Allowable Stress Design Equations and Calculator

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Allowable Stress Design Equations and Calculator

Allowable Stress Design Equations and Calculator

Once an actual stress has been determined, it can be compared to the allowable stress. In engineering design, the term “allowable” always means that a factor of safety has been applied to the governing material strength.

Eq. 1,
allowable stress = material strength / factor of safety

For ductile materials, the material strength used is the yield strength. For steel, the factor of safety ranges from 1.5 to 2.5, depending on the type of steel and the application. Higher factors of safety are seldom necessary in normal, noncritical applications, due to steel’s predictable and reliable performance.

Eq. 2,
ductile
σ_a = S_y / FS

For brittle materials, the material strength used is the ultimate strength. Since brittle failure is sudden and unpredictable, the factor of safety is high (e.g., in the 6 to 10 range).

Eq. 3
brittle
σ_a = S_u / FS

If an actual stress is less than the allowable stress, the design is considered acceptable. This is the principle of the allowable stress design method, also known as the working stress design method.

Eq. 3
σ_actual ≤ σ_a

Where

FS = factor of safety
S_y = yield strength, lbs/in², Pa
S_u = ultimate strength, lbs/in², Pa
σ_a = allowable stress, lbs/in², Pa

Source

Civil Engineering Engineering Reference Reference Manual for the PE Exam for the PE Exam
Fourteenth Edition
Michael R. Lindeburg, PE