Factor of safety

Factor of safety

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 Factor of Safety is given to the engineer as a requirement. The Design Factor is calculated by the engineer.

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.

A design factor of 1.0 implies that the design meets but does not exceed the minimum requirements, with no room for variation nor error. A high design factor sometimes implies "overengineering" which results in excessive weight and/or cost. In aerospace there is another criterium. 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.

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.

Design Factor = Failure Load / Design Load
Margin of Safety = [Failure Load /(Design Load*FoS)] - 1

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 a structure or design is "safe". Many quality assurance, engineering design, manufacturing, installation, and end-use factors may influence whether or not a structure is safe in any particular situation.

Real world examples

Steam boilers

The factor of safety used in pressure vessel is usually between 3 and 4. For example, if the required working pressure is 250 pounds per square inch (psi), and the safety factor is 4, the bursting point must be not less than 1,000 psi. The effects of corrosion are controlled by the used of a "corrosion allowance" which is subtracted from the original wall thickness for strength calculations. For this reason, steam boilers are hydraulically tested, at regular intervals, to 1.5 times or 2 times the working pressure. The requirements for boilers and other vessels are governed in the United States by the American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code (BPVC). This code covers materials, welding, bolting, and safety factor requirements for the construction of new vessels.

Riveted connection

Assume a fastener is able to carry 300N in a wing skin panel but at 190N starts to deform under its loading. Lets assume the Safety Factor of 1.5 is applicable, then the maximum Ultimate Load is 300N/1.5=200N while the maximum Limit Load is only 190N. The latter is thus decisive. Hence if the applied loading is 150N then the Reserve Factor for subject rivet connection becomes RF=190N/150N=1.26, Limit Load criteria.

Pharmaceuticals

Even the most gentle of drugs, such as penicillin, can cause death when administered at excessively large quantities. The farther away the effective dose (ED) is from the lethal dose (LD) defines the margin of safety, or the natural, built-in safety factor, for that particular drug. For example, the effective dose of penicillin, i.e. the quantity that will be effective in treating an infection, is so vastly minute in relation to the multiplicity of doses necessary to prove fatal that penicillin is considered an extremely safe drug.

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