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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,
σa = Sy / 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
σa = Su / 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
σactual ≤ σa


FS = factor of safety
Sy = yield strength, lbs/in2, Pa
Su = ultimate strength, lbs/in2, Pa
σa = allowable stress, lbs/in2, Pa


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