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 }+ T_{xy}^{2}}**

Where:

σ _{max }= maximum principal stress

σ _{x }and σ _{y }= Normal stresses in X and Y direction

T_{xy }= Shear stress in XY plane

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

**σ**** _{max }< σ_{ut}**

Where:

σ_{ut }= Ultimate tensile strength.

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