The stability or tipping safety of an upright body is the better, the greater the distance of the plumb point of the body's center of gravity in the contact area from the edges ( tilt axes or tilt edges ) of this surface. The distance is optimal when it is the same size from all tilting edges.
The stability of structures affects the risk of collapse . As part of the mathematical proof of stability , it is calculated as the quotient between the absorbable and the existing loads on a structure .
Various standards have been developed which define the required stability for certain proof of stability.
To prove the stability, different failure mechanisms have to be proven individually. They can be broken down into system failure and local failure. If the system fails, the entire system becomes unstable. An example of this would be tilting a wall.
In the event of a local failure, a stress that is too great for the material used occurs in a localized area. For example, the maximum stress that can be absorbed for a mortar joint in a masonry wall is exceeded. This can lead to unwanted cracks in the wall. Depending on the bearing reserves in the overall system, a local failure can also lead to a system failure.
The calculation of the stresses (usually stresses ) is carried out by solving differential equations . As a rule, the differential equations cannot be solved exactly. Physical or numerical approximate solutions are therefore determined. An example of a physical approximation is the plate theory , in which the supporting structure of a ceiling is determined using state variables for a surface . An example of a numerical approximation method is the finite element method (FEM).
An example of a simple method for calculating stability is the cantilever method , which uses beam theory .