The ultimate capacity of support structures is checked with extreme loads. This is straightforward when the limit state equations depend on a single load component, and it has become common to report maxima for each load component. However, if more than one load component is influential, e.g., both axial force and bending moments, it is not straightforward how to define an extreme load. The combination of univariate maxima can be too conservative, and many different combinations of load components can result in the worst value of the limit state equations. The use of contemporaneous load vectors is typically non-conservative. Therefore, in practice, limit state checks are done for each possible load vector, from each time step of a simulation. This is not feasible when performing reliability assessments and structural optimization, where additional, time-consuming computations are involved for each load vector. We therefore propose to use Pareto-optimal loads, which are a small set of loads that together represent all possible worst case scenarios. Simulations with two reference wind turbines show that this approach can be very useful for jacket structures, whereas the design of monopiles is often governed by the bending moment only. Even in this case, the approach might be useful when approaching the structural limits during optimization.
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