In the analysis of failure the size of the load is calculated in which the structure cannot, or only under conditions of impermissible deformation, accept any further increase of the load. An exact depiction of the theoretical background is given, for example, in [Hibbi95] [Krätz94] [Mehlh95] [Steup66]. The following terms are of great importance (Image 5.3.3.7.2.2-1).

- Stability problem;
- Breakdown problem;
- Branching problem;
- Stress problem.

A **stability problem** exists exactly when for a particular value of the loading there is the possibility of more than just a displacement condition. Every stability problem is therefore an ambiguous problem. In order to evaluate the ambiguousness of the stability of a carrier construction, it is important to have an exact knowledge of the deformation characteristic. If an extreme value occurs in the load-displacement curve, then one speaks of a **breakdown problem**. In the so-called post-buckling phase, the displacement increases up to the load minimum in the rebound or stability point. After this a static equilibrium and a further increase in load is again possible. The branching of further curves from the load-displacement curve points to a so-called **branching problem**, If, however, the force and displacement are always unambiguously defined over the course of the curve, then it is a case of a **stress problem**. The bearing load of the system in this case is limited in that a cross section cannot absorb the stresses anymore and fails or the deformation grows over-proportionally.