Tresca or maximum-shear stress criteria assumes that yielding occurs when the maximum shear stress reaches a value of the shear stress in the uniaxial tension test. Assume the principal stress being σ1, σ2, σ3 where σ1 is largest, and σ3 is the smallest principal stresses. Find the value of minimum shear stress to cause yielding, given that yield stress in tension is equal to σo?

Tresca or maximum-shear stress criteria assumes that yielding occurs when the maximum shear stress reaches a value of the shear stress in the uniaxial tension test. Assume the principal stress being σ1, σ2, σ3 where σ1 is largest, and σ3 is the smallest principal stresses. Find the value of minimum shear stress to cause yielding, given that yield stress in tension is equal to σo? Correct Answer τ = σo/2

As given in the question, the yielding will occur when maximum shear reaches a value equal to shear stress in tension. Maximum shear stress = (σ1-σ3)/2 Maximum shear stress in pure tension=σo/2 So, τmax = (σ1-σ3)/2=σo/2 Also (σ1-σ3)=σo
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