# Safety factor

Illustration of the safety factor 3 in the stress-strain diagram

The safety factor , also security number , safety coefficient called by which specifies factor the failure limit of a structure , device or material is designed to be higher than it by theoretical determination, such as static calculation would have to be.

## application

A safety factor prevents the component from failing due to tolerances in the material, manufacture, load assumptions and unproven, minor influences. A safety factor of 1 means that the component has no safety reserves against failure. The underlying mechanisms for failure are often: bending , breaking , buckling or fatigue failure (failure of the fatigue limit ).

When determining the load, however, conservative assumptions are often made, which further increases the actual security.

### Metals

In the case of largely isotropic metals, the prevailing stress is often determined from the stress state with a strength criterion such as B. obtained the comparison stress criterion by Richard von Mises . The tolerable stress is then that obtained from uniaxial tensile tests . However, these simplifications are no longer applicable if one - z. B. after forming or because of a prevailing texture - must speak of an anisotropic material. In the case of metals under operating loads, the design is usually not to achieve permanent deformation, and accordingly the yield point is the stress that can be tolerated.

### Fiber-plastic composites

The term safety factor can only be applied to these materials to a limited extent, since advanced failure criteria for fiber-plastic composites always assess a combination of stresses. If, for example, Puck's intermediate fiber breakage criterion reaches a value of more than 1 (a type ), then that stress combination (stress vector) can be increased until a value of 1 is reached. However, it must then be ensured that criteria relating to fiber breakage , delamination , etc. are not violated. ${\ displaystyle RF> 1}$

In the Anglo-American region it should be noted that the term Margin of Safety (MS) is often used there:

${\ displaystyle MS = RF-1}$ .

### Technical ceramics

A distinction must also be made here between isotropic ceramics and structurally anisotropic fiber ceramics. However, there are also size effects in the case of monolithic ceramics (unreinforced), which is why the probability of breakage is also used, e.g. B. after Weibull .

## calculation

The safety factor can be defined as follows:

${\ displaystyle \ gamma = {\ frac {\ text {Failure load}} {\ text {permitted load}}}}$

• ${\ displaystyle RF> 1}$: Component is safe against a defined load limit,
• ${\ displaystyle RF \ leq 1}$: Component cannot withstand the selected load.

With the introduction of the Eurocode , there is practically no global safety factor in Central Europe , since the partial safety concept corresponds to the state of the art , but the global safety factor of partial loads can be calculated. This safety factor is generally the multiplication of the partial safety factor on the material side times the partial safety factor on the action side of the respective partial load:

${\ displaystyle \ gamma = \ gamma _ {E} \ cdot \ gamma _ {R}}$

### Reserve factor

The reserve factor is generally the difference between the legally determined and the calculated safety factor.
As an example: prescribed safety factor = 3; calculated SF = 3.28; → Reserve factor = 0.28

However, the reserve factor is also colloquially equated with the safety factor, with the difference that the tolerable stress is measured as the actual stress, instead of the 5% fractile that is prescribed for the safety coefficient by the Eurocode .

## Determining the size

When determining the safety factor, the following factors, among others, are taken into account:

• Probability of risk
• Extent of damage (e.g .: minor injuries, illnesses, death)
• Material quality (e.g .: regularity)
• Inspection intervals
• Environmental influences

The safety factor on the material side is usually between 1.1 and 2.1, depending on the material used and the safety relevance, 3.0 for materials with large fluctuations in their properties (e.g. for damp wood) and above 10 for extremely safety-relevant components (e.g. B. Elevator ropes).

In the case of constantly acting loads (e.g. dead weight), the relevant standards usually require a safety of around 2. Since there is no uncertainty in the density of water in the case of buoyancy, i.e. there is no uncertainty in the load, a partial safety factor of 1 to 1.05 on the action side is selected in DIN 1054, depending on the design situation.

Safety factors are also used in the calculation against earthquakes. In this load case (as is generally the case with unusual and rare load cases), a relatively small factor (e.g. 1.2) is usually sufficient.

## Unpredictable load

In the case of exceptional load cases that have a very low probability of occurring, such as unexpected accidents or fires in subordinate buildings, the partial safety factor on the action side is set to 1. Often no security is required on the material side against failure. These can be taken into account both by reducing the partial safety factor, but also by allowing stresses that correspond to the strength and, for example , can be above a yield point . This can result in large permanent deformations.

## Individual evidence

1. a b Helmut Schürmann: Constructing with fiber-plastic composites . 2nd Edition. Springer-Verlag, Berlin Heidelberg 2007, ISBN 978-3-540-72189-5 , p. 408 , doi : 10.1007 / 978-3-540-72190-1 ( springer.com [PDF; accessed December 17, 2018]).
2. ^ Alfred Puck: Strength analysis of fiber matrix laminates: Models for practice . Carl Hanser Verlag, Munich Vienna 1996, ISBN 3-446-18194-6 , p. 51 (212 pp., D-nb.info ).
3. a b SAFETYTEAMS CE marking Risk analysis Risk assessment Risk analysis. Retrieved March 11, 2020 .
4. Safety factor of the elevator steel wire rope. Retrieved March 11, 2020 .