## 1 Introduction  
Connections in steel constructions are assembled by different components such as bolts, welds, and plates. The Eurocode EN 1993-1-8 [1] specifies the design rules for these single components. With this so-called \"component method\", (more or less) arbitrary connections can be designed and calculated. Background information and worked examples to the \"component method\" can be found, among others, in [2]. The proof of each of the mentioned components can easily be automated. A problem, which cannot be automated that easily, is the proof of the connection plates. These plates can be loaded in-plane (resulting in tension, compression, and shear stresses), out-of-plane (resulting in bending stresses), and both. Figure 1 shows some typical steel connections used in daily engineering practice (the connection plates are shaded in grey). In addition to the plates, there are additional components with individual behaviour, such as bolts and welds. A possible way to categorize the connection plates was made in Table 1. The categorization is based on the loading situation (in-plane, out-of-plane) and the resulting behaviour of the plates (in- and out-of-plane deformations). Furthermore, the typical failure mechanisms and corresponding proofs (similar to EN 1993-1-8) are also given in Table 1.  
The focus of the presented research is on bolted plates (loads and deformations are in-plane). To check such plates, the designer had to choose a critical net section and had to calculate the corresponding stress components, depending on the geometry and the arrangement of the bolts. In doing so, the _lower bound_ theorem and the Mises failure criterion are typically used. The _lower bound_ theorem, as well as the _upper bound_ theorem, are theorems based on the plasticity theory. A detailed explanation, including proofs of the theorems, can be found, among others, in [3]. Especially, the _lower bound_ theorem is typically chosen when designing steel connections in daily practice, which is also recommended by the Eurocode. Nevertheless, some checks in the EN 1993-1-8 are also based on the _upper bound_ theorem, such as the T-stub model. It should be mentioned that the theorems are only valid for ductile material behaviour, which can be assumed for the typically used mild steel grades (compare [4]). Furthermore, this is ruled in the EN 1993-1-10 [5] when designing steel constructions. Nevertheless, special attention is needed when the full plastic capacity cannot be reached, such as for local buckling problems (compare [6]) or bolts in tension. The cases considered here have drilled bolt holes, which means that stress concentrations will occur at the hole. The holes can be seen as mild notches, and the code rules a minimum distance between the holes. Therefore, it is assumed that the plates can reach their full plastic capacity. Pre-existing cracks, sharp notches, and other problems from fracture mechanics were typically not considered when designing such bolted connections, and is therefore, also not within the scope of this research. As an alternative to the _lower bound_ method in \"hand calculations\", the engineer can also use numerical methods such as the finite element method (FEM). In this case, the geometrical behaviour is usually assumed as linear. The material behaviour can be modelled as linear-elastic or nonlinear. The linear-elastic calculation would often result in a conservative design, whereas the nonlinear simulation is much more realistic (especially when real stress-strain curves were considered [7]), but also computationally intensive (iterative solution methods are required). Furthermore, to calculate the whole connection realistically, even further aspects such as nonlinear contact formulations or appropriate strain criteria must be considered. Commercial software packages often do not provide such contact formulations, and strain criteria are usually not defined in codes, such as the maximum