EN1990: Unravelling expressions 6.10 and 6.10a/6.10b

In EN1990, in persistent and transient design situations, action effects should be derived according to three different sets of combinations of actions: expressions 6.10 or, alternatively, the most adverse between expressions 6.10a and 6.10b or the most adverse between expressions 6.10a modified and 6.10b, being the choice among the three different sets left to the National annex. As the three formulations are not equivalent in terms of structural reliability, the reliability indexes associated which each of them in some simple, but very clear, case studies, have been determined, highlighting the differences and their significance. For each case, and for various ratios between the variable and permanent loads, the resistance of the considered structural member has been set equal to the capacity required by each set of combination of actions considered and the reliability indexes have been determined considering real load combination fitted in turn by one if the alternative sets of expressions, in such a way that the comparison focuses only on the reliability variations induced by combination rules. Results show that the target reliability level indicated in EN 1990 is commonly reached using expression 6.10, while expressions 6.10 a and 6.10b can lead to lower values, especially when the bias of resistance’s distribution is small, the C.O.V. of the resistance is high and the real distribution is fitted by [6.10]. In the authors’ opinion expressions 6.10 a modified and 6.10 b are not to be adopted, leading in some cases to significant reduction of the reliability indexes.