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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