On the reliability of steel frames exposed to snow load. Considering the Effect of Epistemic Uncertainty

Rózsás, Árpád and Vigh, László Gergely (2014) On the reliability of steel frames exposed to snow load. Considering the Effect of Epistemic Uncertainty. In: EUROSTEEL 2014, 10-12. September 2014, Naples, Italy.

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Abstract

This paper examines the reliability level of the Eurocode’s partial factor design (PFD) method for steel frames subjected to snow load. This is motivated by the frequent damage and collapse of structures under heavy snowfall [1, 2]. We present a general approach which can help to comprehensively investigate the compliance of current Eurocode partial factor provisions and to assess whether the collapses most frequently observed at steel structures can be attributed to the deficiency of standardized provisions. To alleviate the limitations of previous studies, the general framework is intended to efficiently perform parametric reliability analysis using state-of-the-art numerical methods, has the potential to identify the crucial parameters, the sufficient modelling level and to justify the assumptions made in previous studies. Additionally the effect of epistemic uncertainties through Bayesian statistical analysis is also taken into account. The presented approach is illustrated through a simple steel frame, which is analysed considering various load-ratios. First, actual snow measurements are evaluated using classical, maximum likelihood based and Bayesian methods. Lognormal, Generalized Extreme Value (GEV) and Gumbel distributions are considered. Using these results partial factor based optimization of the frames is performed. The firefly metaheuristic algorithm is chosen to carry out the optimization [3]. This optimization is used to get fully utilized structures per PFD which is indispensable for reliability assessment of the method. Cross-sectional level limit state function is considered taking into account the global stability of the frame approximately. The objective function is the overall weight of the structure; the constraints are enforced through penalty functions. After the PFD, the safety level of the structures is analyzed. The reliability analysis is performed using FORM, SORM and importance sampling Monte Carlo (ISMC) methods. Based on the completed analyses, the main conclusions are the following: (i) The safety level of steel frames subjected to snow load is fairly sensitive to the distribution type used to describe the dominant variable load. This assertion is valid irrespectively of the load-ratio. (ii) Frames designed per partial factor method in accordance with Eurocode, i.e., using Gumbel distribution assumption and frequentist statistics (MLE) to derive characteristic loads, may not have adequate safety level in the high load-ratio region with the same assumptions made in the reliability analysis. If GEV distribution is used in the reliability analysis the safety level significantly decreases, by ~14% compared to Gumbel model, which means a 7 times increase in the probability of failure. (iii) In case of GEV distribution the Bayesian posterior model gives about 80% higher probability of failure than the GEV-MLE. (iv) The epistemic uncertainty has a significant effect on the reliability of steel frames, in case of Gumbel distribution the incorporation of epistemic uncertainty into the reliability analysis yields to ~35% increase in the probability of failure. For the GEV distribution the increase is about 400-500%. (v) The reliability level substantially varies with the load-ratio, this cannot be captured by one single partial factor of the snow load. It should be emphasized that the statistical analysis is based on a 50-year long observation and the numerical analysis is limited to few examples. The investigation is being extended to further design cases and to the sensitivity analysis of measurements data, to able to draw general conclusions. REFERENCES [1] Geis, J, Strobel, K, Liel, A, “Snow-Induced Building Failures”, Journal of Performance of Constructed Facilities, Vol. 26, pp. 377-388, 2011. [2] Holicky, M, Sykora, M, “Failures of Roofs under Snow Load: Causes and Reliability Analysis” in Forensic Engineering 2009, American Society of Civil Engineers, pp. 444-453, 2009. [3] Yang, X-S, Engineering Optimization: An Introduction with Metaheuristic Applications, John Wiley & Sons, Hoboken, New Jersey, 2010.

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