Octahedral shear theory is referred to as Von Mises theory too. Based on octahedral shear theory, failure takes place if the octahedral shear stress within a system is higher when compared with the octahedral shear stress at yield in a specimen put through to uniaxial tension experiment. This is equivalent in text to the assertion of the previous 2 theories besides that octahedral shear stress is applied as consideration with regard to comparability as towards maximum theory stress used in the Rankine principle or maximum shear stress used in Tresca principle.
This octahedral shear stress is explained with regard to the 3 stresses theory as following below:
τoct = 1/3 [(S1-S2)2 + (S2-S3)2 + (S3-S1)2]0.5
Where:
τoct = Octahedral shear stress
Becuase of the stresses theory explained pertaining to a specimen under uniaxial load previously, that octahedral shear stress on yield in the specimen could be established to become as equation below:
τoct = √2 . Sy / 3
Furthermore, the Von Mises theory expresses that failure takes place in a piping system when octahedral shear stress while in the piping system surpasses (√2 . Sy / 3) or more.
Regarding stress analysis associated computations, almost all of the current time piping rules use a modified version of Tresca principle