| dc.description.abstract | The consideration of the combination of the actions is an inevitable step to design any structure in the civil engineering. In the codes EN 1990-EN 1998, there are given the common expressions of the combinations of the actions for different limit states and design situations. For example, according to EN 1990 [1] paragraph 6.4.3.2(2) the general format of effects of actions is Ed = {γG,j Gk,j; γPP; γQ,1Qk,1; γQ,iΨ0,iQk,i}, j≥1, i≥1; , where E should be understand as a function of an effect of the actions is ; Gk,j, j ∈ {1, ... , n} is a characteristic value of the permanent action, Qk,1 is a characteristic value of the leading variable action; Qk,i, i ∈ {1, ... , m} is characteristic value of accompanying variable actions, n and (m +1) are numbers of permanent and variable actions respectively, P is the relevant representative value of a prestressing action; γG,j, γQ,i, and γP are partial factors of the permanent action Gj, variable action Qi and prestressing action P respectively; γQ,1 is the partial factor for the leading action Qk,1. The direct application of this (commented) equation, as well as other formulas of STR, GEO and serviceability limit states given in paragraphs 6.4.3.2(3), 6.5.3(1) of EN 1990 [1] is restricted because we do not know in advance the leading variable action Q1 and accompanying variable actions Qi. Even though, in general, in advance, we do now favourable and unfavourable variable and permanent actions. Therefore, the practical application of the formulas of the combination of actions given in codes EN 1990 – EN 1998 is possible only in very simple cases, when the number of actions is very few. Only in this case we can distinguish in advance already mentioned leading variable action, favourable and unfavourable variable and permanent actions. In practice, there can be many permanent and variable actions. As a consequence, we cannot know in advance already mentioned leading variable action, favourable and unfavourable variable and permanent actions to design a structure. In this case, to design a structure a combinatorial optimisation problem has to be solved. For this purpose, for the given structure, it is necessary to make a set of all possible combinations of actions for particular limit state and design situation and to solve a combinatorial optimisation problem to determine the most dangerous combination of the actions. The present investigations are devoted to the issues how to determine the set of actions that attains most unfavourable actions for the ultimate and serviceability limit states of the persistent and transient design situations. The proposed methodology is represented in terms of the set theory. [...] | eng |
