Factors of Safety - FOS

Factors of Safety - FOS - are important in engineering designs.

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

FOS = F_fail / F_allow (1)

where

FOS = Factor of Safety

F_fail = failure load (N, lb_f)

F_allow = allowable load (N, lb_f)

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

F_allow = F_fail / FOS (1b)

F_allow = (10000 N) / 5

= 2000 N

Typical overall Factors of Safety

Typical overall Factors of Safety:

FOS - Factors of Safety - Equipment
Equipment	Factor of Safety - FOS -
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
Applications	Factor of Safety - FOS -
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 = σ_fail / σ_allow (2)

where

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

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

FOS for shear stress can be expressed as

FOS = τ_fail / τ_allow (3)

where

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

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

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

Factors of Safety - FOS