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Factors of Safety - FOS

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Factors of Safety - FOS - are a part of engineering design and can for structural engineering typically be expressed as

FOS = Ffail / Fallow                                   (1)


FOS = Factor of Safety

Ffail = failure load (N, lbf)   

Fallow = allowable load (N, lbf)     

Example - Structural Steel Column in a Building

Due to buckling the failure load of a steel column in a building is estimated to 10000 N. With a safety factor FOS = 5 - the allowable load can be estimated by rearranging (1) to

Fallow = Ffail / FOS                    (1b)

Fallow = (10000 N) / 5

         = 2000 N

Typical overall Factors of Safety

Typical overall Factors of Safety:

FOS - Factors of Safety - Equipment
EquipmentFactor of Safety
Aircraft components 1.5 - 2.5
Boilers 3.5 - 6
Bolts 8.5
Cast-iron wheels 20
Engine components 6 - 8
Heavy duty shafting 10 - 12
Lifting equipment - hooks .. 8 - 9
Pressure vessels 3.5 - 6
Turbine components - static 6 - 8
Turbine components - rotating 2 - 3
Spring, large heavy-duty 4.5
Structural steel work in buildings 4 - 6
Structural steel work in bridges 5 - 7
Wire ropes 8 - 9

Design Factors of Safety are often published in technical standards but there is no dedicated standard to the subject. Note that for statutory items such as cranes and pressure vessels FOS are specified in the design codes.

A FOS in design and engineering is determined after considering factors like

  • Yield Strength vs. Ultimate Tensile Strength
  • unpredictable load variations
  • working load conditions - static, dynamic, pulsating ..
  • environmental conditions - corrosion .. 

General recommendations

FOS - Factors of Safety - Applications
ApplicationsFactor of Safety
For use with highly reliable materials where loading and environmental conditions are not severe and where weight is an important consideration 1.3 - 1.5
For use with reliable materials where loading and environmental conditions are not severe 1.5 - 2
For use with ordinary materials where loading and environmental conditions are not severe 2 - 2.5
For use with less tried and for brittle materials where loading and environmental conditions are not severe 2.5 - 3
For use with materials where properties are not reliable and where loading and environmental conditions are not severe, or where reliable materials are used under difficult and environmental conditions 3 - 4

Factor of Safety related to Stress

In general there is a linear connection between load and stress and the factor of safety can within mechanical engineering for normal stress be modified to

FOS = σfail / σallow                            (2)


σfail = failure normal stress (N/m2, psi)

σallow = allowable normal stress (N/m2, psi)   

FOS for shear stress can be expressed as

FOS = τfail / τallow                            (3)


τfail = failure shear stress (N/m2, psi)

τallow = allowable shear stress (N/m2, psi)   

Be aware that in some cases there may not be a linearity between applied load and stress.

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