## 1 Introduction
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Situation** & **Load** & **Deformation** & **Failure Modes and Proofs** \\ \hline Plates with a single bolt & In-plane & In-plane & Net section failure, \\  & & & Bearing resistance \\ Plates with bolt groups & In-plane & In-plane & Bearing resistance for bolt groups, \\ Plates in & & & Block tearing \\ compression/shear & & & Local buckling problems \\ Plates loaded & Out-of-plane & Out-of-plane & Bending capacity (T-stub model) \\ Plates loaded in- and & & In- and out-of-plane & In- and out-of-plane & Interaction criteria including local buckling \\ out-of-plane & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Categorization of connection plates, depending on the loading situation and the deformation behaviour. Figure 1: Typical steel connections. The connection plates are shaded in grey: (**a**) Plate mainly in bending (plate is loaded in- and out-of-plane); (**b**–**d**) plates are loaded in-plane. allowed strains for bearing failure (this will maybe change with the new Eurocode EN 1993-1-14, which is actually under progress). The presented research focuses on an alternative method to overcome the problems mentioned above--the so-called discontinuity layout optimization (DLO). The DLO was first invented in [8; 9] for plane plasticity problems, in analogy to truss layout optimization problems [10; 11]. The first application was focused on geotechnical issues and the analysis of masonry arches [12]. Further research, especially on geotechnical problems, was made, among others, by [13; 14; 15]. Ongoing research was also focused on the extension to three-dimensional geotechnical issues [16; 17]. A gradient-based adaptive solution method (ADLO) was presented in [18]. In addition to the plane plasticity problems, the DLO was also extended to analyze reinforced concrete slabs in [19; 20; 21]. For practical application of the before mentioned problems, the software LimitState [22] was invented. The DLO procedure is based on the _upper bound_ theorem, and therefore, results in an unsafe solution. If a load can be found, which also equals the solution from the _lower bound_ theorem, then the correct loading capacity of the system was found (assuming an ideal-plastic material behaviour). The DLO procedure uses a broad set of possible failure mechanisms to overcome this problem. A linear programming (LP) algorithm tries to find the minimum load that the system collapses. Due to the discretization of the system with a limited number of failure mechanisms, the obtained load is still an _upper bound_ but usually comes very close to the correct capacity [21; 22]. The DLO procedure can be automatized for arbitrary geometries and loading situations, which is not the case for the _lower bound_ method in \"hand calculations\". The DLO procedure is much easier to use compared to the nonlinear FEM. Furthermore, no iterative solution methods are required because the nonlinear material behaviour (ideal-plastic) is implemented in the basic DLO formulation, which makes the technique a very efficient way to obtain the ultimate loads of arbitrary geometries and loading situations. **Research goal and strategy:** Analyzing typical steel connections (as shown in Figure 1), but also more complex connections, is a \"long term\" goal. To reach this goal, the behaviour of the plates and the single components (as given in Table 1) must be analyzed systematically by the DLO approach. This also depends on the numerical implementation of the DLO method (mainly the degrees-of-freedom acting in-plane and out-of-plane). As a good starting point, the presented research focuses on the first row from Table 1. Analyzing plates loaded in-plane with a single bolt is the first step to check if the DLO procedure is suitable to handle such typical problems in steel connections. Furthermore, this research is the basis for further investigations on the other assemblies given in Table 1, but also on more complex connections.