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Mohr-Coulomb Stress Criterion

The Mohr-Coulomb stress criterion is based on the Mohr-Coulomb theory also known as the Internal Friction theory.

This criterion is used for brittle materials with different tensile and compressive properties. Brittle materials do not have a specific yield point and hence it is not recommended to use the yield strength to define the limit stress for this criterion.

The theory predicts failure to occur when the combination of the maximum and minimum principal stress exceeds their respective stress limits.

For the principal stresses σ1, σ2, and σ3 ordered such as | σ1 | > | σ 2 | > | σ 3 |, the Mohr-Coulomb theory predicts failure to occur in the following cases:

State of Principal stresses Failure Criterion FOS
Both principal stresses in tension:

σ1 > 0 and σ3 > 0

σ1 > σTensileLimit ( σ1 / σTensileLimit )-1
Both principal stresses in compression:

σ1< 0 and σ3 < 0

1| > σCompressiveLimit ( |σ1| / σCompressiveLimit )-1
σ1 > 0 in tension, σ3 < 0 in compression σ1 / σTensileLimit + |σ3| / σCompressiveLimit > 1 ( σ1 / σTensileLimit + |σ3| / σCompressiveLimit )-1
σ1 < 0 in compression, σ3 > 0 in tension 1| / σCompressiveLimit + σ3 / σTensileLimit > 1 (|σ1| / σCompressiveLimit + σ3 / σTensileLimit)-1
The σCompressiveLimit has a positive sign in the above equations.

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