Design Philosophy
APPLIEDFAILUREFoS = Failure / AppliedDesign Margin

Factor of Safety

The factor of safety (FoS) is a design margin that ensures a structure or component can withstand loads beyond the expected maximum. It accounts for uncertainties in material properties, manufacturing defects, loading conditions, and environmental factors.

Formula
FoS = Failure Load / Allowable Load
Units
Dimensionless

Typical FoS Values by Application

Design Philosophy
ApplicationFoS RangeTypical FoSNotes
Aerospace1.2 - 1.51.25Weight-critical applications
Automotive1.5 - 2.01.8Safety-critical components
Civil Structures2.0 - 3.02.5Buildings, bridges
Pressure Vessels3.0 - 4.03.5ASME Boiler Code
Heavy Machinery2.0 - 5.03.0Mining, construction
Ductile Materials
YieldUltimateWorkingFoS_yield = σ_yield / σ_working

Yield Strength Based FoS

For ductile materials (metals, alloys), the factor of safety is typically based on yield strength. This prevents permanent deformation and ensures the component returns to its original shape after loading. FoS_yield = Yield Strength / Working Stress.

Formula
FoS_yield = σ_yield / σ_working
Units
Dimensionless

Yield-Based FoS for Ductile Materials

Ductile Materials
MaterialYield StrengthUltimate StrengthFoS (Yield)FoS (Ultimate)Application
Structural Steel250 MPa400 MPa2.03.2Buildings
Aluminum Alloy310 MPa420 MPa1.82.4Aerospace
Stainless Steel210 MPa520 MPa2.23.5Chemical plants
Titanium Alloy830 MPa950 MPa1.51.7Aircraft
Brittle Materials
Sudden FailureNo Plastic DeformationBrittleDuctileFoS_ultimate = σ_ultimate / σ_working

Ultimate Strength Based FoS

For brittle materials (cast iron, ceramics, concrete), the factor of safety is based on ultimate tensile strength because these materials fail suddenly without significant plastic deformation. FoS_ultimate = Ultimate Strength / Working Stress.

Formula
FoS_ultimate = σ_ultimate / σ_working
Units
Dimensionless

Ultimate-Based FoS for Brittle Materials

Brittle Materials
MaterialYield StrengthUltimate StrengthFoS (Yield)FoS (Ultimate)Application
Cast Iron170 MPa300 MPa3.56.0Machine bases
ConcreteN/A35 MPaN/A3.0Buildings
CeramicsN/A250 MPaN/A8.0Turbine blades