# Theories of failure for brittle materials (part-3): Maximum principal stress theory

Maximum principal stress theory is useful for brittle materials. Maximum principal stress theory or maximum principal stress criterion states that failure will occur when maximum principal stress developed in a body exceeds uniaxial ultimate tensile/compressive strength (or yield strength) of the material. Maximum principal stress theory/criterion is also known as normal stress theory, coulomb or rankine criterion.

Maximum principal stress of any stress system could be expressed as:

σ max = (σ x + σ y )/2 + √{[( σ x σ y )/2]2 + Txy2}

Where:

σ max = maximum principal stress

σ x and σ y = Normal stresses in X and Y direction

Txy = Shear stress in XY plane

So as per maximum principal stress theory/criterion, the material will be safe if

σ max < σut

Where:

σut = Ultimate tensile strength.

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Shibashis is a mechanical design engineer by profession and writer/blogger by passion. He has worked in various design projects in automobile, power plant and heavy earth moving equipment domain since 2005.

In his spare time apart from maintaining this blog, he enjoy investing time building his first RC plane