# Proof of stability

A **proof of stability** is a computational proof of stability, a calculation using the methods of statics or structural engineering and technical mechanics or geotechnics .

Other expressions for the term proof of stability are: proof of stability , proof of stability , proof of load-bearing capacity, proof of structural safety, proof of stability (also: static calculation or simply called "statics"). In Switzerland it can be found under the heading "Security Plan".

## Areas of application

The so-called limit state is calculated bearing capacity and often the limit state serviceability . There are safety factors calculated against the failure in different ways against slipping, sliding, lifting, tilting, bulging and other failure modes depending on the application. A slip safety proof or a tilt safety proof can be part of a stability proof.

The proof of stability of structures is the calculation and dimensioning of a supporting structure so that it can absorb the assumed loads (dead weight, attachments, etc., snow / wind / traffic loads ...) for its service life.

There are also proof of stability in other areas, e.g. B. geotechnical evidence against terrain and slope stability , bearing capacity , in terrain jumps z, for mountain and rock. B. in tunnel and cavern construction. Next there is proof of stability for dams (according to DIN 19700 ), for temporary structures according to DIN EN 13782, for scaffolding according to EN 12811, for platforms that are built temporarily for vehicles (there usually a Kippsicherheitsnachweis ) etc.

Certain individual verifications only consider a partial aspect of stability or certain failure mechanisms. These are, for example: slip safety proof , tilt safety proof , crack width proof , usability proof .

## Procedure

Proof of stability means that the loads and effects (forces, tensions) that occur must be compared with the existing resistances (e.g. tensile, compressive and shear strength). Their ratio is the safety factor . The loads that occur must be diverted into the subsoil or the stand area without endangering the stability of the supporting structure and thus presenting a risk to the user. In the case of proof of stability, calculation models are used that simulate the structure more or less precisely. The verification generally has to be carried out for different load cases, which can have different safety factors. The less often a load case can occur, the lower the safety factor can be.

In the case of a proof of stability, the effects that occur must be compared with the existing resistances (strengths), whereby a sufficient safety margin must be maintained. The effects occurring (loads, external forces) create stresses and forces (internal forces, compressive, tensile and shear stresses). The safety margin that one has to demand and achieve depends on the statistical spread in the calculation assumptions ( parameters , strengths ) and on the accuracy of the calculation.

In addition, the usability must be satisfied, i.e. there must be no major deformations (e.g. sagging beams) or other damage (cracks in the concrete, susceptibility to vibration in a ceiling, etc.). These deficiencies affect i. d. Usually not the stability of a supporting member / structure, but disturb the appearance and make further expansion difficult.

Depending on the size and type of the structure, proof of stability may be carried out by engineers or, in the case of low-difficulty building projects, by state-certified structural engineers . If the proof of stability comes to the conclusion that the stability is not sufficient, the structure must be dimensioned more heavily , for example with stronger building material, more reinforcement, larger girder cross-sections, thicker supports, smaller spans, larger contact areas, etc.

### Regulations in Germany

The building authorities demand in Germany for any type of building of a certain size stability analyzes, for issuing the building permit must be submitted. The evidence that must be provided differs depending on the type of structure. They are usually prescribed in DIN standards, for example in DIN 1045 for concrete structures. There is evidence for entire structures (global security) and individual verifications for parts of a structure (local security).

Stability proofs are mostly carried out according to the rules of DIN EN standards, the Eurocodes . The following are examples:

- DIN EN 1992 deals with the stability of reinforced concrete structures.
- DIN EN 1993 deals with stability in steel construction.
- DIN EN 1995 deals with the stability of wooden structures.
- DIN EN 1996 deals with the stability of masonry.
- DIN EN 1997 deals with the stability of supporting structures, embankments and slopes, in particular with terrain fracture calculations.

- DIN 19700 deals with the stability of dam structures.
- DIN 18008 requires proof of stability and usability for glass

## swell

- ↑ http://www.bfe.admin.ch/php/modules/publikationen/stream.php?extlang=de&name=de_527009429.pdf Safety of dams, basic document on constructive safety, "safety plan", Federal Office for Water and Geology (Switzerland ), 2002.
- ↑ TUM Geotechnical Center: embankments and terrain jumps.
- ↑ DVWK-Heft 242: Calculation method for gravity dams, 1996.