Factor of Safety FOS Review

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Factor of Safety (FOS) for structural applications is the ratio of the allowable working unit stress, allowable stress or working stress. The term was originated for determining allowable stress. The ultimate strength of a given material divided by an arbitrary factor of safety, dependant on material and the use to which it is to be put, gives the allowable stress.


Sm = Allowable working unit stress
sw = Working stress (Allowable stress)
fs = Factor of Safety

In present design and engineering practice, it is customary to use allowable stress as specified by recognized industry standards or authorities as applicable rather than to use an arbitrary factor of safety. One reason for this is that the factor of safety is misleading, in that it implies a greater degree of safety than may actually exists. For example, a factor of safety multiple of 4 does not mean that a component or assembly application can carry a load four times as great as that for which it was designed. It should also be clearly understood that, even though each part of a machine may be designed with the same factor of safety, the machine as a whole does not have that factor of safety. In the event that one part is stressed beyond the proportional limit, or particularly the yield point, the load or stress distribution may be completely changed throughout the entire machine or structure, and its ability to function at rated load may be changed, even though no part has failed or ruptured.

The following should be considered when designing and analyzing a structural or machine component or assembly:

  • Effects of associated assemblies or components.
  • Thermal cycling and operating or extreme temperature effects.
  • Intensity of stress concentrations.
  • Effects of wear
  • Likely ness of structural or machine abuse. Controls may not be in place to prevent an overstress condition. Classic example is the general public exceeding automotive (truck) rated towing capacity. Such events particularly when repeated, tend accelerate wear and failure of critical mechanical drive train components and assemblies.
  • Quality or likeness of scheduled maintenance.
  • Dimensional control and effects on quality of assembly. Excessive internal stresses can never be properly estimated. Material stresses induced by non-perfect geometry are difficult to model. Stresses can also be introduced by assembly misalignment between components.
  • Influence of fatigue loading over the life cycle of the machine or structure.

Although no definite or universal rules can be given , if a factor of safety needs to be determined or established, the following circumstances should be taken into account in its selection:

  1. When the ultimate strength of the material is known within narrow limits, as for structural steel for which tests of samples have been made, when the load is entirely a steady one of a known value a factor of safety should be adopted is 3.
  2. When circumstances of (1) are modified by a portion of the load being variable, as in, gear boxes, floors or warehouse operations, the factor of safety should not be less than 4.
  3. When the whole load , or nearly the whole, is likely to be alternately put on and taken off, as in suspension rods as used with suspension floors or bridges, the factor should be 5 or 6.
  4. When the stresses are reversed in direction from tension to compression, as in some structural load bearing diagonals and parts of machines, the factor should be not less than 6.
  5. When the components are subjected to repeated shock loading the factor should not be less than 10.
  6. When the structure or component is subjected to deterioration from corrosion the components or structure factor of safety should be sufficiently increased to allow for a definite amount of material reduction before the system is weakened by the process.
  7. When the strength of the material or the amount of the load or both are uncertain the factor of safety should be increased by an allowance sufficient to cover the amount of the uncertainty.
  8. When the stress and strains are complex and of uncertain amount, such as those in the crankshaft of a reversing engine, a very high factor is necessary, possibly even as high as 40 or more.
  9. If property loss caused by failure of the part or system may be large or if loss of life may result, the factor of safety should be large and the structure or machine performance should be verified by functional static or fatigue testing.

Industry Standard where available

The factor of safety is often specified in a design code or standard, such as:

  • American Institute of Steel Construction (AISC) steel buildings & bridges
  • American Society of Mechanical Engineers (ASME) pressure vessels, boilers, shafts.
  • American Concrete Institute (ACI)
  • National Forest Products Associ ation (NFPA) wood structures.
  • Aluminum Association (AA) aluminum buildings & bridges.
  • Codes often specify a minimum factor of safety
  • Designer's responsibility to determine if a code or standard applies. Codes are often specified by law. (BOCA, UBC, etc.)
  • Factors which affect the factor of safety
    • Material strength basis:
    • brittle Materials use ultimate strength
    • ductile Materials use yield strength
  • Manner or loading:
    • Static applied slowly; remains applied or is infrequently removed.
    • Repeated fatigue failure may occur at stresses lower than static load failure.
    • Impact high initial stresses develop.
  • Possible misuse designer must cons ider any reasonable foreseeable use & misuse of product.
  • Complexity of stress analysis the actu al stress in a part isn't always known.
  • Environment temperature, weat her, radiation, chemical, etc..

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