imperfection, material, structural, probability, fuzzy. Summary The paper deals with the stochastic and fuzzy analyses of uncertainty of the behaviour of steel strut with imperfections. The dispersions that can be obtained in the statistic analysis in the event that the random variables, which are not or cannot be obtained experimentally, are assigned as subjective statistical characteristics of input random variables according to expert knowledge is illustrated. A strut of non-dimensional slenderness lambda^-=1.0 defined according to EC3 [1] was solved. The load-carrying capacity of a strut with is very sensitive to the variability of the imperfection e₀ [2]. According to results of experimental research [3], the dominant shape of initial curvature is given as one half-wave of the sine function. Information on the statistical characteristics of the amplitude e₀ is dissonant due to varying conditions under which the measurements were performed. In the event that the amplitude e₀ is measured for a higher number of struts, the positive and negative realizations should occur with the same frequency. However, the statistical evaluation is frequently performed only for the positive values. Expert opinion on the statistical characteristics and type of density functions may however vary. In view of the fact that imperfection e0 is the dominant variable, we are interested in how the uncertainty of variants of different subjectively selected distribution types and statistical characteristics will manifest on the statistical characteristics (histograms) of the random load-carrying capacity. The seventh random variable of e₀, is considered in several variants. Variants were chosen subjectively because experts' opinion on what frequency of realization will be found within the tolerance limits (which are also chosen subjectively) may differ. The statistical analysis of the load-carrying capacity was evaluated by means of the Monte Carlo method. The load-carrying capacity was computed with the elastic Timoshenko solution [4]. The variants of the statistic solution demonstrate the vague uncertainty of the random load-carrying capacity due to the vague uncertainty of the input statistical characteristics of the amplitude e₀ of the initial strut curvature. The theory of fuzzy sets can be employed for the analysis of this problem. Kurtosis, which is the input parameter of the Hermite density function, was considered as a fuzzy number. The fuzzy analysis output is the fuzzy set of the density functions of the load-carrying capacity. References 1 EN 1993-1-1:2005 (E): Eurocode 3: Design of Steel Structures - Part 1-1: General Rules and Rules for Buildings, CEN, 2005. 2 Kala Z., "Sensitivity Analysis of the Stability Problems of Thin-walled Structures", Journal of Constructional Steel Research, 61, pp. 415-422, 2005. doi:10.1016/j.jcsr.2004.08.005 3 Fukumoto Y., Kajina N., Aoki T., "Evaluation of Column Curves Based on Probabilistic Concept", In Proc. of Int. Conference on Stability, Prelim. Rep., publ. by Gakujutsu Bunken Fukyu - Kai, Tokyo, pp. 1-37, 1976. 4 Timoshenko S., Gere J., Theory of Elastic Stability, McGraw-Hill, New York, 1961. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £145 +P&P)
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