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Summary of Failure Criteria

The following table summarizes the failure criteria used to assess the safety of designs.


Factor of Safety

Material Type

Maximum von Mises stress

 slimit / svonMises


Maximum shear stress

slimit /(2*tmax)


Mohr-Coulomb stress

s1sTensileLimit  if s1 > 0 and s3 > 0


s3  ≥ - sCompressiveLimit  if s1  < 0 and s3 < 0


{s1 / sTensileLimit + s3  / sCompressiveLimit} (-1)


< 1  if s1 ≥ 0 and s3  ≤ 0

Brittle materials with different tensile and compressive strengths

Maximum normal stress

 slimit  / s1


Maximum stress criterion (composites)

F.O.S. = 1/F.I.


Tsai-Hill Failure criterion (composites)

 F.O.S. = 1/F.I.


Tsai-Wu Failure criterion (composites)

F.O.S. = 1/F.I.


Click on each of the failure criterion for composites to know the meaning of the different symbols. 1 and 2 stand for material directions. X and S are normal and shear strengths of the composite.

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