Model uncertainty related to designers' choice : A probabilistic analysis

Abstract: Today, in structural design, a structure is verified against failure by using the partial coefficient method provided by the Eurocodes. The verification method is, in its nature, a deterministic method where the input variables for load and resistance are assigned partial coefficients to ensure that the resistance is exceeded by the load effect. Since these coefficients are calibrated by using probabilistic methods, the partial coefficient method is also called a semi-probabilistic method. As an alternative, the verification is possible by using probabilistic methods. Instead of assigning partial coefficients to load- and resistance variables, they are treated as stochastic variables considering any physical- and statistical uncertainties associated with the same. For a complete probabilistic analysis, however, the model uncertainty must be considered. This uncertainty is associated with the mathematical models that are used to transform load- and material values into load effects and resistance and also uncertainties due to variations and simplifications of e.g. geometrical quantities and failure modes. There is another uncertainty not explicitly dealt with in the Eurocodes and the background material to the codes, that is the uncertainties related to the designers’ choice. That is, how the designer interprets given design conditions and existing codes and also due to the assumptions- and simplifications that takes place when the designer, based on a realistically given design task, must presume e.g. geometrical dimensions, loads and other necessary parameters when designing a structural element. As a basis for this study is a large statistical material, were a number of structural engineers have solved the exact same task which includes the calculation of loads- and load effects and to design a number of elements in an industrial single-storey building in steel. Statistical parameters, associated with the load effect variations due to the designers’ choice, has been estimated using mathematical statistics. Based on this results, a probabilistic level 2 method has been carried out in order to assess how the failure probability is affected when this model uncertainty is varied. It was found in the study that, using a 95% confidence interval, the coefficient of variance of the calculated load effects, defined herein as the model uncertainty due to the designers’ choice and denoted VθS, varies somewhat between 0 – 0,3 depending on the load combination- and type. By using simple examples, including only one variable load, it was shown that the variations in the model uncertainty VθS increases the failure probability thus decrease the reliability index β. The magnitude of these effects depends on the ratio φ between the permanent- and variable load. As an example, when φ = 0,75 (75% of the total load is variable thus 25% is permanent) and VθS = 0,3 then β ≈ 3,24 as compared to the target reliability index βt = 4,75 of safety class 3, which is a 32% reduction. Moreover, it was shown in the examples that the negative effects of increasing VθS, in terms of a decreased reliability index β, is more eminent in the case when the permanent load dominates the variable load, i.e. as φ = 0,25. Thus, increasing VθS from 0,1 to 0,2 decreases the reliability index by 30% (as compared to a 16% reduction when φ = 0,75).