Equivalent Geometric Imperfections for Steel Shell Structures Subject to Combined Loading

The inevitable deviations from the nominal data of the resistance parameters have to be included in a numerical calculation of the load-bearing capacity of shells, because these structures are very imperfection-sensitive. In addition to simpler methods, the new European code for the resistance verification of steel shell structures EN 1993-1-6:2005 allows a geometrically and materially nonlinear analysis with imperfections included. The assumed imperfections are fundamental for this most sophisticated numerical buckling strength verification, because they have to cover the influence of all accidental imperfections of the structure in a consistent manner. According to the Eurocode, the influence of all various deviations should be included by only geometric equivalent imperfections. In spite of the intensive research efforts in the last decades, many problems are still residual, which have to be solved in order to apply the mentioned most realistic basic principle of the Eurocode to shell buckling cases, which are not yet sufficiently investigated. Equivalent geometric imperfections are called consistent, if nonlinear numerical analyses including these imperfections result in the experimentally based buckling resistance. Consistent equivalent geometric imperfections have been developed during the last years for the basic buckling cases of the circular cylindrical steel shell ([

1

], [

2

]).

The situation at shells subject to combined loading is more difficult, because not so much experimental data are available. Fundamental problems and previous proposals for assuming equivalent imperfections at combined loading are discussed in the contribution. In particular, it is mooted, if the equivalent geometric imperfections have to be chosen without regard to the loading case, because imperfections of real shells are caused by manufacturing and not by loading. Reasons are given for, why this is not the case at equivalent imperfections of a numerical simulation. The conception of quasi-collapse-affine imperfections [

3

], which has already been proved at the basic buckling cases, can also be applied to shells under combined loading. General information for the application is given on the basis of two relevant buckling cases under combined loading.