According to the distortion-energy theory, the yield strength in shear is

Concept:

Maximum distortion energy theory (Von mises theory)

According to this theory, the failure or yielding occurs at a point in a member when the distortion strain energy per unit volume reaches the limiting distortion energy (i.e. distortion energy at yield point) per unit volume as determined from simple tension test.

Equivalent stress under triaxial condition is given by:

\({\left( {{\sigma _1} - {\sigma _2}} \right)^2} + {\left( {{\sigma _2} - {\sigma _3}} \right)^2} + {\left( {{\sigma _3} - {\sigma _1}} \right)^2} \le 2\left( {\frac{{{S_Y}}}{{FOS}}} \right)\) 

In shear σ₁ = τ, σ₂ = -τ, σ₃ = 0

Substituting all the values,

\(\tau = \frac{{{S_Y}}}{{\sqrt 3 }} = 0.577\;{S_Y}\)