Factor of safety

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Factor of safety (FoS) can mean either the fraction of structural capability over that required, or a multiplier applied to the maximum expected load (force, torque, bending moment or a combination) to which a component or assembly will be subjected. The two senses of the term are completely different in that the first is a measure of the reliability of a particular design, while the second is a requirement imposed by law, standard, specification, contract or custom. Careful engineers refer to the first sense as a factor of safety, or, to be explicit, a realized factor of safety, and the second sense as a design factor, but usage is inconsistent and confusing, so engineers need to be aware of both.

The difference between the safety factor and design factor is as follows. The design factor is what the part IS REQUIRED to be able to withstand. The safety factor is how much the designed part actually WILL be able to withstand. The design factor is for an application, the safety factor is for actual part that was designed. This sounds the same, but consider this: Say a beam in a structure is required to have a design factor of 3. The engineer chose a beam that will be able to withstand 10 times the load. The design factor is still 3, because it is the requirement that must be met, the beam just happens to exceed the requirement and its safety factor is 10. The safety factor should always meet or exceed the required design factor or the design is not adequate. Meeting the required design factor implies that the design meets but does not exceed the minimum allowable requirements. A high safety factor well over the required design factor sometimes implies "overengineering" which results in excessive weight and/or cost. In colloquial use the term, "required safety factor" is functionally equivalent to the design factor.

Appropriate factors of safety are based on several considerations. Prime considerations are the accuracy of load, strength, and wear estimates, the consequences of engineering failure, and the cost of overengineering the component to achieve that factor of safety. For example, components whose failure could result in substantial financial loss, serious injury or death usually can use a safety factor of four or higher (often ten). Non-critical components generally might have a design factor of two. Risk analysis, failure mode and effects analysis, and other tools are commonly used.

Buildings commonly use a factor of safety of 2.0 for each structural member. The value for buildings is relatively low because the loads are well understood and most structures are redundant. Pressure vessels use 3.5 to 4.0, automobiles use 3.0, and aircraft and spacecraft use 1.4 to 3.0 depending on the materials. Ductile, metallic materials use the lower value while brittle materials use the higher values. The field of aerospace engineering uses generally lower design factors because the costs associated with structural weight are high. This low design factor is why aerospace parts and materials are subject to more stringent quality control. The usually applied Safety Factor is 1.5, but for pressurized fuselage it is 2.0 and for main landing gear structures it is often 1.25.

In aerospace there is another criterion. At Limit Load the structure may not fail neither have permanent (structural) deformation of the structure. At Ultimate Load (usually the Limit Load multiplied with the Safety Factor) the aircraft structure is allowed to fail. Before Ultimate Load no failure is allowed but permanent deformation is allowed. An (civil) aircraft structure has to meet both Limit Load and Ultimate Load criteria.

Margin of Safety & Reserve Factor

Many government agencies and aerospace companies require the use of a Margin of Safety (M.S.) to describe the ratio of the strength of the structure to the requirements. Margin of safety can be conceptualized with the reserve factor (explained below), to represent how much of the structure's capacity is held "in reserve." The margin of safety basically says if the part is loaded to the maximum load it should ever see in service, how many more loads of the same force can it withstand before failing. In effect, margin of safety is a measure of excess capacity. If the margin is 0 or less, the part will not take any additional load before it fails. If the margin is 1, it can withstand one additional load of equal force to the maximum load it was designed to support (i.e. twice what it was designed to support).

Margin of Safety = (Failure Load / Design Load) - 1
MoS = FoS - 1

Some definitions of the margin of safety are based on the design factor, in other words, the margin of safety is calculated after applying the design factors. In the case of a margin of 0, the part will still have an actual safety factor of 3, but is at exactly the required strength (safety factor equal to the design factor). If there is a part with a required design factor of 3 and a margin of 1, the part would have an actual safety factor of 6 (capable of supporting two loads equal to its design factor of 3), or supporting six times the design load before failure. If the margin is less than 0 in this definition, although the part will not necessarily fail, the legal requirement has not been met.

If the design factor is included in the calculation:
Design Factor = [Provided as requirement]
Margin of Safety = [Failure Load /(Design Load*Design Factor)] - 1

• Design load being the maximum load the part should ever see in service.

For a successful design, the Design Factor must always equal or exceed the required Factor of Safety and the Margin of Safety is greater than zero. The Margin of Safety is sometimes, but infrequently, used as a percentage, i.e., a 0.50 M.S vs. a 50% M.S. When a structure meets all requirements it is said to have a "positive margin".

A measure of strength frequently used in Europe is the Reserve Factor (RF). With the strength and applied loads expressed in the same units, the Reserve Factor is defined as:

RF = Proof Strength / Proof Load
RF = Ultimate Strength / Ultimate Load

Note: M.S. = RF - 1

The applied loads have any factors, including factors of safety applied.

The use of a factor of safety does not imply that an item, structure, or design is "safe". Many quality assurance, engineering design, manufacturing, installation, and end-use factors may influence whether or not something is safe in any particular situation.

See also

• Limit state design
• Redundancy (total quality management)
• Probabilistic design
• Reliability
• Statistical interference
• Verification and validation