I have searched for this and all I could find is the following:
TAUoct=(1/3)*sqrt[(sigma1- sigma2)^2+(sigma2-sigma3)^2+( sigma3-sigma1)^2]
This equation is all over the books and sources but I reckon sigma1 to sigma3 are principal stresses. Now for a plane having both normal and shear stresses what is the equation for octahedral stress? Can you introduce the source as well?
Thanks in advance,
Take a look at: https://en.wikipedia.org/wiki/Von_Mises_yield_criterion
there you can find the general equation (when stresses are not given in the principal components) of the von Mises equivalent stress; which is related to the octahedral stress by a constant. You can also read https://en.wikipedia.org/wiki/Cauchy_stress_tensor.
Tau_oct = sqrt[(2/3)*J2]
where J2 = 1/6*[(sx-sy)^2+(sy-sz)^2+(sz-sx)^2]+Tauxy^2+Tauyz^2+Tauxz^2
and s = sigma
Refer to: Plasticity in Reinforced Concrete, Wai-Fah Chen
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